R-optimal designs for multi-factor models with heteroscedastic errors

In this paper, we consider the R-optimal design problem for multi-factor regression models with heteroscedastic errors. It is shown that a R-optimal design for the heteroscedastic Kronecker product model is given by the product of the R-optimal designs for the marginal one-factor models. However, R-optimal designs for the additive models can be constructed from R-optimal designs for the one-factor models only if sufficient conditions are satisfied. Several examples are presented to illustrate and check optimal designs based on R-optimality criterion.     

On the welfare effects of affirmative actions in school choice

Recent evidence, from both academia and practice, indicates that implementing affirmative action policies in school choice problems may induce substantial welfare losses on the intended beneficiaries. This paper addresses the following two questions: what are the causes of such perverse consequences, and when we can effectively implement affirmative action policies without unsatisfactory outcomes. Using the minority reserve policy in the student optimal stable mechanism as an example, I show that two acyclicity conditions, type-specific acyclicity and strongly type-specific acyclicity, are crucial for the effective implementations of minority reserve policies. I further illustrate how restrictive these two acyclicity conditions are, and the intrinsic difficulty of embedding diversity goals into stable matching mechanisms. Under some regularity conditions, I demonstrate that the minority reserve policy is very unlikely to cause welfare losses on any minority students when the number of schools is sufficiently large.     

Bayesian estimation based on ranked set sample from Morgenstern type bivariate exponential distribution when ranking is imperfect

In this paper we consider Bayes estimation based on ranked set sample when ranking is imperfect, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. Bayes estimators under squared error loss function and LINEX loss function for the mean of the study variate Y, when (X, Y) follows a Morgenstern type bivariate exponential distribution, are obtained based on both usual ranked set sample and extreme ranked set sample. Estimation procedures developed in this paper are illustrated using simulation studies and a real data.     

Almost sure central limit theorem for the products of <Emphasis Type="Italic">U</Emphasis>-statistics

Let (X _n ) be a sequence of i.i.d random variables and U _n a U-statistic corresponding to a symmetric kernel function h, where h ₁(x ₁) = Eh(x ₁, X ₂, X ₃, . . . , X _m ), μ = E(h(X ₁, X ₂, . . . , X _m )) and ? ₁ = Var(h ₁(X ₁)). Denote \({\gamma=\sqrt{\varsigma_{1}}/\mu}\), the coefficient of variation. Assume that P(h(X ₁, X ₂, . . . , X _m ) > 0) = 1, ? ₁ > 0 and E|h(X ₁, X ₂, . . . , X _m )|³ < ∞. We give herein the conditions under which

$\lim_{N\rightarrow\infty}\frac{1}{\log N}\sum_{n=1}^{N}\frac{1}{n}g\left(\left(\prod_{k=m}^{n}\frac{U_{k}}{\mu}\right)^{\frac{1}{m\gamma\sqrt{n}}}\right) =\int\limits_{-\infty}^{\infty}g(x)dF(x)\quad {\rm a.s.}$

for a certain family of unbounded measurable functions g, where F(·) is the distribution function of the random variable \({\exp(\sqrt{2} \xi)}\) and ξ is a standard normal random variable.

     

A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings

Let U ₁, U ₂, . . . , U _n–1 be an ordered sample from a Uniform [0,1] distribution. The non-overlapping uniform spacings of order s are defined as \({G_{i}^{(s)} =U_{is} -U_{(i-1)s}, i=1,2,\ldots,N^\prime, G_{N^\prime+1}^{(s)} =1-U_{N^\prime s}}\) with notation U ₀ = 0, U _n = 1, where \({N^\prime=\left\lfloor n/s\right\rfloor}\) is the integer part of n/s. Let \({ N=\left\lceil n/s\right\rceil}\) be the smallest integer greater than or equal to n/s, f _m (u), m = 1, 2, . . . , N, be a sequence of real-valued Borel-measurable functions. In this article a Cramér type large deviation theorem for the statistic \({f_{1,n} (nG_{1}^{(s)})+\cdots+f_{N,n} (nG_{N}^{(s)} )}\) is proved.     

Dispersive ordering of fail-safe systems with heterogeneous exponential components

Let X ₁, . . . , X _n be independent exponential random variables with respective hazard rates λ₁, . . . , λ _n , and Y ₁, . . . , Y _n be independent and identically distributed random variables from an exponential distribution with hazard rate λ. Then, we prove that X _2:n , the second order statistic from X ₁, . . . , X _n , is larger than Y _2:n , the second order statistic from Y ₁, . . . , Y _n , in terms of the dispersive order if and only if

$\lambda\geq \sqrt{\frac{1}{{n\choose 2}}\sum_{1\leq i < j\leq n}\lambda_i\lambda_j}.$

We also show that X _2:n is smaller than Y _2:n in terms of the dispersive order if and only if

$ \lambda\le\frac{\sum^{n}_{i=1} \lambda_i-{\rm max}_{1\leq i\leq n} \lambda_i}{n-1}. $

Moreover, we extend the above two results to the proportional hazard rates model. These two results established here form nice extensions of the corresponding results on hazard rate, likelihood ratio, and MRL orderings established recently by Pǎltǎnea (J Stat Plan Inference 138:1993–1997, 2008), Zhao et al. (J Multivar Anal 100:952–962, 2009), and Zhao and Balakrishnan (J Stat Plan Inference 139:3027–3037, 2009), respectively.

