Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C _pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.     

Confidence Intervals for the Youden Index and Corresponding Optimal Cut-Point

A global measure of biomarker effectiveness is the Youden index, the maximum difference between sensitivity, the probability of correctly classifying diseased individuals, and 1-specificity, the probability of incorrectly classifying healthy individuals. The cut-point leading to the index is the optimal cut-point when equal weight is given to sensitivity and specificity. Using the delta method, we present approaches for estimating confidence intervals for the Youden index and corresponding optimal cut-point for normally distributed biomarkers and also those following gamma distributions. We also provide confidence intervals using various bootstrapping methods. A comparison of interval width and coverage probability is conducted through simulation over a variety of parametric situations. Confidence intervals via delta method are shown to have both closer to nominal coverage and shorter interval widths than confidence intervals from the bootstrapping methods.     

A Copula‐Based Non‐parametric Measure of Regression Dependence

Abstract. This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non‐parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non‐parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study.     

Proposition of a General Formula for Price Indices

In this article, we propose a general formula for aggregative price indices that satisfies most postulates coming from the axiomatic price index theory. We show that the ideal Fisher index, Laspeyres and Paasche formulas, and a lot of other indices are particular cases of the proposed formula. Moreover, using the general formula we can easily define new indices, that would satisfy given postulates. We also present an interesting result for the proposed formula.     

Generalized Jackknife-Based Estimators for Univariate Extreme-Value Modeling

In this article, we revisit the importance of the generalized jackknife in the construction of reliable semi-parametric estimates of some parameters of extreme or even rare events. The generalized jackknife statistic is applied to a minimum-variance reduced-bias estimator of a positive extreme value index—a primary parameter in statistics of extremes. A couple of refinements are proposed and a simulation study shows that these are able to achieve a lower mean square error. A real data illustration is also provided.     

First- and Second-order Asymptotics for the Tail Distortion Risk Measure of Extreme Risks

The tail distortion risk measure at level p was first introduced in Zhu and Li (2012 Zhu, L., Li, H. (2012). Tail distortion risk and its asymptotic analysis. Insur. Math. Econ. 51(1):115–121.[Crossref], [Web of Science ®] , [Google Scholar]), where the parameter p ∈ (0, 1) indicates the confidence level. They established first-order asymptotics for this risk measure, as p↑1, for the Fréchet case. In this article, we extend their work by establishing both first-order and second-order asymptotics for the Fréchet, Weibull, and Gumbel cases. Numerical studies are also carried out to examine the accuracy of both asymptotics.     

Zenga Distribution and Inequality Ordering

The aim of this article is to establish an ordering related to the inequality for the recently introduced Zenga distribution. In addition to the well-known order based on the Lorenz curve, the order based on I(p) curve is considered. Since the Zenga distribution seems to be suitable to model wealth, financial, actuarial, and, especially, income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. This investigation shows that for the Zenga distribution, two of the three parameters are inequality indicators.     

Time-varying clustering of multivariate longitudinal observations

Abstract

We propose a statistical method for clustering multivariate longitudinal data into homogeneous groups. This method relies on a time-varying extension of the classical K-means algorithm, where a multivariate vector autoregressive model is additionally assumed for modeling the evolution of clusters' centroids over time. Model inference is based on a least-squares method and on a coordinate descent algorithm. To illustrate our work, we consider a longitudinal dataset on human development. Three variables are modeled, namely life expectancy, education and gross domestic product.     

Exponential Inequalities in Stochastic Inverse Problems Using an Iterative Method

We consider an iterative method in order to solve linear inverse problems. We establish exponential inequalities for the probability of the distance between the approximated solution and the exact one for a calibration problem. The approximate is given by an iterative method with Gaussian errors. We treat an operator equation of the form Ax = u, where A is a compact operator.     

A unified approach to multilevel sample selection models

Abstract

We propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman’s two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation.