Showing papers on "U-statistic published in 2014"

A U-statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens–Fisher setting

Abstract: A two-sample test statistic is presented for testing the equality of mean vectors when the dimension, , exceeds the sample sizes, , and the distributions are not necessarily normal. Under mild assu ...

Evaluation and comparison of estimations in the generalized exponential-Poisson distribution

Abstract: The uniformly minimum variance unbiased, maximum-likelihood, percentile and least-squares estimators of the probability density function and the cumulative distribution function are derived for the generalized exponential-Poisson distribution. This model has shown to be useful in reliability and lifetime data modelling, especially when the hazard rate function has a bathtub shape. Simulation studies are also carried out to show that the maximum-likelihood estimator is better than the uniformly minimum variance unbiased estimator (UMVUE) and that the UMVUE is better than others.

On the Stochastic Restricted Almost Unbiased Estimators in Linear Regression Model

Abstract: In this article, the stochastic restricted almost unbiased ridge regression estimator and stochastic restricted almost unbiased Liu estimator are proposed to overcome the well-known multicollinearity problem in linear regression model. The quadratic bias and mean square error matrix of the proposed estimators are derived and compared. Furthermore, a numerical example and a Monte Carlo simulation are given to illustrate some of the theoretical results.

On the weighted least-squares, the ordinary least-squares and the best linear unbiased estimators under a restricted growth curve model

Abstract: Necessary and sufficient conditions are given for a restricted growth curve model to be consistent. The general expressions of the weighted least-squares estimators (WLSEs), the ordinary least-squares estimators (OLSEs) and the best linear unbiased estimator (BLUE) under this model are also derived. Moreover, some algebraic and statistical properties of these estimators are presented by rank method.

Unbiased Estimators for Entropy and Class Number

Abstract: We introduce unbiased estimators for the Shannon entropy and the class number, in the situation that we are able to take sequences of independent samples of arbitrary length.

Qualitative robustness of von Mises statistics based on strongly mixing data

Abstract: In this article, the property of qualitative robustness is studied for von Mises statistics in the situation where the observations are not necessarily independent but are drawn from a strongly mixing sequence of identically distributed random variables. The notion of qualitative robustness is taken from “Zahle (2012, submitted)” where Huber’s version of Hampel’s original definition was adapted to the case of dependent observations. The main result is illustrated by means of several examples including the sample variance, the sample Gini’s mean difference and the Cramer–von Mises statistic.

Separate Ratio Estimators for the Population Variance in Stratified Random Sampling

Abstract: We propose separate ratio estimators for population variance in stratified random sampling. We obtain mean square error equations and compare proposed estimators about efficiency with each other. By these comparisons, we find the conditions which make proposed estimators more efficient than others. It has been shown that proposed classes of estimators are more efficient than usual unbiased estimator. We find that separate ratio estimators are more efficient than combined ratio estimators for population variance. The theoretical results are supported by a numerical illustration with original data. A simulation study is also carried out to investigate empirical performance of estimators.

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information in Stratified Random Sampling

Abstract: This article addresses the problem of estimating the population mean in stratified random sampling using the information of an auxiliary variable. A class of estimators for population mean is defined with its properties under large sample approximation. In particular, various classes of estimators are identified as particular member of the suggested class. It has been shown that the proposed class of estimators is better than usual unbiased estimator, usual combined ratio estimator, usual product estimator, usual regression estimator and Koyuncu and Kadilar (2009) class of estimators. The results have been illustrated through an empirical study.

Estimation and Prediction Based on K-Record Values from Logistic Distribution

Abstract: In this paper, we introduce the k-record values arising from normal distribution. After computing the means, variances and covariances of the k-record values, we determine the best linear unbiased estimators for the location and scale parameters of normal distribution based on k-record values. The best linear unbiased predictor of future k-record values is also determined. Finally, a real data is given to illustrate the inference procedures developed in this paper.

A Note on the Hartley-Ross Unbiased Ratio Estimator

Abstract: In this article, we will construct an alternative Hartley-Ross unbiased ratio estimator for the population mean of a study variable when related auxiliary information is available. We will also present some efficiency comparisons and related results and give a numerical illustration.

Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation

Abstract: This paper introduces ratio estimators of the population mean using the coefficient of variation of study variable and auxiliary variables together with the coefficient of correlation between the study and auxiliary variables under simple random sampling and stratified random sampling. These ratio estimators are almost unbiased. The mean square errors of the estimators and their estimators are given. Sample size estimation in both sampling designs are presented. An optimal sample size allocation in stratified random sampling is also suggested. Based on theoretical study, it can be shown that these ratio estimators have smaller MSE than the unbiased estimators. Moreover, the empirical study indicates that these ratio estimators have smallest MSE compared to the existing ones.

Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model

Abstract: This paper is concerned with the parameter estimator in linear regression model. To overcome the multicollinearity problem, two new classes of estimators called the almost unbiased ridge-type principal component estimator (AURPCE) and the almost unbiased Liu-type principal component estimator (AULPCE) are proposed, respectively. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a Monte Carlo simulation study is given to illustrate the performance of the proposed estimators.

Unbiased random sequences from measurements of Poisson processes

Abstract: We consider the problem of true random bit generation from source vectors of independent geometric random variables, reduced modulo M for practical implementation. Independent geometric random variables result from measurements of discretized Poisson processes, which are good models for a number of physical sources. We propose a generalization of the classical approach by Elias, compute theoretical bounds, and evaluate the efficiency of the scheme by means of experiments. The proposed technique shows a significant advantage with respect to the classical approach.

Two-Term Edgeworth Expansions for the Classes of U- and V-statistics

Abstract: Much effort has been devoted to deriving Edgeworth expansions for various classes of statistics that are asymptotically normally distributed, with derivations tailored to the individual structure of each class. Expansions with smaller error rates are needed for more accurate statistical inference. Two such Edgeworth expansions are derived analytically in this paper. One is a two-term expansion for the standardized U-statistic of order m, m ⩾ 3, with an error rate o(n− 1). The other is an expansion with the same error rate for the distribution of the standardized V-statistic of the same order. In deriving the Edgeworth expansion, we made use of the close connection between the V- and U-statistics, which permits to first derive the needed expansion for the related U-statistic, then extend it to the V-statistic, taking into consideration the estimation of all difference terms between the two statistics.

Majorized Algorithm and Best Efficiency Unbiased Estimation of Life Functions Parameter in Reliable Analysis of Existence and Life

Abstract: This article, on the basis of several kinds of essential random truncated distribution functions in reliable analysis of existence and life, discusses the best efficiency unbiased estimation of the life distribution function parameter. It suppliijes reliable basis and efficient algorithm for solving the relative problem on reliable analysis of existence and on the best unbiased estimation in prediction of communication engineering and electrical load. The article is of extensive value in theory and in practice.

Piecewise cause-specific association analyses of multivariate untied or tied competing risks data.

Abstract: In this paper we extend the bivariate hazard ratio to multivariate competing risks data and show that it is equivalent to the cause-specific cross hazard ratio. Two approaches are proposed to estimate these two equivalent association measures. One extends the plug-in estimator, and the other adapts the pseudo-likelihood estimator for bivariate survival data to multivariate competing risks data. The asymptotic properties of the extended estimators are established by using empirical processes techniques. The extended plug-in and pseudo-likelihood estimators have comparable performance with the existing U-statistic when the data have no tied events. However, in many applications, there are tied events in which all the three estimators are found to produce biased results. To our best knowledge, we are not aware of any association analysis for multivariate competing risks data that has considered tied events. Hence we propose a modified U-statistic to specifically handle tied observations. The modified U-statistic clearly outperforms the other estimators when there are rounding errors. All methods are applied to the Cache County Study to examine mother-child and sibship associations in dementia among this aging population, where the event times are rounded to the nearest integers. The modified U performs consistently with our simulation results and provides more reliable results in the presence of tied events.

Tests for Two-Sample Location Problem Based on Subsample Quantiles

Abstract: This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.

Some modified exponential type unbiased estimators in simple random sampling

Abstract: The main concentration of this paper is to suggest product efficiency numerically. ABSTRACT The main concentration of this paper is to suggest modified exponential type product estimator s using auxiliary attribute in simple random sampling efficiency is carried out between suggested and existing estimators theoretically as well as numerically.

An almost unbiased estimator for population mean using known value of population parameter(s)

Abstract: In this paper we have proposed an almost unbiased estimator using known value of some population parameter(s) with known population proportion of an auxiliary variable. A class of estimators is defined which includes [1], [2] and [3] estimators. Under simple random sampling without replacement (SRSWOR) scheme the expressions for bias and mean square error (MSE) are derived. Numerical illustrations are given in support of the present study. Key words: Auxiliary information, proportion, bias, mean square error, unbiased estimator.

Almost unbiased estimator using Known Value of Population Parameter (s) in Sample Surveys

Abstract: In this paper we have proposed an almost unbiased estimator using known value of some population parameter(s). A class of estimators is defined which includes Singh and Solanki [1] and Sahai and Ray [2], Sisodia and Dwivedi [3], Singh et. al. [4], Upadhyaya and Singh [5], Singh and Tailor [6] estimators. Under simple random sampling without replacement (SRSWOR) scheme the expressions for bias and mean square error (MSE) are derived. Numerical illustrations are given in support of the present study. Key words: Auxiliary information, bias, mean square error, unbiased estimator.