Maximum likelihood estimation of a binomial proportion using one‐sample misclassified binary data

In this article, we construct two likelihood‐based confidence intervals (CIs) for a binomial proportion parameter using a double‐sampling scheme with misclassified binary data. We utilize an easy‐to‐implement closed‐form algorithm to obtain maximum likelihood estimators of the model parameters by maximizing the full‐likelihood function. The two CIs are a naïve Wald interval and a modified Wald interval. Using simulations, we assess and compare the coverage probabilities and average widths of our two CIs. Finally, we conclude that the modified Wald interval, unlike the naïve Wald interval, produces close‐to‐nominal CIs under various simulations and, thus, is preferred in practice. Utilizing the expressions derived, we also illustrate our two CIs for a binomial proportion parameter using real‐data example.     

The proportion of blocking coalitions in atomless economies

In this paper we investigate the number of coalitions that block a given non-competitive allocation. In an atomless economy with a finite number of types we identify coalition with its profile. Considering profiles π that represent coalitions with the same proportions of types as in the whole society, we prove that there is a ball B_π with π as its center so that ‘almost half’ of the profiles in B_π are blocking. This result is an analogous result to that of Mas-Colell (1978) who dealt with large finite markets.     

On Tests for a Normal Mean with Known Coefficient of Variation

Hinkley (1977) derived two tests for testing the mean of a normal distribution with known coefficient of variation (c.v.) for right alternatives. They are the locally most powerful (LMP) and the conditional tests based on the ancillary statistic for μ. In this paper, the likelihood ratio (LR) and Wald tests are derived for the one‐ and two‐sided alternatives, as well as the two‐sided version of the LMP test. The performances of these tests are compared with those of the classical t, sign and Wilcoxon signed rank tests. The latter three tests do not use the information on c.v. Normal approximation is used to approximate the null distribution of the test statistics except for the t test. Simulation results indicate that all the tests maintain the type‐I error rates, that is, the attained level is close to the nominal level of significance of the tests. The power functions of the tests are estimated through simulation. The power comparison indicates that for one‐sided alternatives the LMP test is the best test whereas for the two‐sided alternatives the LR or the Wald test is the best test. The t, sign and Wilcoxon signed rank tests have lower power than the LMP, LR and Wald tests at various alternative values of μ. The power difference is quite large in several simulation configurations. Further, it is observed that the t, sign and Wilcoxon signed rank tests have considerably lower power even for the alternatives which are far away from the null hypothesis when the c.v. is large. To study the sensitivity of the tests for the violation of the normality assumption, the type I error rates are estimated on the observations of lognormal, gamma and uniform distributions. The newly derived tests maintain the type I error rates for moderate values of c.v.     

Tests for location-scale families based on the empirical characteristic function

A class of procedures is presented for using random samples to test the fit of location-scale families—distributions F(·;θ₁,θ₂) such that Z=(X−θ₁)/θ₂ has distribution Working with empirically standardized data, the test statistic is a measure of distance between the empirical characteristic function, and the c.f. of Z under the null hypothesis, ϕ₀(t). The closed-form test statistic is derived by integrating over the product of a weight function times Using as weight function for each location-scale family the squared modulus of ϕ₀ itself presents a unified test procedure. Included as special cases are well-known tests for normal and Cauchy laws. Small-sample powers are compared with those of Anderson-Darling tests for each of seven univariate location-scale families.     

On the upper and lower semicontinuity of the Aumann integral

Let (T,τ,μ) be a finite measure space, X be a Banach space, P be a metric space and let L₁(μ,X) denote the space of equivalence classes of X-valued Bochner integrable functions on (T,τ,μ). We show that if φ:T×P→2^X is a set-valued function such that for each fixed pεP, φ(·,p) has a measurable graph and for each fixed tεT, φ(t,·) is either upper or lower semicontinuous then the Aumann integral of φ, i.e.,∫_Tφ(t,p)dμ(t)= {∫_Tx(t)dμ(t):xεS_φ(p)}, where S_φ(p)= {yεL₁(μ,X):y(t)εφ(t,p)μ−a.e.}, is either upper or lower semicontinuous in the variable p as well. Our results generalize those of Aumann (1965, 1976) who has considered the above problem for X=Rⁿ, and they have useful applications in general equilibrium and game theory.     

Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators

Subsampling and the m out of n bootstrap have been suggested in the literature as methods for carrying out inference based on post-model selection estimators and shrinkage estimators. In this paper we consider a subsampling confidence interval (CI) that is based on an estimator that can be viewed either as a post-model selection estimator that employs a consistent model selection procedure or as a super-efficient estimator. We show that the subsampling CI (of nominal level 1−α for any α(0,1)) has asymptotic confidence size (defined to be the limit of finite-sample size) equal to zero in a very simple regular model. The same result holds for the m out of n bootstrap provided m²/n→0 and the observations are i.i.d. Similar zero-asymptotic-confidence-size results hold in more complicated models that are covered by the general results given in the paper and for super-efficient and shrinkage estimators that are not post-model selection estimators. Based on these results, subsampling and the m out of n bootstrap are not recommended for obtaining inference based on post-consistent model selection or shrinkage estimators.     

On the structure of Pareto optimal cake partitions

We study Pareto optimal partitions of a “cake” among n players. Each player uses a countably additive non-atomic probability measure to evaluate the size of pieces of cake. We present two geometric pictures appropriate for this study and consider the connection between these pictures and the maximization of convex combinations of measures, which we studied in Barbanel and Zwicker [Barbanel, J.B., Zwicker, W., 1997. Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division. Theory and Decision 43, 203–207].     

Structural instability of the core

Let σ be a q-rule, where any coalition of size q, from the society of size n, is decisive. Let w(n,q)= 2q-n+1 and let W be a smooth ‘policy space’ of dimension w. Let U(W)^N be the space of all smooth profiles on W, endowed with the Whitney topology. It is shown that there exists an ‘instability dimension’ w^*(σ) with 2w^*(σ)w(n,q) such that:

1. (i) if ww^*(σ), and W has no boundary, then the core of σ is empty for a dense set of profiles in U(W)^N (i.e., almost always),

2. (ii) if ww^*(σ)+1, and W has a boundary, then the core of σ is empty, almost always,

3. (iii) if ww^*(σ)+1 then the cycle set is dense in W, almost always,

4. (iv) if ww^*(σ)+2 then the cycle set is also path connected, almost always.

The method of proof is first of all to show that if a point belongs to the core, then certain generalized symmetry conditions in terms of ‘pivotal’ coalitions of size 2q−n must be satisfied. Secondly, it is shown that these symmetry conditions can almost never be satisfied when either W has empty boundary and is of dimension w(n,q) or when W has non-empty boundary and is of dimension w(n,q)+1.     

Representing preferences with nontransitive indifference by a single real-valued function

Let be an interval order on a topological space (X, τ), and let x _˜^* y if and only if [y z x z], and x _˜^** y if and only if [z x z y]. Then _˜^* and _˜^** are complete preorders. In the particular case when is a semiorder, let x _˜⁰ y if and only if x _˜^* y and x _˜^** y. Then _˜⁰ is a complete preorder, too. We present sufficient conditions for the existence of continuous utility functions representing _˜^*, _˜^** and _˜⁰, by using the notion of strong separability of a preference relation, which was introduced by Chateauneuf (Journal of Mathematical Economics, 1987, 16, 139–146). Finally, we discuss the existence of a pair of continuous functions u, υ representing a strongly separable interval order on a measurable topological space (X, τ, μ, ).     

Continua of stochastic dominance relations for unbounded probability distributions

Let P = {F,G,…} be the set of all probability distribution functions with support (0, ∞). An unrestricted stochastic dominance relation>_∞ is defined on P for each real ∞ 1, where F >_∞ G means that ^x_y = 0 (x - y)^{∞ - 1} dG(y) ^x_{n = 0}(x − y)^∞−1 dG(y) for all ∞ 0, with < for some x. These relations are partial orders that increase as ∞ increases with limit relation>_∞. A class U_∞ of utility functions u on (0, ∞) is defined in such a way that F >_∞ G iff udF > udG for all u ε U_∞. The U_∞ decrease as ∞ increases and have a non-empty intersection U_∞. Each u ε U_∞ is an increasing function that has derivatives of all orders that alternate in sign. Criteria which tell when F eventually dominates G in the sense of F >_∞ G are noted. Comparisons with bounded stochastic dominance results are made in several places.     

A fuzzy-QFD approach to supplier selection

This article suggests a new method that transfers the house of quality (HOQ) approach typical of quality function deployment (QFD) problems to the supplier selection process. To test its efficacy, the method is applied to a supplier selection process for a medium-to-large industry that manufactures complete clutch couplings.The study starts by identifying the features that the purchased product should have (internal variables “WHAT”) in order to satisfy the company's needs, then it seeks to establish the relevant supplier assessment criteria (external variables “HOW”) in order to come up with a final ranking based on the fuzzy suitability index (FSI). The whole procedure was implemented using fuzzy numbers; the application of a fuzzy algorithm allowed the company to define by means of linguistic variables the relative importance of the “WHAT”, the “HOW”–“WHAT” correlation scores, the resulting weights of the “HOW” and the impact of each potential supplier.Special attention is paid to the various subjective assessments in the HOQ process, and symmetrical triangular fuzzy numbers are suggested to capture the vagueness in people's verbal assessments.     

