Showing papers in "Metrika in 1997"
Journal Article•
609 citations
Journal Article•
72 citations
TL;DR: In this paper, a Bernstein type estimate of the regression functionm(x)=E[Y|X=x] was proposed and various local and global asymptotic properties of this estimate were studied.
Abstract: In this paper we propose a Bernstein type estimate of the regression functionm(x)=E[Y|X=x]. Various local and global asymptotic properties of this estimate are studied.
58 citations
TL;DR: In this paper, an almost unbiased multivariate ratio estimator was proposed, which has a smaller mean squared error than the conventional biased multivariate regression estimator and with the same precision as the multivariate regressive estimator.
Abstract: The goal of this paper is to investigate the repeated substitution method (seeSrivastava, 1967) estimating population variance in finite population sample surveys. We propose an almost unbiased multivariate ratio estimator that has a smaller mean squared error than the conventional biased multivariate ratio estimator (established byIsaki (1983)) and with the same precision as the multivariate regression estimator. Furthermore, it is a computationally much more interesting estimator since to compute it we only need to have knowledge of correlation among available variables, which it is common to have in several practical situations. A comparison of the multivariate ratio estimator proposed and the multivariate regression estimator is given.
36 citations
TL;DR: In this article, a weighted simplex-centroid design for a class of mixture models is proposed. But it is restricted to homogeneous functions of degree one and cannot be applied to a general class of models, and it cannot be used to obtain A-, D- and I-optimal allocations for Becker's models.
Abstract: Extending Scheffe’s simplex-centroid design for experiments with mixtures, we introduce aweighted simplex-centroid design for a class of mixture models. Becker’s homogeneous functions of degree one belong to this class. By applying optimal design theory, we obtainA-, D- andI-optimal allocations of observations for Becker’s models.
34 citations
TL;DR: In this paper, the authors obtained some recurrence relationships for conditional expectations of nonadjacent order statistics and record values when the distribution function is continuous and proved that the distribution is uniquely determined by the distribution of conditioned record values and by the expected values of these records.
Abstract: In this paper, we obtain some recurrence relationships for conditional expectations of nonadjacent order statistics and record values when the distribution function is absolutely continuous, and we prove that the distribution function is uniquely determined by the distribution of conditioned record values and by the expected values of these records. Further, different distributions are characterized by these relationships.
25 citations
TL;DR: In this paper, the authors obtained uniformly minimum variance unbiased estimators of P(X < Y) for both, unknown and known common location parameters, using two independent samples from Weinman multivariate exponential distributions with unknown scale parameters.
Abstract: Based on two independent samples from Weinman multivariate exponential distributions with unknown scale parameters, uniformly minimum variance unbiased estimators ofP(X
24 citations
TL;DR: A new method for locally adaptive histogram construction that doesn’t resort to a standard distribution and is easy to implement: the multiresolution histogram, based on aL2 analysis of the mean integrated squared error with Haar wavelets.
Abstract: We introduce a new method for locally adaptive histogram construction that doesn’t resort to a standard distribution and is easy to implement: the multiresolution histogram. It is based on aL 2 analysis of the mean integrated squared error with Haar wavelets and hence can be associated with a multiresolution analysis of the sample space.
23 citations
TL;DR: In this article, a family of density functions is considered which contains several life-testing models as specific cases, and uniformly minimum variance unbiased estimators are obtained for the positive and negative powers of the parameter, moments and reliability function.
Abstract: A family of density functions is considered which contains several life-testing models as specific cases. Uniformly minimum variance unbiased estimators are obtained for the positive and negative powers of the parameter, moments and reliability function. These general results provide the estimators for the specific models.
22 citations
TL;DR: In this paper, the authors illustrate how certain design problems can be simplified by reparametrization of the response function, which provides further insights than the more traditional approaches, like minimax, Bayesian or sequential techniques.
Abstract: In this paper we illustrate how certain design problems can be simplified by reparametrization of the response function. This alternative viewpoint provides further insights than the more traditional approaches, like minimax, Bayesian or sequential techniques. It will also improve a practitioner’s understanding of more general situations and their “classical” treatment.
22 citations
TL;DR: In this paper, the authors argue that any component of any smooth test of fit is strictly non-diagnostic when used conventionally, and that a proper rescaling of components does indeed achieve the desired "directed diagnosis".
