Domains of convergence for the EM algorithm: a cautionary tale in a location estimation problem

The EM algorithm is a popular method for maximizing a likelihood in the presence of incomplete data. When the likelihood has multiple local maxima, the parameter space can be partitioned into domains of convergence, one for each local maximum. In this paper we investigate these domains for the location family generated by the t-distribution. We show that, perhaps somewhat surprisingly, these domains need not be connected sets. As an extreme case we give an example of a domain which consists of an infinite union of disjoint open intervals. Thus the convergence behaviour of the EM algorithm can be quite sensitive to the starting point.     

Supply chain agility as an acclimatisation process to environmental uncertainty and organisational vulnerabilities: insights from British SMEs

Abstract

Even though supply chain agility (SCA) has been considered an essential concept in supply chain management (SCM) research, the way it is experienced and manifested, especially by small and medium-sized enterprises (SMEs), has received much less attention. Our purpose is to focus on SME organisational vulnerabilities in the context of increased environmental uncertainty, and explore how SCA is developed and applied by SMEs amid their vulnerabilities. By relying on insights from comparative case studies of three British SMEs, we examine SME SCA as an acclimatisation process and delve into SMEs’ experiences of facing environmental uncertainty while developing and applying SCA. Our findings highlight that organisational attitudes underlie how SMEs perceive environmental uncertainty, tackle organisational vulnerabilities and develop SCA as an acclimatisation process. Our findings also reveal that resource constraints, supply chain relationships, interorganisational power dynamics, and access to information play important roles in developing SCA.     

Stochastic analysis of covariance when the error distribution is long-tailed symmetric

In this study, we consider stochastic one-way analysis of covariance model when the distribution of the error terms is long-tailed symmetric. Estimators of the unknown model parameters are obtained by using the maximum likelihood (ML) methodology. Iteratively reweighting algorithm is used to compute the ML estimates of the parameters. We also propose new test statistic based on ML estimators for testing the linear contrasts of the treatment effects. In the simulation study, we compare the efficiencies of the traditional least-squares (LS) estimators of the model parameters with the corresponding ML estimators. We also compare the power of the test statistics based on LS and ML estimators, respectively. A real-life example is given at the end of the study.     

Variable selection in elliptical linear mixed model

Variable selection in elliptical Linear Mixed Models (LMMs) with a shrinkage penalty function (SPF) is the main scope of this study. SPFs are applied for parameter estimation and variable selection simultaneously. The smoothly clipped absolute deviation penalty (SCAD) is one of the SPFs and it is adapted into the elliptical LMM in this study. The proposed idea is highly applicable to a variety of models which are set up with different distributions such as normal, student-t, Pearson VII, power exponential and so on. Simulation studies and real data example with one of the elliptical distributions show that if the variable selection is also a concern, it is worthwhile to carry on the variable selection and the parameter estimation simultaneously in the elliptical LMM.     

Robust Liu estimator for regression based on an M-estimator

Consider the regression model y = beta 0 1 + Xbeta + epsilon. Recently, the Liu estimator, which is an alternative biased estimator beta L (d) = (X'X + I) -1 (X'X + dI)beta OLS , where 0<d<1 is a parameter, has been proposed to overcome multicollinearity . The advantage of beta L (d) over the ridge estimator beta R (k) is that beta L (d) is a linear function of d. Therefore, it is easier to choose d than to choose k in the ridge estimator. However, beta L (d) is obtained by shrinking the ordinary least squares (OLS) estimator using the matrix (X'X + I) -1 (X'X + dI) so that the presence of outliers in the y direction may affect the beta L (d) estimator. To cope with this combined problem of multicollinearity and outliers, we propose an alternative class of Liu-type M-estimators (LM-estimators) obtained by shrinking an M-estimator beta M , instead of the OLS estimator using the matrix (X'X + I) -1 (X'X + dI).     

Legal pluralism and the Shari'a: a comparison of Greece and Turkey

The creation of a national and unified legal system was an important aspect of the rise of the modern state and national citizenship. However, this interpretation of legal rationalization has been challenged by sociologists of law such as Eugene Ehrlich (1862–1922) who claimed that this juridical theory of state‐centred law masked the presence of customary laws outside this formal system. In critical theories of the law, legal pluralism is proposed against the idea of legal sovereignty or legal centralism. In this article we explore the implications of the growth of the Shari'a as an example of legal pluralism. We take Turkey and Greece as two interesting but different examples of legal pluralism and consider the implications of these case studies for debates about liberalism, multiculturalism and citizenship in multi‐faith societies.     

Correction to: Why perceived organizational and supervisory family support is important for organizations? Evidence from the field

Review of Managerial Science - Under Table&nbsp;1, the explanation regarding the dummy variables that represent gender is reverse coded.     

A new family of multivariate slash distributions

In this article, a new form of multivariate slash distribution is introduced and some statistical properties are derived. In order to illustrate the advantage of this distribution over the existing generalized multivariate slash distribution in the literature, it is applied to a real data set.     

Functions of Concordance and Dependence with Related Measures

Some functions that serve as building blocks for construction of a wider range of modes of concordance and dependence are pointed. We probe into interplays of such modes. From the standpoint of their conformity to stochastic dominance ordering of distributions within a Fréchet class, all such derived modes display some parallelism under certain conditions. We finally suggest a novel numeric measure of dependence that covers similar existing measures in literature.     

Why perceived organizational and supervisory family support is important for organizations? Evidence from the field

Review of Managerial Science - The relationship between perceived organizational support and its work-outcomes were usually based on social exchange theories. By keeping the social exchange...