scispace - formally typeset
Search or ask a question
Author

Hammou El Barmi

Bio: Hammou El Barmi is an academic researcher from City University of New York. The author has contributed to research in topics: Estimator & Stochastic ordering. The author has an hindex of 12, co-authored 53 publications receiving 448 citations. Previous affiliations of Hammou El Barmi include Baruch College & Kansas State University.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, a peakedness ordering restriction is considered as a one-sided alternative to equality, and the asymptotic distributions of the likelihood ratio test statistics are obtained and are shown to be of the chi-bar squared type.
Abstract: Likelihood ratio tests concerning the parameters of two multinomial populations are discussed. A peakedness ordering restriction is considered as a one sided alternative to equality. The asymptotic distributions of the likelihood ratio test statistics are obtained and are shown to be of the chi-bar squared type. Exact expressions for the weights in the mixture of chi-squared distributions are also provided. The procedures are illustrated by applying them to a data set on lung cancer mortality in South Australia.

7 citations

Journal ArticleDOI
TL;DR: This paper provides consistent estimators in the k -sample case, with and without censoring, and develops a new algorithm for isotonic regression that may be of independent interest.

7 citations

Journal ArticleDOI
TL;DR: Simulation results show the EL testing procedure performs well in a variety of scenarios when X and Y are strictly PQD, and a distribution-free test statistic is created that integrates a localized EL ratio test statistic with respect to the empirical joint distribution ofX and Y.
Abstract: We develop an empirical likelihood (EL) approach to test independence of two univariate random variables X and Y versus the alternative that X and Y are strictly positive quadrant dependent (PQD). ...

7 citations

Journal ArticleDOI
TL;DR: In this article, the authors derived the likelihood ratio test and its asymptotic distribution for testing for or against an order restriction placed upon the odds ratios, and showed that the limiting distributions are of chi-bar square type and gave the expression of the weighting values.
Abstract: Consider data arranged into k × 2 × 2 contingency tables. The principal result of this paper is the derivation of the likelihood ratio test and its asymptotic distribution for testing for or against an order restriction placed upon the odds ratios. We will show that the limiting distributions are of chi-bar square type and give the expression of the weighting values.

6 citations

Journal ArticleDOI
TL;DR: In this article, a projection-type estimator was proposed for the nonparametric maximum likelihood estimator of a distribution function under uniform stochastic ordering, where the NPMLE also fails to be consistent.
Abstract: A random variable X is symmetric about 0 if X and -X have the same distribution. There is a large literature on the estimation of a distribution function (DF) under the symmetry restriction and tests for checking this symmetry assumption. Often the alternative describes some notion of skewness or one-sided bias. Various notions can be described by an ordering of the distributions of X and -X. One such important ordering is that $P(0

6 citations


Cited by
More filters
Journal ArticleDOI

6,278 citations

Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

Book ChapterDOI
01 Jan 2011
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

3,554 citations

Journal ArticleDOI
TL;DR: This tutorial paper collects together in one place the basic background material needed to do GP modeling, and shows how to recognize functions and problems compatible with GP, and how to approximate functions or data in a formcompatible with GP.
Abstract: A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.

1,215 citations

01 Jan 1997

892 citations