Continua of stochastic dominance relations for bounded probability distributions

Let P={F,G,…} be the set of probability distribution functions on [0,b]. For each αε[1, ∞), F_αG means that ∫^x_o(x−y^α−1dF(y)∫^x_o(x−y)^α−1dG(y) for all xε[0, b], and F>_αG means that F_αG and F≠G. Each _α is reflexive and transitive and each>_α is asymmetric and transitive. Both _α and>_α increase as α increases but their limits are not complete. A class U_α of utility functions is defined to give F>_αG iff ∫udF>∫udG for all uεU_α. These classes decrease as α increases, and their limit is empty. Similar decreasing classes are defined for each _α, and their limit is essentially the constant functions on (0, b].     

Die messende Prüfung bei Abweichung von der Normalverteilungsannahme

Summary For sampling inspection by variables in the one-sided case (item bad if variablex>a) under the usual assumption of normality with known variance ₂ the operating characteristic is given by , wherep denotes the fraction defective. If instead of a normal distribution ((·–a–)/) there is a distributionF((·–a–)/) whereF is sufficiently regular and normed like , one has the approximative operating characteristic . It is shown that for arbitrarily fixed parametersn andc the function takes the valueL _n,c ⁽⁾ (p) at the pointp _F (p)=1–F(–^–1(p)). Sufficient conditions for a simple behavior of the differencep _F (p)–p are given. In the cases of rectangular and symmetrically truncated normal distribution these conditions are shown to be fulfilled.     

Increasing human and social capital by applying job embeddedness theory

Most modern lives are complicated. When employees feel that their organization values the complexity of their entire lives and tries to do something about making it a little easier for them to balance all the conflicting demands, the employees tend to be more productive and stay with those organizations longer. Job embeddedness captures some of this complexity by measuring both the on-the-job and off-the-job components that most contribute to a person's staying. Research evidence as well as ample anecdotal evidence (discussed here and other places) supports the value of using the job embeddedness framework for developing a world-class retention strategy based on corporate strengths and employee preferences.To execute effectively their corporate strategy, different organizations require different knowledge, skills and abilities from their people. And because of occupational, geographic, demographic or other differences, these people will have needs that are different from other organizations. For that reason, the retention program of the week from international consultants won’t always work. Instead, organizations need to carefully assess the needs/desires of their unique employee base. Then, these organizations need to determine which of these needs/desires they can address in a cost effective fashion (confer more benefits than the cost of the program). Many times this requires an investment that will pay off over a longer term – not just a quarter or even year. Put differently, executives will need to carefully understand the fully loaded costs of turnover (loss of tacit knowledge, reduced customer service, slowed production, lost contracts, lack of internal candidates to lead the organization in the future, etc., in addition to the obvious costs like recruiting, selecting and training new people). Then, these executives need to recognize the expected benefits of various retention practices. Only then can leaders make informed decisions about strategic investments in human and social capital.

Selected bibliography

A number of articles have influenced our thinking about the importance of connecting employee retention strategies to business strategies:

• R. W. Beatty, M. A. Huselid, and C. E. Schneier. “New HR Metrics: Scoring on the Business Scorecard,” Organizational Dynamics, 2003, 32 (2), 107–121.

• Bradach. “Organizational Alignment: The 7-S Model,” Harvard Business Review, 1998.

• J. Pfeffer. “Producing Sustainable Competitive Advantage Through the Effective Management of People,” Academy of Management Executive, 1995 (9), 1–13.

• C. J. Collins, and K. D. Clark. “Strategic Human Resources Practices and Top Management Team Social Networks: An Examination of the Role of HR Practices in Creating Organizational Competitive Advantage,” Academy of Management Journal, 2003, 46, 740–752.

The theoretical development and empirical support for the Unfolding Model of turnover are captured in the following articles:

• T. Lee, and T. Mitchell. “An Alternative Approach: The Unfolding Model of Voluntary Employee Turnover,” Academy of Management Review, 1994, 19, 57–89.

• B. Holtom, T. Mitchell, T. Lee, and E.Inderrieden. “Shocks as Causes of Turnover: What They Are and How Organizations Can Manage Them,” Human Resource Management, 2005, 44(3), 337–352.

