A directional test of exponentiality based on maximum correlations

In Fortiana and Grané (J Stat Plann Infer 108:85–97), we study a scale-free statistic, based on Hoeffding’s maximum correlation, for testing exponentiality. This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics. Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics. In this paper, we propose a scale-free adaptive statistic for testing exponentiality with optimal power against a specific alternative and obtain its exact distribution. An empirical power study shows that the test based on this new statistic has the same level of performance than the best tests in the statistical literature.     

Hypothesis testing and parameter estimation based onM-statistics ink samples with unequal variances

Summary Ink samples with unequal variances,M-tests for homogeneity ofk location parameters are proposed. The asymptoticχ ²-distributions of the test statistics and the robustness of the tests are investigated. NextM-estimators (ME’s) of parameters are discussed. Furthermore positive-part shrinkage versions (PSME’s) of theM-estimators for the location parameters are considered along with modified James-Stein estimation rule. In asymptotic distributional risks based on a special feasible loss, it is shown that the PSME’s dominate the ME’s, and preliminary test and shrinkageM-versions fork≧4.     

Assessment of Interjudge Reliability in the Open-Ended Questions Coding Process

In the process of coding open-ended questions, the evaluation of interjudge reliability is a critical issue. In this paper, using real data, the behavior of three coefficients of reliability among coders, Cohen’s K, Krippendorff’s α and Perreault and Leigh’s I _r are patterned, in terms of the number of judges involved and the categories of answer defined. The outcome underlines the importance of both variables in the valuations of interjudge reliability, as well as the higher adequacy of Perreault and Leigh’s I _r and Krippendorff’s α for marketing and opinion research.     

A general class of univariate skew distributions considering Stein’s lemma and infinite divisibility

In this article, we consider a general form of univariate skewed distributions. We denote this form by GUS(λ; h(x)) or GUS with density s(x|λ, h(x)) = 2f(x)G(λ h(x)), where f is a symmetric density, G is a symmetric differentiable distribution, and h(x) is an odd function. A special case of this general form, normal case, is derived and denoted by GUSN(λ; h(x)). Some representations and some main properties of GUS(λ; h(x)) are studied. The moments of GUSN(λ; h(x)) and SN(λ), the known skew normal distribution of Azzalini (1985), are compared and the relationship between them is given. As an application, we use it to construct a new form for skew t-distribution and skew Cauchy distribution. In addition, we extend Stein’s lemma and study infinite divisibility of GUSN(λ; h(x)).     

The origins of the mean-variance approach in finance: revisiting de Finetti 65 years later

Abstract In a recent critical review of de Finetti’s paper “Il problema dei pieni’’, the Nobel Prize winner Harry Markowitz recognized the primacy of de Finetti in applying the mean-variance approach to finance, but pointed out that de Finetti did not solve the problem for the general case of correlated risks. We argue in this paper that a more fair sentence would be: de Finetti did solve the general problem but under an implicit hypothesis of regularity which is not always satisfied. Moreover, a natural extension of de Finetti’s procedure to non-regular cases offers a general solution for the correlation case and shows that de Finetti anticipated a modern mathematical programming approach to mean-variance problems. Mathematics Subject Classification (2000): 91B30, 90C20 Journal of Economic Literature Classification: G11, C61, B23, D81, G22     

The conservative equal costs rule, the serial cost sharing rule and the pivotal mechanism: asymptotic welfare loss comparisons for the case of an excludable public project

We examine the asymptotic behavior of two strategyproof mechanisms discussed by Moulin for public goods – the conservative equal costs rule (CER) and the serial cost sharing rule (SCSR) – and compare their performance to that of the pivotal mechanism (PM) from the Clarke–Groves family. Allowing the individuals’ valuations for an excludable public project to be random variables, we show under very general assumptions that expected welfare loss generated by the CER, as the size of the population increases, becomes arbitrarily large. However, all moments of the SCSR’s random welfare loss asymptotically converge to zero. The PM does better than the SCSR, with its welfare loss converging even more rapidly to zero.     

Su Una Estensione Bidimensionale del Teorema di Scomposizione di Peccati

Facendo ricorso all’introduzione di una opportuna condizione di sincronia fra due coppie di tassi (i, j), esterna, e (i*, j*), interna, si dimostra che condizione necessaria e sufficiente per la validità finanzíaria di una estensione hidimensionale del teorema di scomposizione di Peccati è che le due coppie (i, j) e (i*, j*) soddisfino tale proprietà di sincronia.

