Kiefer–Wolfowitz algorithm under quasi-associated random errors

In this article, we study the algorithm of Kiefer–Wolfowitz underquasi-associated random errors. We establish the complete convergence and obtain an exponential bound. Additionally, we build a confidence interval for the minimum. Numerical examples are sketched out to confirm the theoretical results and show the accuracy of the algorithm.     

Women’s Decision to Divorce in Light of Failure in Marital Status and Dignity

In Iranian society, divorce, as an instability index of family, has been on the increase over the last decade. In particular, this separation is fraught with considerable difficulties for wives with children. The overall aim of this study is to investigate the nature of the process of deciding to separate by the divorced women despite having children. Resting on the grounded theory method, this study was conducted among 20 divorced women with children in the city of Tehran. The findings show that having a child is not a determining factor for the women to remain married; rather, what determines the separation of women with children is experiencing a status loss within their marital life, an experience that originates from losing her status after a woman has gotten married. Of course, women’s agency within the domain of family disintegration happens when they have the ability to overcome social fears and also have economic support. Through this course of events, although children are of enormous importance for the mothers, they are temporarily neglected while the mothers, for a short period, think primarily of saving themselves. Making their final decision to get separated leads to reactivating the role of their children; then, the mothers proceed to make the optimal decision.     

Estimation of the mean of a spherically symmetric distribution with constraints on the norm

The authors consider the problem of estimating, under quadratic loss, the mean of a spherically symmetric distribution when its norm is supposed to be known and when a residual vector is available. They give a necessary and sufficient condition for the optimal James‐Stein estimator to dominate the usual estimator. Various examples are given that are not necessarily variance mixtures of normal distributions. Consideration is also given to an alternative class of robust James‐Stein type estimators that take into account the residual vector. A more general domination condition is given for this class.     

Consistency of stochastic approximation algorithm with quasi-associated random errors

ABSTRACT

Many mathematical and physical problems are led to find a root of a real function f. This kind of equation is an inverse problem and it is difficult to solve it. Especially in engineering sciences, the analytical expression of the function f is unknown to the experimenter, but it can be measured at each point x_k with M(x_k) as expected value and induced error ξ_k. The aim is to approximate the unique root θ under some assumptions on the function f and errors ξ_k. We use a stochastic approximation algorithm that constructs a sequence (x_k)_{k ? 1}. We establish the almost complete convergence of the sequence (x_k)_k to the exact root θ by considering the errors (ξ_k)_k quasi-associated and we illustrate the method by numerical examples to show its efficiency.     

Bayesian alignment of proteins via Delaunay tetrahedralization

An active area of research in bioinformatics is finding structural similarity of proteins by alignment. Among many methods, the popular one is to find the similarity based on statistical features. This method involves gathering information from the complex biomolecule structure and obtaining the best alignment by maximizing the number of matched features. In this paper, after reviewing statistical models for matching the structural biomolecule, it is shown that local alignment based on the Delaunay tetrahedralization (DT) can be used for Bayesian alignment of proteins. In this method, we use DT to add a priori structural information of protein in the Bayesian methodology. We demonstrate that this method shows advantages over competing methods in achieving a global alignment of proteins, accelerating the convergence rate and improving the parameter estimates.     

Spatio-temporal Trend Analysis of Spring Arrival Data for Migratory Birds

There is increasing interest in spatio-temporal analysis of environmental and ecological responses to changes in the climate due to the recent concerns about climate change. In this work, we propose a spatio-temporal modeling framework for analyzing environmental and ecological data while accounting for spatial and temporal structure, as well as climate effects. As an example, we consider data on bird migration in the United States and analyze the spring arrival dates of Purple Martins between historical data (1905–1940) from the North American Bird Phenology Program and recent data (2001–2010) from the Purple Martin Conservation Association. The proposed approach allows researchers to compare mean arrival dates while accounting for spatial and temporal variability. Our results for Purple Martins showed statistically significant earlier spring arrivals in parts of United States over the recent years. The proposed approach provides a useful tool for statistical analysis of spatio-temporal data related to studies of climate change.     

Trace of the Variance-Covariance Matrix in Natural Exponential Families

In this article, we introduce the notion of trace variance function which is the trace of the variance-covariance matrix. Under some conditions, we prove that this trace variance function characterizes the Natural Exponential Family (NEF). We apply this characterization in order to estimate the distribution which belongs to some NEFs. Therefore, we introduce the estimator of this trace variance function. We give the asymptotic properties of this estimator. Finally, we illustrate our results using a simulation study.     

Board of directors and insider trading with share repurchase programs

This study examines the relationship between insider trading and board of directors’ characteristics around stock repurchase announcements. It is hypothesized that information disparity between insiders and shareholders from share repurchases announcements creates opportunities for insiders to time their trading. However, there is little evidence on whether board characteristics reduce the probability of insider trading with repurchase announcements. Using data from firms listed on Forbes 500 between 1998 and 2004, we found that insider trading is related to share repurchase announcements. In order to focus on board of directors’ role, we controlled for board characteristics that may change the repurchase decision. Our results provide corroborative evidence of insider net selling around repurchase announcements and the advantages of board characteristics to offset insider trading. In particular, the results suggest that board tenure, directors’ ownership and board directorship change positively insider trading around repurchase announcements. Hence, Securities and Exchange Commission should consider rigorous restrictions on share repurchase announcements and be aware of potential influence of the corporate governance device.