The development of job embeddedness theory is captured in the following articles:

• T. Mitchell, B. Holtom, T. Lee, C. Sablynski, and M. Erez. “Why People Stay: Using Job Embeddedness to Predict Voluntary Turnover,” Academy of Management Journal, 2001, 44, 1102–1121.

• T. Mitchell, B. Holtom, and T. Lee. “How To Keep Your Best employees: The Development Of An Effective Retention Policy,” Academy of Management Executive, 2001, 15(4), 96–108.

• B. Holtom, and E. Inderrieden. “Integrating the Unfolding Model and Job Embeddedness To Better Understand Voluntary Turnover,” Journal of Managerial Issues, in press.

• D.G. Allen. “Do Organizational Socialization Tactics Influence Newcomer Embeddedness and Turnover?” Journal of Management, 2006, 32, 237–257.

Executive SummaryEmployee turnover is costly to organizations. Some of the costs are obvious (e.g., recruiting, selecting, and training expenses) and others are not so obvious (e.g., diminished customer service ability, lack of continuity on key projects, and loss of future leadership talent). Understanding the value inherent in attracting and keeping excellent employees is the first step toward investing systematically to build the human and social capital in an organization. The second step is to identify retention practices that align with the organization's strategy and culture. Through extensive research, we have developed a framework for creating this alignment. We call this theory job embeddedness. Across multiple industries, we have found that job embeddedness is a stronger predictor of important organizational outcomes, such as employee attendance, retention and performance than the best, well-known and accepted psychological explanations (e.g., job satisfaction and organizational commitment). The third step is to implement the ideas. Throughout this article we discuss examples from the Fortune 100 Best Companies to Work For and many others to demonstrate how job embeddedness theory can be used to build human and social capital by increasing employee retention.     

E-Leadership and Virtual Teams

In this paper we have identified some key challenges for E-leaders of virtual teams. Among the most salient of these are the following:

• The difficulty of keeping tight and loose controls on intermediate progress toward goals

• Promoting close cooperation among teams and team members in order to integrate deliverables

• Encouraging and recognizing emergent leaders in virtual teams

• Establishing explicit processes for archiving important written documentation

• Establishing and maintaining norms and procedures early in a team’s formation and development

• Establishing proper boundaries between home and work

Virtual team environments magnify the differences between good and bad projects, organizations, teams, and leaders. The nature of such projects is that there is little tolerance for ineffective leadership. There are some specific issues and techniques for mitigating the negative effects of more dispersed employees, but these are merely extensions of good leadership—they cannot make up for the lack of it.

SELECTED BIBLIOGRAPHY

An excellent reference for research on teams is M. E. Shaw, R. M. McIntyre, and E. Salas, “Measuring and Managing for Team Performance: Emerging Principles from Complex Environments,” in R. A. Guzzo and E. Salas, eds., Team Effectiveness and Decision Making in Organizations (San Francisco: Jossey-Bass, 1995). For a fuller discussion of teleworking and performance-management issues in virtual teams, see W. F. Cascio, “Managing a Virtual Workplace,” Academy of Management Executive, 2000, 14(3), 81–90, and also C. Joinson, “Managing Virtual Teams,” HRMagazine, June 2002, 69–73. Several sources discuss the issue of trust in virtual teams: D. Coutu, “Trust in Virtual Teams,” Harvard Business Review, May–June 1998, 20–21; S. L. Jarvenpaa, K. Knoll, and D. E. Leidner, “Is Anybody Out There? Antecedents of Trust in Global Virtual Teams,” Journal of Management Information Systems, 1998, 14(4), 29–64. See also Knoll and Jarvenpaa, “Working Together in Global Virtual Teams,” in M. Igbaria and M. Tan, eds., The Virtual Workplace (Hershey, PA: Idea Group Publishing, 1998).Estimates of the number of teleworkers vary. For examples, see Gartner Group, Report R-06-6639, November 18, 1998, and also Telework America survey, news release, October 23, 2001. We learned about CPP’s approach to managing virtual work arrangements through David Krantz, personal communication, August 20, 2002, Palo Alto, CA.There are several excellent references on emergent leaders. For example, see G. Lumsden and D. Lumsden, Communicating in Groups and Teams: Sharing Leadership (Belmont, CA: Wadsworth, 1993); Lumsden and Lumsden, Groups: Theory and Experience, 4th ed. (Boston: Houghton, 1993); R. W. Napier and M. K. Gershenfeld, Groups: Theory and Experience, 4th ed. (Boston: Houghton, 1989); and M. E. Shaw, Group Dynamics: The Psychology of Small Group Behavior, 3rd ed. (New York: McGraw-Hill, 1981).An excellent source for e-mail style is D. Angell and B. Heslop, The Elements of E-mail Style: Communicate Effectively via Electronic Mail (Reading, MA: Addison-Wesley Publishing Company, 1994). To read more on the growing demand for flexible work arrangements, see “The New World of Work: Flexibility is the Watchword,” Business Week, 10 January 2000, 36.For more on individualism and collectivism, see H. C. Triandis, “Cross-cultural Industrial and Organizational Psychology,” in H. C. Triandis, M. D. Dunnette, and L. M. Hough, eds., Handbook of Industrial and Organizational Psychology, 2nd ed., vol. 4 (Palo Alto, CA: Consulting Psychologists Press, 1994, 103–172).Executive SummaryAs the wired world brings us all closer together, at the same time as we are separated by time and distance, leadership in virtual teams becomes ever more important. Information technology makes it possible to build far-flung networks of organizational contributors, although unique leadership challenges accompany their formation and operation. This paper describes the growth of virtual teams, the various forms they assume, the kinds of information and support they need to function effectively, and the leadership challenges inherent in each form. We then provide workable, practical solutions to each of the leadership challenges identified.     