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A two-dimensional extension of peccati’s decomposition theorem

Summary This paper keeps as starting poing the Peccati’s decomposition of the d.c.f. of an enterpreneural project seen as a present value of single-period results, recently given by the author in an unidimensional framework. The goal of the paper is twofold: the first is to provide a bidimensional extension of the decomposition in order to keep account of mixed projects, that is projects that according to any internal couple (i*, j*) reveal alternance of investment and respectively collection periods. A straightforward extension is given on the basis of a simple analogic argument. But a more careful evaluation of the problem suggests that if we require that the decomposition be meaningful from a financial point of view. things are no more simple either in one or in two dimensions. To solve the problem we introduce a proper synchrony condition: precisely, the pair of couples (i, j) and (i*, j*) are said to satisfy the synchrony condition if and only if the sequences of the signs of the partial balancesM _t (i, j) andM _t (i*, j*) are the same. After that we are able to show that, with reference to a couple (i, j) of external rates, a bidimensional decomposition centered on an internal couple (i*, j*) is meaningful if and only if the pair (i, j) and (i*, j*) satisfy the synchrony condition. Formally, the result comes as a nice byproduct of a rule on the factorization of particular bivariate polynomials recently given by Stucchi. In particular going back to a one-dimensional world, it turns out that for pure investment (Soper) projects the synchrony condition works as a condition of applicability of the Peccati’s decomposition.

Il testo è frutto di una riflessione congiunta degli autori che ne condividono l’impostazione generale e i risultati. In dettaglio, la stesura dell’introduzione e delle conclusioni deriva da una claborazione comune, quella dei paragrafi 4, 5 e 7 è dovuta a Pressacco mentre quella dei rimanenti è dovuta a Stucchi. Il lavoro è stato svolto nell’ambito della ricerca nazionale “Modelli per la Finanza Matematica”.     

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

In this game [Aruka in Avatamsaka game structure and experiment on the web. In: Aruka Y (ed) Evolutionary controversies in economics. Springer, Tokyo, pp 115–132, 2001], selfishness may not be determined even if an agent selfishly adopts the strategy of defection. Individual selfishness can only be realized if the other agent cooperates, therefore gain from defection can never be assured by defection alone. The sanction by defection as a reaction of the rival agent cannot necessarily reduce the selfishness of the rival. In this game, explicit direct reciprocity cannot be guaranteed. Now we introduce different spillovers or payoff matrices, so that each agent may then be faced with a different payoff matrix. A ball in the urn is interpreted as the number of cooperators, and the urn as a payoff matrix. We apply Ewens’ sampling formula to our urn process in this game theoretic environment. In this case, there is a similar result as in the classic case, because there is “self-averaging” for the variances of the number who cooperate. Applying Pitman’s sampling formula to the urn process, the invariance of the random partition vectors under the properties of exchangeability and size-biased permutation does not hold in general. Pitman’s sampling formula depends on the two-parameter Poisson–Dirichlet distribution whose special case is just Ewens’ formula. In the Ewens setting, only one probability α of a new entry matters. On the other hand, there is an additional probability θ of an unknown entry, as will be argued in the Pitman formula. More concretely, we will investigate the effects of different payoff sizes from playing a series of different games for newly emerging agents. As Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007) and Aoki (J Econ Interact Coord 3:1–3, 2008) dealt with a product innovation and a process innovation, they criticized Lucas’ representative method and the idea that players face micro shocks drawn from the same unchanged probability distribution. In the light of Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007), we show the same argument in our Avatamsaka game with different payoffs. In this setting, innovations occurring in urns may be regarded as increases of the number of cooperators in urns whose payoffs are different.     

A lower bound for the normal approximation ofU-statistics

Summary In this paper, the rates of convergence to the normal distribution are investigated forU-statistics. Using Stein’s method, we derive a lower bound of the uniform distance between the distributions ofU-statistics and the standard normal distribution.     