Abstract: Smooth goodness of fit tests were introduced by Neyman (1937). They can be regarded as a compromise between globally consistent (“omnibus”) tests of fit and procedures having high power in the direction of a specific alternative. It is commonly believed that components of smooth tests like, e.g., skewness and kurtosis measures in the context of testing for normality, have special diagnostic properties in case of rejection of a hypothesisH 0 in the sense that they constitute direct measures of the kind of departure fromH 0. Recent years, however, have witnessed a complete change of attitude towards the diagnostic capabilities of skewness and kurtosis measures in connection with normality testing. In this paper, we argue that any component of any smooth test of fit is strictly non-diagnostic when used conventionally. However, a proper rescaling of components does indeed achieve the desired “directed diagnosis”.
TL;DR: In this article, Qin and Lawless have proposed an alternative estimator for estimating the distribution function of a population in the presence of auxiliary information under a semiparametric model and established the weak convergence of this estimator to a Gaussian process and showed that the asymptotic variance function of the estimator is uniformly smaller than that of Fn.
Abstract: For estimating the distribution functionF of a population, the empirical or sample distribution functionFn has been studied extensively. Qin and Lawless (1994) have proposed an alternative estimator\(\hat F_n \) for estimatingF in the presence of auxiliary information under a semiparametric model. They have also proved the point-wise asymptotic normality of\(\hat F_n \). In this paper, we establish the weak convergence of\(\hat F_n \) to a Gaussian process and show that the asymptotic variance function of\(\hat F_n \) is uniformly smaller than that ofFn. As an application of\(\hat F_n \), we propose to employ the meanOpen image in new window and varianceŜn2 of\(\hat F_n \) to estimate the population mean and variance in the presence of auxiliary information. A simulation study is presented to assess the finite sample performance of the proposed estimators\(\hat F_n \), andŜn2.
TL;DR: A new process capability index (Cpq) has been introduced, which is easy to compute and performs well when compared with its natural competitor (Cpm).
Abstract: In this paper a new process capability index (C pq ) has been introduced, which is easy to compute and performs well when compared with its natural competitor (C pm ).
TL;DR: In this paper, the scale matrix of a multivariatet model with unknown location vector and scale matrix is estimated by using the sample sum of product matrix to improve upon the usual estimators.
Abstract: This paper deals with the estimation of the scale matrix of a multivariatet-model with unknown location vector and scale matrix to improve upon the usual estimators based on the sample sum of product matrix. The well-known results of the estimation of the scale matrix of the multivariate normal model under the assumption of entropy loss function have been generalized to that of a multivariatet-model.
TL;DR: In this paper, it was shown that the natural selection rule is minimax under a monotone permutation-invariant loss function with respect to a permutation invariant prior for every variance balanced design.
Abstract: We consider a problem of selecting the best treatment in a general linear model. We look at the properties of the natural selection rule. It is shown that the natural selection rule is minimax under to “0–1” loss function and it is a Bayes rule under a monotone permutation invariant loss function with respect to a permutation invariant prior for every variance balanced design. Some other condition on the design matrix is given so that a Bayes rule with respect to a normal prior will be of simple structure.
Journal Article•
TL;DR: In this article, it was shown that for general linear models, all admissible linear estimators are limits of the linear estimator that is uniquely best at some point in an extended parameter set.
Abstract: In a general linear model, it is shown that all admissible linear estimators are limits of linear estimators that are uniquely best at some point in an extended parameter set. The principal result shows that a linear estimator that is uniquely best at a pointW
2 among multiple linear estimators that are best at a pointW
1 is the limit of uniquely best estimators at points approachingW
1 along the line joiningW
1 andW
2.
TL;DR: In this paper, the authors present several stochastic analogs of classical formulas for the gamma function, which provide representation of some random variables as finite or infinite products of independent random variables.
Abstract: The aim of this paper is to present several stochastic analogs of classical formulas for the gamma function. The obtained results provide representation of some random variables as finite or infinite products of independent random variables. Examples include generalized gamma, normal, beta and other distributions.
TL;DR: In this article, the problem of testing the null hypothesis of no change against the alternative of exactly one change point is considered, and the proposed tests are based on generalized two-sample U-statistic processes.
Abstract: We consider the problem of testing the null hypothesis of no change against the alternative of exactly one change point. The proposed tests are based on generalized two-sample U-statistic processes. We drive the limiting null distributions of the proposed tests. Some applications in Statistical Reliability are given.
TL;DR: In this article, it was shown that if the nth k-record value of an infinite sequence of independent, identically distributed random variables with common continuous distribution function F has an increasing failure rate (IFR), then Yk,n(l k) has also a DFR distribution.