     

A new measure of association between random variables

We propose a new measure of association between two continuous random variables X and Y based on the covariance between X and the log-odds rate associated to Y. The proposed index of correlation lies in the range [\(-1\), 1]. We show that the extremes of the range, i.e., \(-1\) and 1, are attainable by the Fr\(\acute{\mathrm{e}}\)chet bivariate minimal and maximal distributions, respectively. It is also shown that if X and Y have bivariate normal distribution, the resulting measure of correlation equals the Pearson correlation coefficient \(\rho \). Some interpretations and relationships to other variability measures are presented. Among others, it is shown that for non-negative random variables the proposed association measure can be represented in terms of the mean residual and mean inactivity functions. Some illustrative examples are also provided.     

Organizational Socialization and Psychological Contract: the Vulnerability of Temporary Newcomers. A Case Study from an Italian <Emphasis Type="Italic">Call Center</Emphasis>

This study aims to analyze the link between the construction of an effective psychological contract with the organization and the success of the socialization process. To this purpose 241 employees of a Call Center organization have been contacted. A questionnaire composed by measures of Organizational Socialization (Haueter et al. Journal of Vocational Behavior, 63, 20–39, 2003), Psychological Contract (Rousseau 1995), Job Satisfaction (Wanous et al. Journal of Applied Psychology, 82, 247–252, 1997) and Organizational Committment (Allen and Meyer 1990) was administered. Results have underlined that organizational socialization may influence the development of the psychological contract thus determining job satisfaction and organizational commitment. This research has been developed in an interdisciplinary perspective, taking into account the peculiarity of the Italian legal framework. In this regard, the analysis has been focused on how the E.U. flexicurity strategy has been implemented in Italy, according to the recent reform of labour market regulation (2012–13) and on the specific regulations introduced for call centres.     

New axioms for immediate acceptance

Following Kojima and Ünver (Econ Theory 55(3):515–544, 2014) and Afacan (Math Soc Sci 66(2):176–179, 2013), this paper provides two characterizations of the Boston school choice mechanism determined by the student-proposing immediate acceptance algorithm. A mechanism is the Boston mechanism if and only if it satisfies one of the following two groups of axioms: favoring higher ranks and weak fairness; favoring higher ranks, rank monotonicity, and rank rationality.     

Asymptotic non-deficiency of the Bayes sequential estimation in a family of transformed Chi-square distributions

Bayes sequential estimation in a family of transformed Chi-square distributions using a linex loss function and a cost c > 0 for each observation is considered in this paper. It is shown that an asymptotic pointwise optimal rule (A.P.O.) is asymptotically non-deficient, i.e., the difference between the Bayes risk of the A.P.O. rule and the Bayes risk of the optimal procedure is of smaller order of magnitude than c, the cost of single observation, as c → 0.     

The changing role of network ties and critical capabilities in an international new venture’s early development

The importance of networks for firm internationalization has been pointed out for several decades. Especially for small and new firms, networks have been found to be an important tool to gain access to resources and to overcome liabilities of newness, smallness and foreignness. Yet, there is a lack of understanding regarding which types of capabilities are developed through networking and how and when networks are used. The aim of this article is to explore how and when different networking activities develop critical capabilities during different phases of an international new venture’s early development. The article is based on a longitudinal, in-depth case study of a Swedish international new venture from the medical-technology industry. We find that the development process is greatly affected by how the individual key actors leverage their network ties to develop critical capabilities – they use existing network ties and different indirect ties during the pre-founding, start-up and establishment of production phases. During the commercialization and sales growth phases, however, many new network ties are developed. The heterogeneity of the individual actors’ backgrounds plays an important role during the different developmental phases. We conclude by advancing a number of propositions in relation to how critical capabilities are developed through networking during different developmental phases.     

Unbiased estimates for a lognormal regression problem and a nonparametric alternative

Given a normal sample with means \({{\bf x}_{1}^{\prime} {\bf \varphi}, \ldots, {\bf x}_{n}^{\prime} {\bf \varphi}}\) and variance v, minimum variance unbiased estimates are given for the moments of L, where log L is normal with mean \({{\bf x}^{\prime} {\bf \varphi}}\) and variance v. These estimates converge to wrong values if the normality assumption is false. In the latter case estimates based on any M-estimate of \({{\bf \varphi}}\) are available of bias \({O\left(n^{-1}\right)}\) and \({O\left(n^{-2}\right)}\). More generally, these are given for any smooth function of \({\left({\bf \varphi}, F\right)}\), where F is the unknown distribution of the residuals. The regression functions need not be linear.     