Stratified studies about risk ratios in 2 × 2 tables with structural zero

Incomplete correlated 2 × 2 tables are common in some infectious disease studies and two‐step treatment studies in which one of the comparative measures of interest is the risk ratio (RR). This paper investigates the two‐stage tests of whether K RRs are homogeneous and whether the common RR equals a freewill constant. On the assumption that K RRs are equal, this paper proposes four asymptotic test statistics: the Wald‐type, the logarithmic‐transformation‐based, the score‐type and the likelihood ratio statistics to test whether the common RR equals a prespecified value. Sample size formulae based on hypothesis testing method and confidence interval method are proposed in the second stage of test. Simulation results show that sample sizes based on the score‐type test and the logarithmic‐transformation‐based test are more accurate to achieve the predesigned power than those based on the Wald‐type test. The score‐type test performs best of the four tests in terms of type I error rate. A real example is used to illustrate the proposed methods.     

Estimation of the parameters in the gravity model for trip distribution : A new method and solution algorithm

For the unique determination of the parameters in the doubly constrained gravity model with exponential friction function two approaches are common: (1) entropy maximization and (2) application of a travel cost budget. This paper shows by making use of geometric programming that both of these approaches are equivalent with another natural criterion: the minimization of the deviation between the observed [t_1j] and the estimated [x_1j] table for a base year. By means of calculating the derivative of total cost as a function of σ the construction of an efficient algorithm for estimation of σ is made possible.     

An alternative approach to housing market segmentation using hedonic price data

Much empirical research has been devoted to housing market segmentation and the implications for the application of the Hedonic Price Model. Market segmentation is demonstrated empirically in (J. Urban Econ., 3:2, 146–166 (1976); J. Urban Econ., 7:1, 102–108 (1980); Rev. Econ. Statist., 66:3, 404–406 (1974)). There appears to be theoretical evidence (J. Pol. Econ., 82:1, 34–55 (1974)) that such empirical efforts may have been less than adequate. Unfortunately, the empirical applications of Rosen's model (J. Environ. Econ. Manag., 5, 81–102 (1978); J. Urban Econ., 5, 3, 357–369 (1978)) do not seem to effectively account for the complexity of the factors which cause multiple equilibria (market segmentation). This paper demonstrates empirically that market segments can be defined along more dimensions than hitherto have been included in any analysis.     

Locally minimax test of independence in elliptically symmetrical distributions with additional observations

Summary LetX=(X _ij )=(X ₁, ...,X _n )’,X’ _i =(X _i1, ...,X _ip )’,i=1,2, ...,n be a matrix having a multivariate elliptical distribution depending on a convex functionq with parameters, 0,σ. Let ϱ²=ϱ ₂ ^-2 be the squared multiple correlation coefficient between the first and the remainingp ₂+p ₃=p−1 components of eachX _i . We have considered here the problem of testingH ₀:ϱ²=0 against the alternativesH ₁:ϱ ₁ ^-2 =0, ϱ ₂ ^-2 >0 on the basis ofX andn ₁ additional observationsY ₁ (n ₁×1) on the first component,n ₂ observationsY ₂(n ₂×p ₂) on the followingp ₂ components andn ₃ additional observationsY ₃(n ₃×p ₃) on the lastp ₃ components and we have derived here the locally minimax test ofH ₀ againstH ₁ when ϱ ₂ ^-2 →0 for a givenq. This test, in general, depends on the choice ofq of the familyQ of elliptically symmetrical distributions and it is not optimality robust forQ.