Abstract: LetYk,n denote the nth (upper) k-record value of an infinite sequence of independent, identically distributed random variables with common continuous distribution function F. We show that if the nth k-record valueYk,n has an increasing failure rate (IFR), thenYl,n(l k) has also a DFR distribution. We also present some results concerning log convexity and log concavity ofYk,n.
TL;DR: In this paper, the second-order approximations for the bias and mean squared error of the proposed estimator of the reliability function, first under a general setup, and then under some specific sequential sampling strategies, already available in the literature.
Abstract: Sequential estimation problems for the mean parameter of an exponential distribution has received much attention over the years. Purely sequential and accelerated sequential estimators and their asymptotic second-order characteristics have been laid out in the existing literature, both for minimum risk point as well as bounded length confidence interval estimation of the mean parameter. Having obtained a data set from such sequentially designed experiments, the paper investigates estimation problems for the associatedreliability function. Second-order approximations are provided for the bias and mean squared error of the proposed estimator of the reliability function, first under a general setup. An ad hoc bias-corrected version is also introduced. Then, the proposed estimator is investigated further under some specific sequential sampling strategies, already available in the literature. In the end, simulation results are presented for comparing the proposed estimators of the reliability function for moderate sample sizes and various sequential sampling strategies.
TL;DR: In this paper, both absolutely continuous random variables and discrete random variables are considered and the results lead to the characterization of a family of distributions, which is almost uniquely determined under the stated conditions.
Abstract: Using conditional expectations, we present results that lead to the characterization of several distributions. Both absolutely continuous random variables and discrete random variables are considered. In the case of absolutely continuous random variables, the results lead to the characterization of a family of distributions while in the case of discrete random variables, the distribution is almost uniquely determined under the stated conditions.
Journal Article•
TL;DR: In this article, a strong law of large numbers for a triangular array of strictly stationary associated random variables is proved, which is used to derive the pointwise strong consistency of kernel type density estimator of the one-dimensional marginal density function of a strictly stationary sequence of associated variables.
Abstract: A strong law of large numbers for a triangular array of strictly stationary associated random variables is proved. It is used to derive the pointwise strong consistency of kernel type density estimator of the one-dimensional marginal density function of a strictly stationary sequence of associated random variables, and to obtain an improved version of a result by Van Ryzin (1969) on the strong consistency of density estimator for a sequence of independent and identically distributed random variables.
TL;DR: In this article, the authors derived the D-and G-efficiencies of product designs in a multifactor experiment in terms of the D and G-efficiency of the designs in the marginal models.
Abstract: We derive theD- andG-efficiencies of product designs in a multifactor experiment in terms of theD- andG-efficiencies of the designs in the marginal models.
Posted Content•
TL;DR: Optimal design for multiway cross classifications in which the blocking factors exhibit interaction and the incidence structure of the blocking factor describes an orthogonal array is studied in this article. But this work assumes that the orthogonality is of sufficient strength to allow the estimation of all of the interaction terms.
Abstract: Optimal design is studied for multiway cross classifications in which the blocking factors exhibit interaction and in which the incidence structure of the blocking factors describes an orthogonal array. Assuming the orthogonal array to be of sufficient strength (enough to allow orthogonal estimation of all of the interaction terms), easily used forms of the information matrix for treatment estimation are derived, and optimality conditions are stated. Some illustrative construction examples are given.
TL;DR: In this paper, the authors established a method of selecting the best regression equation on the basis of F-test, which was applied to the well-known data from Hald (1952) and Gorman & Toman (1966).
Abstract: In this article, we establish a method of selecting the best regression equation on the basis of F-test. The basic idea is to select the most significant regression equation, which corresponds to the minimum P-value of F-test. We also present upper and lower bounds for the P-value together with approximations for these bounds which are simple to compute. Using this method, not only can we find out the best regression equation, we also obtain its significance probability. When the method is applied to the well-known data from Hald (1952) and Gorman & Toman (1966), the results are satisfactory.
TL;DR: In this article, the canonical moments of a class of distributions with nearly equal weights at the arcsin points were determined for all polynomial models with a degree less than the number of support points of the design.
Abstract: In his book Pukelsheim [8] pointed out that designs supported at the arcsin points are very efficient for the statistical inference in a polynomial regression model. In this note we determine the canonical moments of a class of distributions which have nearly equal weights at the arcsin points. The class contains theD-optimal arcsin support design and theD1-optimal design for a polynomial regression. The results allow explicit representations ofD-, andD1-efficiencies of these designs in all polynomial models with a degree less than the number of support points of the design.