Asymptotic inference for a one-dimensional simultaneous autoregressive model

A nonstationary simultaneous autoregressive model \({X^{(n)}_k=\alpha \Big(X^{(n)}_{k-1}+X^{(n)}_{k+1}\Big)+\varepsilon_k, k=1, 2, \ldots , n-1}\), is investigated, where \({X^{(n)}_0}\) and \({X^{(n)}_n}\) are given random variables. It is shown that in the unstable case α = 1/2 the least squares estimator of the autoregressive parameter converges to a functional of a standard Wiener process with a rate of convergence n ², while in the stable situation |α| < 1/2 the estimator is biased but asymptotically normal with a rate n ^1/2.     

Multivariate saddlepoint tests on the mean direction of the von Mises–Fisher distribution

This article provides P values for two new tests on the mean direction of the von Mises–Fisher distribution. The test statistics are obtained from the exponent of the saddlepoint approximation to the density of M-estimators, as suggested by Robinson et al. (Ann Stat 31:1154–1169, 2003). These test statistics are chi-square distributed with asymptotically small relative errors. Despite the high dimensionality of the problem, the proposed P values are accurate and simple to compute. The numerical precision of the P values of the new tests is illustrated by some simulation studies.     

The method of constant stimuli with three rating categories and the use of Rasch models

Logistic Models support an alternative general solution to compute the point of subjective equality (Vidotto et al., I modelli simple logistic e rating scale nella determinazione del punto di eguaglianza soggettivo: una nuova prospettiva per il metodo degli stimoli costanti, 1996) when the Method of Constant Stimuli is used (Bock and Jones, The Measurement and Prediction of Judgment and Choice, 1968). The Extended Logistic Models (Andrich, Appl. Psychol. Meas. II:581–594, 1978) offer the theoretical frame to compute individual and general thresholds when the method of constant stimuli is applied using a forced choice with more than two alternatives. As an example of the advantages of the application of this procedure, we show a data-set derived from an experiment on rhythm perception (Maestrini, La percezione del cambiamento nei ritmi uditivi, 2003), where two groups of experimental and naïve subjects were asked to judge whether the listened rhythm was constant, accelerated or decelerated. We have computed individual and general thresholds differentiating constancy from both acceleration and deceleration for all the different experimental conditions. The main advantage of this solution, compared to traditional psychophysical techniques, is not only related to better estimates of the individual point of subjective equality. The improvement can be summarized in the available fit tests to verify the agreement between the model both for stimuli and subjects.     

The concept of weak exchangeability and its applications

A finite sequence of binary random variables is called a weak exchangeable sequence of order m if the sequence consists of m random vectors such that the elements within each random vector are exchangeable in the usual sense and the different random vectors are dependent. The exact and asymptotic joint distributions of the m-dimensional random vector whose elements include the number of successes in each exchangeable sequence are derived. Potential applications of the concept of weak exchangeability are discussed with illustrative examples.     

A note on the uniform distribution on the arcsin points

In his book Pukelsheim [8] pointed out that designs supported at the arcsin points are very efficient for the statistical inference in a polynomial regression model. In this note we determine the canonical moments of a class of distributions which have nearly equal weights at the arcsin points. The class contains theD-optimal arcsin support design and theD ₁-optimal design for a polynomial regression. The results allow explicit representations ofD-, andD ₁-efficiencies of these designs in all polynomial models with a degree less than the number of support points of the design.     

The variance of the discrepancy distribution of rounding procedures,and sums of uniform random variables

When \(\ell \) probabilities are rounded to integer multiples of a given accuracy n, the sum of the numerators may deviate from n by a nonzero discrepancy. It is proved that, for large accuracies \(n \rightarrow \infty \), the limiting discrepancy distribution has variance \(\ell /12\). The relation to the uniform distribution over the interval \([-1/2, 1/2]\), whose variance is 1 / 12, is explored in detail.     

On theE-optimality of certain asymmetrical designs under mixed effects model

TheE-optimality of the following designs within the class of all proper and connected designs with givenb, k andv under mixed effects model are established.

1. A group divisible design with λ₂ = λ₁ + 1.
2. A group divisible design with λ₁ = λ₂ + 1 and group size 2.
3. A linked block design.
4. The dual of design (i)
5. The dual of design (ii).

All these designs are known to satisfy the same optimality property under fixed effects model whenk<v, while the design (i) is known to beE-optimal even whenk>v. From the results proved here, theE-optimality of designs (ii, (iii), (iv) and (v) under fixed effects model in the situation whenk >v also follows.     

Versatile networks in combining qualitative and quantitative data

Following a series of special volumes on the DISC conferences in the past, this themed issue focuses on versatile network forms particularly in combining qualitative and quantitative data. This special issue also celebrates the second publication born out of the DISC conferences under the Quality and Quantity.