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.     

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.

     

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.     

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.     

Revisiting the difference between mixed methods and multimethods: Is it all in the name?

The literature on mixed methods and multimethods has burgeoned over the last 20 years, and researchers from a growing number and diversity of fields have progressively embraced these approaches. However, rapid growth in any movement inevitably gives rise to gaps or shortcomings, such as “identity crises” or divergent conceptual views. Although some authors draw a clear and sometimes opinionated distinction between mixed methods and multimethods, for others, they are synonymous. The concepts underlying both terms therefore have become blurred and generated much confusion. The aim of this article is to explore the origins of the confusion, describe our view of mixed methods and multimethod studies, and by doing so, help to clearly delineate the two concepts. The authors have presented their opinion of how these terms and concepts should be distinguished and call for a constructive debate of the issues involved in the mixed methods and multimethod literature. This is a way truly to propel the field forward.     

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.     

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.     

“Speculative Influence Network” during financial bubbles: application to Chinese stock markets

We introduce the Speculative Influence Network (SIN) to decipher the causal relationships between sectors (and/or firms) during financial bubbles. The SIN is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of regime-switching between a normal market phase represented by a geometric Brownian motion and a bubble regime represented by the stochastic super-exponential Sornette and Andersen (Int J Mod Phys C 13(2):171–188, 2002) bubble model. The calibration of the HMM provides the probability at each time for a given security to be in the bubble regime. Conditional on two assets being qualified in the bubble regime, we then use the transfer entropy to quantify the influence of the returns of one asset i onto another asset j, from which we introduce the adjacency matrix of the SIN among securities. We apply our technology to the Chinese stock market during the period 2005–2008, during which a normal phase was followed by a spectacular bubble ending in a massive correction. We introduce the Net Speculative Influence Intensity variable as the difference between the transfer entropies from i to j and from j to i, which is used in a series of rank ordered regressions to predict the maximum loss (%MaxLoss) endured during the crash. The sectors that influenced other sectors the most are found to have the largest losses. There is some predictability obtained by using the transfer entropy involving industrial sectors to explain the %MaxLoss of financial institutions but not vice versa. We also show that the bubble state variable calibrated on the Chinese market data corresponds well to the regimes when the market exhibits a strong price acceleration followed by clear change of price regimes. Our results suggest that SIN may contribute significant skill to the development of general linkage-based systemic risks measures and early warning metrics.     

Relations for product moments and covariances of <Emphasis Type="Italic">k</Emphasis>th records from discrete distributions

The aim of this paper is to establish recurrence relations satisfied by product moments and covariances of kth records arising from discrete distributions. They will be evaluated for geometric underlying distribution. Then we use these results to obtain formulas for correlation coefficients of geometric kth records. We consider all three known types of kth records: strong, ordinary, and weak.     

Humiliation at Work and Union Interest: An Empirical Analysis of Community Union Satisfaction as Related to Status Enhancement

How noneconomic benefits claimed by labor unions relate to union interest is not well articulated. Based on Torres and Bergner’s (Journal of the American Academy of Psychiatry and the Law, 38, 195–204, 2010; Psychotherapy, 49, 492–501, 2012) analysis of severe public humiliation, in which status enhancement underlies recovery, we examined an augmented relationship between humiliation at work (the underside of dignity at work) and willingness to join a union. As hypothesized, nonunion employees who were less detached from work showed more willingness to join when presented with evidence that members of a union were satisfied with community aspects of membership related to status enhancement above and beyond their satisfaction with economic aspects. Implications for union interest research and applications are discussed.     

Economics of evaluation (with special reference to promotion and tenure committees)

Previous research suggests that universities that fear tenuring bad candidates more than they fear rejecting good candidates would optimally have both department and outside evaluating committees. I find that a higher relative cost of accepting bad candidates is neither necessary nor sufficient for the optimality of more than one committee. Also, with some probability, t, the administration will tenure one with split recommendations from two committees, if one committee is more accurate than the other, one structure will have fewer errors of both types for some range of t, and possibly a lower expected loss from errors for all t.     

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.     

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.     

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.     

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.     

The airport problem with capacity constraints

The original airport problem is concerned with the cost sharing of an airstrip among airplanes assuming that one airstrip is sufficient to serve all airplanes. In this paper, we generalize the original airport problem by imposing capacity constraints to consider the situation when one airstrip cannot serve all airplanes and investigate how to share the cost among airplanes. We introduce the sequential equal contributions rule for our problem and show that it coincides with the Shapley value of the corresponding airport game when the worth of a coalition is defined to be the minimum cost of serving all members of the coalition. The sequential equal contributions rule requires each airplane to contribute equally to the cost of a given section of any airstrip as long as the length of the section is less than or equal to its desired length even though the airplane cannot use the airstrip. Each airplane’s contribution is the sum of terms, one for each section of the airstrip whose length is less than or equal to its desired length. We also present an axiomatic characterization of the rule by imposing the axioms of efficiency, the equal share lower bound, smaller-cost monotonicity, and population fairness.     

Network design in games with spillovers

How should an organization be designed in order to provide its members with minimal incentives to defect? And how does the optimal design depend on the type of strategic interaction between defectors and remaining organizational members? This paper addresses such issues in a game theoretic model of cooperation, in which an organization is formally represented by a connected network, and where gains from cooperation are given by a partition function. We show that critical structural features of the organization depend in a clear-cut way on the sign of spillovers. In particular, positive spillovers favor the adoption of dispersed and centralized forms, while negative spillovers favor cohesive and horizontal ones. Moreover, if the organizational form determines all the communication possibilities of members, a highly centralized organization—the star—emerges under positive spillovers, whereas two horizontal architectures—the circle and the complete—emerge under negative spillovers.     

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.     

Asymptotics of self-weighted M-estimators for autoregressive models

In this paper, we consider a stationary autoregressive AR(p) time series \(y_t=\phi _0+\phi _1y_{t-1}+\cdots +\phi _{p}y_{t-p}+u_t\). A self-weighted M-estimator for the AR(p) model is proposed. The asymptotic normality of this estimator is established, which includes the asymptotic properties under the innovations with finite or infinite variance. The result generalizes and improves the known one in the literature.