Proportional Sampling in Life Length Studies

In studying electron tube life, measuring the life of a tube in service in a system whose age is T amounts to lifelength proportional sampling. The problems of estimating mean life from such data are considered for finite T and for “equilibrium” (large T). Several variations on the straight-forward life-biased sampling plan which are avilable to the experimenter are mentioned and conditions are found under which these other sampling schemes would be better than the life-proportional scheme. Particular attention is paid to the gamma and Weibull families of distributions. Other applications of these results are discussed.     

Goodness-of-fit tests for logistic regression models when data are collected using a complex sampling design

Logistic regression models are frequently used in epidemiological studies for estimating associations that demographic, behavioral, and risk factor variables have on a dichotomous outcome, such as disease being present versus absent. After the coefficients in a logistic regression model have been estimated, goodness-of-fit of the resulting model should be examined, particularly if the purpose of the model is to estimate probabilities of event occurrences. While various goodness-of-fit tests have been proposed, the properties of these tests have been studied under the assumption that observations selected were independent and identically distributed. Increasingly, epidemiologists are using large-scale sample survey data when fitting logistic regression models, such as the National Health Interview Survey or the National Health and Nutrition Examination Survey. Unfortunately, for such situations no goodness-of-fit testing procedures have been developed or implemented in available software. To address this problem, goodness-of-fit tests for logistic regression models when data are collected using complex sampling designs are proposed. Properties of the proposed tests were examined using extensive simulation studies and results were compared to traditional goodness-of-fit tests. A Stata ado function svylogitgof for estimating the F-adjusted mean residual test after svylogit fit is available at the author's website http://www.people.vcu.edu/~kjarcher/Research/Data.htm.     

Goodness-of-fit testing in growth curve models: A general approach based on finite differences

Growth curve models are routinely used in various fields such as biology, ecology, demography, population dynamics, finance, econometrics, etc. to study the growth pattern of different populations and the variables linked with them. Many different kinds of growth patterns have been used in the literature to model the different types of realistic growth mechanisms. It is generally a matter of substantial benefit to the data analyst to have a reasonable idea of the nature of the growth pattern under study. As a result, goodness-of-fit tests for standard growth models are often of considerable practical value. In this paper we develop some natural goodness-of-fit tests based on finite differences of the size variables under consideration. The method is general in that it is not limited to specific parametric forms underlying the hypothesized model so long as an appropriate finite difference of some function of the size variables can be made to vanish. In addition it allows the testing process to be carried out under a set up which manages to relax most of the assumptions made by Bhattacharya et al. (2009); these assumptions are generally reasonable but not guaranteed to hold universally. Thus our proposed method has a very wide scope of application. The performance of the theory developed is illustrated numerically through several sets of real data and through simulations.     

An Empirical Evaluation of Probability Estimation with Neural Networks

Recent interest in neural networks by researchers across a wide spectrum of disciplines has provided convincing evidence of their ability to address classification problems. In this article, we consider the issue of evaluating the predictive capability of neural networks when the output values are to be treated as probabilities. We propose the use of a variant of a chi-square statistic, based on the Hosmer–Lemeshow statistic from logistic regression, to measure the goodness-of-fit of neural network models for two-group membership problems. Through experimentation with a large real-world database, we demonstrate the application of this statistic, and examine the effects of varying the number of nodes in the hidden layer on its value. Our empirical results suggest that this statistic can be very useful in identifying significant differences in the probability estimation accuracy of neural network models.       

Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests

This paper analyzes the evolution of the asymptotic theory of goodness-of-fit tests. We emphasize the parallel development of this theory and the theory of empirical and quantile processes. Our study includes the analysis of the main tests of fit based on the empirical distribution function, that is, tests of the Cramér-von Mises or Kolmogorov-Smirnov type. We pay special attention to the problem of testing fit to a location scale family. We provide a new approach, based on the Wasserstein distance, to correlation and regression tests, outlining some of their properties and explaining their limitations. Dedicated to Miguel Martín Díaz whose scientific criticism has greatly inspirated our research by years. Research partially supported by DGICYT, grants PB98-0369-C02-01 and 02. E. del barrio and C. Matrán have also been supproted by PAPIJCL grant VA08/97.     

Assessing device reliability based on scheduled discrete degradation measurements

Degradation measurements are increasingly important in reliability studies because few failures are observed during the short time of many experiments. In this article, we assess device reliability from discrete degradation processes under scheduled inspections. In some particular situations, since the degradation quantities of the device characteristic are only observed specifically at the scheduled time points, the exact occurrence time and the corresponding damage amount of each degradation event are not recorded. For this sort of situation, there are plenty of examples such as the amount of shock damages of the database in a computer system, the amount of fatigues of the shock absorber for a car, and the amount of growth of a metal crack on an aircraft.     

Progressive censoring methodology: an appraisal

Properties of progressively censored order statistics and inferential procedures based on progressively censored samples have recently attracted considerable attention in the literature. In this paper, I provide an overview of various developments that have taken place in this direction and also suggest some potential problems of interest for further research. This invited paper is discussed in the comments available at: , , , , , , , , , .     

Construction of a structural equation model to identify public acceptance factors for hydrogen refueling stations under the provision of risk and safety information

Hydrogen refueling stations (HRSs) are an inevitable infrastructure for the utility of fuel cell vehicles; however, they can raise public safety concerns. The aim of this study is to establish a framework for public acceptance of HRSs in Japan upon the provision of risk and/or safety measure information on HRSs. We executed an in-person interview survey asking the respondents about their acceptance of HRSs and then constructed a structural equation model on HRS acceptance with four endogenous factors. The common factors to determine acceptability were “Dread” and “Independent”. “Balance” was added to the factors for the risk-informed group. If risk information was provided, people tended to judge based on their inherent sense of “Balance”; however, if it was not provided, their judgment was based on their intuitive “Dread” of HRSs or hydrogen. This study reveals risk perception characteristics and attempts to promote improved risk communication prior to HRS installation.