A ranked set sample consists entirely of independently distributed order statistics and can occur naturally in many experimental settings, including problems in reliability. The modifications needed to obtain similar results in unbalanced cases are also discussed. In structural reliability, new and useful properties of system signatures are developed. The selection of topics is specifically designed to provide students with a substantial conceptual foundation, from which to achieve a thorough and mature understanding of statistical applications within the fields. Mathematics chair DeWitt Sumners, Dean Donald Foss and Myles Hollander on the occasion of Myles' Robert O. Annals of the Institute of Statistical Mathematics 27:45-55. Topics of special interest include nonparametric inference, nonparametric curve fitting, linear model theory, Bayesian nonparametrics, change point problems, time series analysis and asymptotic theory.
The competition between a Bayesian and a frequentist is viewed as a contest with the following components: a random observable, a true prior distribution unknown to both statisticians, an operational prior used by the Bayesian, a fixed frequentist rule used by the frequentist, and a fixed loss criterion. Further examples of contexts requiring the asymmetric treatment of estimation errors are given in papers by Shao and Chow 1991 , who treat estimation problems regarding release dates of certain pharmaceutical products, by Thompson and Basu 1996 , who treat asymmetric problems arising in reliability and by Zellner and Palm 1974 , who considers a variety of problems in the area of econometrics. Some of the literature on system signatures, defined in the context in which a system's components have independent and identically distributed i. Related estimators of the lifetime density and failure rate functions are also obtained, and their theoretical and numerical properties are described. This paper establishes the foundations for studying the efficacy of Bayesian updating in estimating nonidentifiable parameters in the competing risks framework.
The result is a product estimator that is consistent and compares favorably with the nonparametric maximum likelihood estimator proposed by Boyles and Samaniego, as indicated by graphs of mean squared error and Kolmogorov-Smirnov distance. Related estimators of the lifetime density and failure rate functions are also obtained, and their theoretical and numerical properties are described. We will explore the situation in which inference concerning the strength distribution G is of interest, but the random variable Y cannot be observed directly. Includes an extensive, up-to-date bibliograpy. The computational advantages of the former, and the interpretive richness of the latter, beg the question: how are the two related? The aim of this article is to provide an overview of some of the recent developments relating to the theory of signatures and their role in the study of dynamic reliability, systems with shared components and nonparametric inference for a component lifetime distribution. Its existence and uniqueness is demonstrated, and a general numerical procedure is presented and is shown to converge to F.
Consistent regression estimation with fixed design points under dependence conditions. Possible extensions beyond the i. A remark on quadratic mean differentiability. Asymptotic distribution of the likelihood function in the independent not identically distributed case. Myles Hollander, with his parents Ruth and Joseph Hollander, Catskill Mountains, New York, 1954.
In this paper, we assume that auxiliary data in the form of a variable K, the number of failed components at the time of system failure, is available along with the system's lifetime. Twenty-five research papers related to this period are specifically listed in the report. Many of the papers are focused on themes that Professor Bhattacharya has published on research. While the endeavor has been dead, or at least dormant, for some 20 years, the findings in the present article suggest that the question above is by no means settled. Statistics and Its Interface, 3 2 , 159-168. In the present paper, we consider the situation when a system failure is observed, and we assume that the only information available is the time of failure, t, and the number of failed components, k, at failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature.
This volume is dedicated to the memory of Professor Wassily Hoeffding, a pioneer in the field of nonparametric statistics. Petersburg, Russia in 1994, 1996, 1998, 2001, 2005, and 2009. System signatures have been found to be quite useful tools in the study and comparison of engineered systems. The applicability of the notion of uniform stochastic ordering in reliability and life testing is discussed. The first is conventional, and is based on treating each of the estimation problems separately; it is shown that these mixture estimators are consistent, and their asymptotic behaviours are characterized. Dean, School of Physical and Mathematical Sciences, 1978-1979. However, there is very little literature on this problem that treats such inferences from a nonparametric perspective, and less literature still that allows the systems of interest to be of arbitrary design.
Nonparametric estimation in mixing sequences of random variables. In the final section, we give some guidance for deciding, in advance, which type of shrinkage one might wish to employ in a particular application. Statistics and Probability Letters, Special Silver Volume, July 2007. This book is developed from the International Conference on Robust Rank-Based and Nonparametric Methods, held at Western Michigan University in April 2015. Optimal allocation of components in parallel-series and series-parallel systems. Not everyone knew, at that time, that we were getting much more! In contrast to the preposterior analysis of this question offered by Kadane, we examine the question conditionally, given the information provided by the experiment. In the general nonparametric estimation problem, F̂rss is shown to be inadmissible relative to integrated squared error loss.
Frequentist Shrinkage in Multivariate Normal Problems. He maintained a special interest, throughout his career, in topics such as regression analysis, both parametric and nonparametric, change point problems, asymptotic theory, stochastic processes and sequential analysis. The question of whether, and when, the Bayesian approach produces worthwhile answers is investigated. Proceedings, International Congress of Applied Mathematics pp. As a consequence, if 1n represents the empirical survival function, or the Kaplan-Meier estimator, the estimator 1n inherits the strong and uniform convergence properties, as well as the optimal rates of convergence of the empirical survival function and Kaplan-Meier estimator respectively. By means of a Skorokhod-type embedding of these cumulative sums on Brownian Motion paths, it is shown that under certain conditions the sample paths of these normalized sums converge in a certain sense to a process obtained from the Brownian Motion by a transformation of the time-axis. It is obtained by solving multiple point-wise maximum likelihood estimation problems simultaneously, and combining the separate estimators, each at fixed time points, to obtain an overall estimator of the reliability function.