Prediction of <Emphasis Type="Italic">k</Emphasis>-records from a general class of distributions under balanced type loss functions

We study the problem of predicting future k-records based on k-record data for a large class of distributions, which includes several well-known distributions such as: Exponential, Weibull (one parameter), Pareto, Burr type XII, among others. With both Bayesian and non-Bayesian approaches being investigated here, we pay more attention to Bayesian predictors under balanced type loss functions as introduced by Jafari Jozani et al. (Stat Probab Lett 76:773–780, 2006a). The results are presented under the balanced versions of some well-known loss functions, namely squared error loss, Varian’s linear-exponential loss and absolute error loss or L ₁ loss functions. Some of the previous results in the literatures such as Ahmadi et al. (Commun Stat Theory Methods 34:795–805, 2005), and Raqab et al. (Statistics 41:105–108, 2007) can be achieved as special cases of our results. Partial support from Ordered and Spatial Data Center of Excellence of Ferdowsi University of Mashhad is acknowledged by J. Ahmadi. M. J. Jozani’s research supported partially by a grant of Statistical Research and Training Center. é. Marchand’s research supported by NSERC of Canada. A. Parsian’s research supported by a grant of the Research Council of the University of Tehran.     

Streuungszerlegung für Paar-Vergleiche

Zusammenfassung Pl?ne für Paar-Vergleich Versuche werden gegeben und die Auswertung solcher Versuche wird beschrieben. Die Arbeit st?tzt sich auf das vonBock (1958) abge?nderte Modell vonThurstone undMosteller (1951a). Die Pl?ne sind so, da? sie zu unabh?ngig verteilten Fehlern führen. Zu ihrer Auswertung kann bedenkenlos die Streuungszerlegung angewendet werden. Die Konstruktion von ausgewogenen Pl?nen (allek(k−1)/2 m?glichen Paare werden verglichen) wird beschrieben und teilweise ausgewogene Pl?ne (nicht alle m?glichen Paare werden verglichen) für bis zu 10 Objekte sind tabelliert. Es wird gezeigt, da? die Auswertung solcher Versuche mit der Auswertung von Versuchen in unvollst?ndigen Bl?cken identisch ist. Zur leichteren Auswertung der teilweise ausgewogenen Versuche sind die Inversen der Koeffizientenmatrix der Normalgleichungen tabelliert. Ein Anwendungsbeispiel aus der Wollforschung wird durchgerechnet.

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Summary Designs for paired comparisons are given and their analysis is discussed. The paper is based onBock’s modification (1958) ofThurstone andMosteller’s (1951a) model. The designs lead to independently distributed errors and analysis of variance can be applied. The construction of balanced designs (in which allk(k−1)/2 possible comparisons are made) is described and partially balanced designs (in which not all possible comparisons are made) for up to 10 objects are tabulated. It is shown that the analysis of paired comparison experiments is identical to the analysis of incomplete block experiments. To simplify the analysis of the partially balanced designs the inverses of the matrices comprising the coefficients of the normal equations are tabulated. A worked example of application to a problem in wool research is given.

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Die Arbeit wurde im South African Wool Textile Research Institute, Rhodes University, Grahamstown, Südafrika, geschrieben.     

Workplace Bullying: Application of Novak’s (1998) Learning Theory and Implications for Training

This paper applies Novak’s (1998) theory of learning to the problem of workplace bullying. Novak’s theory offers an understanding of how actions of bullying and responses to bullying can be seen as deriving from individualized conceptualizations of workplace bullying by those involved. Further, Novak’s theory suggests that training involving Ausubel’s concept of meaningful learning (Ausubel Educational Theory 11(1): 15–25, 1961; Ausubel et al. 1978) which attends to learners’ pre-existing knowledge and allows for new meaning to be constructed regarding workplace bullying can lead to new actions related to workplace bullying. Ideally, these new actions can involve both a reduction in workplace bullying prevalence, and responses to workplace bullying which recognize and are informed by the negative consequences of this workplace dynamic.     

Measuring opinion distributions

In this study it will be argued that the perceived distribution of opinions among others is important for opinion research. Three different ways of measuring the perception of opinion distributions in survey research are compared: (a) by means of a questionwhat most people think about an issue, (b) by means of a questionhow many people are perceived to agree with an issue-statement, (c) by means of ‘line-production-boxes’, a special version ofmagnitude estimation. The results indicate that ‘line-production-boxes’ can improve data quality, but have also some drawbacks which will have to be dealt with. ‘Line-production-boxes’ give a wealth of information about individual differences in the forms of perceived opinion distributions. Although the normal distribution is used often, many other distribution forms are also used. The method of ‘line-production-boxes’ is compared with the method of estimating percentage points. Although high correlations suggest a good concurrent validity, some systematic differences do exist. New research directions are suggested.     

