ROBUST ESTIMATION UNDER TYPE II CENSORING

The properties of robust M-estimators with type II censored failure time data are considered. The optimal members within two classes of ψ-functions are characterized. The first optimality result is the censored data analogue of the optimality result described in Hampel et al. (1986); the estimators corresponding to the optimal members within this class are referred to as the optimal robust estimators. The second result pertains to a restricted class of ψ-functions which is the analogue of the class of ψ-functions considered in James (1986) for randomly censored data; the estimators corresponding to the optimal members within this restricted class are referred to as the optimal James-type estimators. We examine the usefulness of the two classes of ψ-functions and find that the breakdown point and efficiency of the optimal James-type estimators compare favourably with those of the corresponding optimal robust estimators. From the computational point of view, the optimal James-type ψ-functions are readily obtainable from the optimal ψ-functions in the uncensored case. The ψ-functions for the optimal robust estimators require a separate algorithm which is provided. A data set illustrates the optimal robust estimators for the parameters of the extreme value distribution.     

On C pk Assessment in the Presence of Tool Wear

Process capability indices are routinely used in manufacturing industries for process monitoring. A basic assumption while using process capability indices is that there are no assignable causes of variation present. However, when variation due to an assignable cause is present and is tolerated, the conventional methods of capability measurement become inaccurate. In this article, we suggest an estimate of C_pk assuming that the process capability changes dynamically. We obtain an exact form of the sampling distribution in the presence of a systematic assignable cause. We discuss the problem of testing whether a given process is capable. The critical values for different sample sizes are obtained based on the sampling distribution. An example involving tool wear problem is presented.     

Prediction of Times to Failure of Censored Items for a Simple Step-Stress Model with Regular and Progressive Type I Censoring from the Exponential Distribution

The problem of predicting times to failure of units from the Exponential Distribution which are censored under a simple step-stress model is considered in this article. We discuss two types of censoring—regular and progressive Type I—and two kinds of predictors—the maximum likelihood predictors (MLP) and the conditional median predictors (CMP) for each type of censoring. Numerical examples are used to illustrate the prediction methods. Using simulation studies, mean squared prediction error (MSPE) and prediction intervals are generated for these examples. MLP and the CMP are then compared with respect to MSPE and the prediction interval.     

Estimation of the multi-criteria worths of the alternatives in a hierarchical structure of comparisons

The aggregated worths of the alternatives, when compared with respect to several criteria, are estimated in a hierarchical comparisons model introduced by Saaty (1980). A multiplicative model is used for the paired comparisons data which are collected in a ratio scale in this set-up in any level of this hierarchy. An iterative scheme is found for the maximum likelihood estimation of the worth parameters in this multiplicative model. The iterative values are shown to be convergent monotonically to the estimates. We also obtain the asymptotic dispersion matrix of the maximum likelihood estimates of the relative worths of the alternatives according to a single criterion as well as those according to the over-all suitability when compared under several criteria. A numerical example is presented to illustrate the method developed in this paper. Simulation techniques are employed to find the average number of iterations required for the convergence of the above iterative scheme.     

Estimation of Disaggregate-Level Poverty Incidence in Odisha Under Area-Level Hierarchical Bayes Small Area Model

Sustainable development goal-1 of the United Nations is to end poverty in all its forms everywhere. The estimates of poverty related parameters obtained from large scale sample survey are often available at large domain level (e.g. state level). But, poverty rates are not uniformly distributed across the regions. The regional variations are masked in such large domain level estimates. However, for monitoring the progress of poverty alleviation programmes aimed at reduction of poverty often require micro or disaggregate level estimates. The traditional survey estimation approaches are not suitable for generating the reliable estimates at this level because of sample size problem. It is the main endeavor of Small Area Estimation (SAE) approach to produce micro level statistics with acceptable precision without incurring any extra cost and utilizing existing survey data. In this study, the Hierarchical Bayes approach of SAE has been applied to generate reliable and representative district level poverty incidence for the State of Odisha in India using the Household Consumer Expenditure Survey 2011–2012 data of National Sample Survey Office and linked with Population Census 2011. The results show the precise performance of model based estimates generated by SAE method to a greater extent than the direct survey estimates. A poverty map has also been produced to observe the spatial inequality in poverty distribution.

     

Wealth Inequality: Historical Trends and Cross‐National Differences

This article provides an overview of the recent literature on wealth inequality from a comparative and historical perspective. I first discuss how the stock, composition, and distribution of wealth changed from the 18^th century onwards. In the second part of the paper, I move on to the causal questions: What factors drive wealth inequality? Why does the distribution of wealth vary across nations? In the third and concluding section I briefly discuss the socio‐political challenges posed by increasing wealth inequality, and identify several key questions for research going forward.     

Skewness:asymptotic critical values for a test related to Pearson's measure

We examine the asymptotic distribution of, and give critical values for, a test related to Pearson's measure of skewness. The test detects the asymmetry of a continuous distribution about a specified median. Two sets of data are tested using our method.eabs:     

Effects of soccer on stock markets: The return–volatility relationship

This paper assesses the effects of domestic soccer teams’ performances against foreign rivals on stock market returns as well as on the return–volatility relationship. Data from Chile, Spain, Turkey and the United Kingdom support propositions that soccer teams results in international cups affect stock market returns and the return–volatility relationship. Evidence from Spain and the UK, soccer powerhouses, suggests that losses are associated with lower returns and higher risk aversion but evidence from Chile and Turkey, where soccer is the most important sport but teams are not as successful, reveals that wins are associated with higher returns and lower risk aversion.     

Sociology of Debt: States,Credit Markets,and Indebted Citizens

Within the context of the recent financial crisis, the causes and implications of mounting levels of household indebtedness have begun to be examined from a variety of angles: Why have nations differed so drastically, historically speaking, in terms of the level of debt that their citizens carry? Why have patterns converged over the past few decades, with levels of indebtedness increasing across the board? This paper considers these questions from a sociological perspective. I first consider the role of political, institutional, economic, and cultural factors, as well as individual characteristics, in shaping the demand for and supply of credit and the degree and nature of household indebtedness in and across nations. I then attempt to explain the cross‐national convergence towards rising indebtedness over the past few decades by situating the transformation of these various demand and supply side factors under the neoliberal regime.     

On the ‘optimal’ density power divergence tuning parameter

The density power divergence, indexed by a single tuning parameter α, has proved to be a very useful tool in minimum distance inference. The family of density power divergences provides a generalized estimation scheme which includes likelihood-based procedures (represented by choice α=0 for the tuning parameter) as a special case. However, under data contamination, this scheme provides several more stable choices for model fitting and analysis (provided by positive values for the tuning parameter α). As larger values of α necessarily lead to a drop in model efficiency, determining the optimal value of α to provide the best compromise between model-efficiency and stability against data contamination in any real situation is a major challenge. In this paper, we provide a refinement of an existing technique with the aim of eliminating the dependence of the procedure on an initial pilot estimator. Numerical evidence is provided to demonstrate the very good performance of the method. Our technique has a general flavour, and we expect that similar tuning parameter selection algorithms will work well for other M-estimators, or any robust procedure that depends on the choice of a tuning parameter.