General results of complete convergence and complete moment convergence for weighted sums of some class of random variables

ABSTRACT

In the article, the complete convergence and complete moment convergence for weighted sums of sequences of random variables satisfying a maximal Rosenthal type inequality are studied. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. Our partial results generalize and improve the corresponding ones of Shen (2013 Shen, A.T. (2013). On strong convergence for weighted sums of a class of random variables. Abstr. Appl. Anal.2013, Article ID 216236: 1–7. [Google Scholar]).     

An extension of the multivariate Chebyshev's inequality to a random vector with a singular covariance matrix

ABSTRACT

We extend Chebyshev's inequality to a random vector with a singular covariance matrix. Then we consider the case of a multivariate normal distribution for this generalization.     

A note on the satterthwaite confidence interval for a variance

When using a Satterthwaite chi-squared approximation, it is generally thought that the approximation is satisfactory when it is applied to a positive linear combination of mean squares. In this note, we describe how the Williams - Tukey idea for getting a confidence interval for the among groups variance in a random one-way model can be incorporated into Satterthwaite’s procedure for getting a confidence interval for a variance. This adjusted Satterthwaite procedure insures that his chi-squared approximation is always applied to positive linear combinations of mean squares. A small simulation is included which suggests that the adjustment to the Satterthwaite procedure is effective.     

Extensions of Samuelson's Inequality

In this note we obtain upper and lower bounds for the kth largest number in a set of real numbers in terms of their mean and standard deviation. For each inequality necessary and sufficient conditions for equality are given.     

Bounds on expected generalized order statistics

We establish the upper nonpositive and all the lower bounds on the expectations of generalized order statistics based on a given distribution function with the finite mean and central absolute moment of a fixed order. We also describe the distributions for which the bounds are attained. The methods of deriving the lower nonpositive (upper nonnegative) and lower nonnegative (upper nonpositive) bounds are totally different. The first one, the greatest convex minorant method is the combination of the Moriguti and well-known Hölder inequalities and the latter one is based on the maximization of some norm on the properly chosen convex set. The paper completes the results of Cramer et al. [Evaluations of expected generalized order statistics in various scale units. Appl Math. 2002;29:285–295].     

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, the Rosenthal-type maximal inequalities and Kolmogorov-type exponential inequality for negatively superadditive-dependent (NSD) random variables are presented. By using these inequalities, we study the complete convergence for arrays of rowwise NSD random variables. As applications, the Baum–Katz-type result for arrays of rowwise NSD random variables and the complete consistency for the estimator of nonparametric regression model based on NSD errors are obtained. Our results extend and improve the corresponding ones of Chen et al. [On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl. 2007;52(2):393–397] for arrays of rowwise negatively associated random variables to the case of arrays of rowwise NSD random variables.     

Expanding our sociolinguistic horizons? Geographical thinking and the articulatory potential of commodity chain analysis

Conceptual linearity and analytic parochialism (aka focus) can make it more difficult for sociolinguists or discourse analysts to apprehend the far‐reaching, exploitative ways inequality is nowadays produced. A suitably material‐cum‐materialist class critique certainly entails empirical and phenomenological worlds flagged by, for example, multi‐sited ethnographies but otherwise side‐lined as merely “extra‐situational” in much talk/text‐directed scholarship. I propose we think more geographically by properly engaging spatiality à la Harvey (1990) and especially the radical politics of simultaneity (Massey, 2005)—the literal, “right‐now” connectedness of places and people. To this end, and allied with deepening interest in political economy, I combine the principles of articulation theory with the procedures of commodity chain analysis for picking apart an epitomic, contemporary manifestation of extreme privilege: the business‐class meal. The proposed discourse‐centred commodity chain analysis offers an ecumenical but systematic framework for tracking how commodity fetishism is actually and discursively accomplished (or not) across dispersed voices, stories, and social meanings.     

The Infringement of the Right to Establish a Family for Jewish Spouses Who Are Mutually Proscribed from Marrying Each Other

Abstract

The article focuses on one of the most painful experiences in intimate relationships and unveils a hitherto unexplored type of human right infringement, namely the right to establish a family in Israel, purported to be a democratic state. Thousands of couples are proscribed from marrying each other every year in Israel. This paper focuses on Jewish couples consisting of male Cohanim (descendants of Jewish priests) and female divorcées, as one among other types of forbidden marriages. Four themes emerged from data analysis of narratives of 26 interviewees, which converged to a common motif of liminality of Cohen-divorcée couples. Based on empirical data, I describe the predicament attendant to this human rights violation which is transmitted to offspring of these couples. The article argues that this liminality undermines the basic rationale of the prevailing millet (personal law) system and discusses the implications of this liminality for human rights and religion-state relations.     

Socioeconomic inequality and adjustments in children’s perceptions of their agency as they age in South Korea

This paper explores how children's perceptions of their agency, as something that is closely associated with its exercise, appear in relation to social structural factors, especially their socioeconomic positions, as they age. Using data from 862 10–18 years old in South Korea, we examine how children's expressed optimism about their ability to achieve their occupational choices can conceal the impact of structural factors on their ‘choices’ and dispositions for (non‐)action over time. Based on the findings, we argue for a more careful interpretation of children's sense of agency that recognises its propensity to continuously adjust in contexts of structural inequality.