Two-sample rank tests with truncated populations

LetX ₁,…,X _m andY ₁,…,Y _n be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S ₍₁₎,…,S _(n)), whereS _(j)=# (X _i ’s≤Y _(j)) andY _(j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test. We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests based onS ₍₁₎ andS _(n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c).     

The mean residual of record values at the level of previous records

In the study of reliability of the technical systems, records model plays an important role. Suppose that a technical system is subject to shocks, e.g. peaks of voltages or stresses. The successive large shocks may be viewed as realizations of records from a sequence of identically independent voltages. Assume that the lower limit value of the mth record voltage (stress) is v > 0. Under these conditions, we propose a mean residual of records (MRR’s) for the future records. We study several properties of MRR. We show that the proposed MRR uniquely characterizes the distribution function that generated the sequence of records. It is proved that when the model under study has an increasing hazard rate the corresponding MRR is decreasing. We also compare between two record systems based on their MRR’s when these systems are ordered in terms of their hazard rates.     

A Q-Analysis of Census Data: Intra-Household Income Allocation and School Attendance in Chiapas, Mexico

Q-analysis, introduced by a mathematician Ron Atkin, is a useful tool to explore social structures. I introduce essential concepts and techniques of q-analysis to show q-analysis’s potential ability to analyze and extract information from census data – the work that most researchers have done mainly with statistical methods. Using Mexican census and q-analysis, I examine whether children of female-headed household aged 15–19 were more likely to attend school than male-headed household children in Chiapas, Mexico in 2000. My findings are consistent with the large body of previous research, many of which were conducted with statistical methods: women’s control of income tends to results in a better welfare for their children, defined as children’s school attendance by the sex of heads of household in my study. I evaluate the advantages and disadvantages of a-analysis of census data. I conclude that while it has some weaknesses, q-analysis is a complimentary method to statistical methods for analysis of census data that may overcome some limitations that statistical methods often face such as an incapability of handling a small sample.     

An improved combinatorial approach for pricing Parisian options

Parisian options are path-dependent options whose payoff depends on whether the underlying asset’s price remains continuously at or above a given barrier over a given time interval. Costabile’s (Decis Econ Finance 25(2):111–125, 2002b) algorithm for pricing Parisian options based on a combinatorial approach in binomial tree has a time complexity of O( n³){O\left( {n^{3}}\right)}. We improve that algorithm to yield one with a time complexity of only O(n²){O\left({n^{2}}\right)}.     

Organizations undertaking complex projects in uncertain environments

Recent evidence suggests that firms’ environments are becoming more complex and uncertain. This paper investigates the relationship between the complexity of a firm’s activities, environmental uncertainty and organizational structure. We assume agents are arranged hierarchically, but decisions can be made at different levels. We model a firm’s activity set as a modified NK landscape. Via simulations, we find that centralized decision making generates a higher payoff in more complex and uncertain environments, and that a flatter structure is better for the organization with centralized decision making, provided the cost of information processing is low enough. Financial Support from Zengin Foundation for Studies on Economics and Finance is gratefully acknowledged.     

Exploring the relationship between media coverage and participation in entrepreneurship: Initial global evidence and research implications

Using a set of variables measured in the Global Entrepreneurship Monitor (GEM) study, our empirical investigation explored the influence of mass media through national culture on national entrepreneurial participation rates in 37 countries over 4 years (2000 to 2003). We found that stories about successful entrepreneurs, conveyed in mass media, were not significantly associated with the rate of nascent (opportunity searching) or the rate of actual (business activities commenced up to 3 months old) start-up activity, but that there was a significant positive association between the volume of entrepreneurship media stories and a nation’s volume of people running a young business (that is in GEM terminology, a business aged greater than 3 but less than 42 months old). More particularly, such stories had strong positive association with opportunity oriented operators of young businesses. Together, these findings are compatible with what in the mass communications theory literature may be called the ‘reinforcement model’. This argues that mass media are only capable of reinforcing their audience’s existing values and choice propensities but are not capable of shaping or changing those values and choices. In the area covered by this paper, policy-makers are committing public resources to media campaigns of doubtful utility in the absence of an evidence base. A main implication drawn from this study is the need for further and more sophisticated investigation into the relationship between media coverage of entrepreneurship, national culture and the rates and nature of people’s participation in the various stages of the entrepreneurial process.