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U-statistic
About: U-statistic is a research topic. Over the lifetime, 1209 publications have been published within this topic receiving 32898 citations.
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TL;DR: In this article, the problem of unbiased estimation of the distribution function of a two-parameter exponential population using order statistics based on a random sample from the population was considered and necessary and sufficient conditions for the existence of an unbiased estimator based on an arbitrary set of order statistics were given.
Abstract: In this article, we consider the problem of unbiased estimation of the distribution function of a two-parameter exponential population using order statistics based on a random sample from the population. We give necessary and sufficient conditions for the existence of an unbiased estimator based on an arbitrary set of order statistics and suggest unbiased estimators in some situations where unbiased estimators exist. A few properties of the suggested estimators for some special cases have also been discussed.
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TL;DR: In this paper, the authors present new estimators under different sampling plans that are either unbiased or that have reduced bias relative to those already in use as well as generally improve on the mean square error.
Abstract: Estimation using pooled sampling has long been an area of interest in the group testing literature. Such research has focused primarily on the assumed use of fixed sampling plans (i), although some recent papers have suggested alternative sequential designs that sample until a predetermined number of positive tests (ii). One major consideration, including in the new work on sequential plans, is the construction of debiased estimators which either reduce or keep the mean square error from inflating. Whether, however, under the above or other sampling designs unbiased estimation is in fact possible has yet to be established in the literature. In this paper, we introduce a design which samples until a fixed number of negatives (iii), and show that an unbiased estimator exists under this model, while unbiased estimation is not possible for either of the preceding designs (i) and (ii). We present new estimators under the different sampling plans that are either unbiased or that have reduced bias relative to those already in use as well as generally improve on the mean square error. Numerical studies are done in order to compare designs in terms of bias and mean square error under practical situations with small and medium sample sizes.
TL;DR: In this article, Rang et al. proposed a method to preserve unbiased estimators in the poisson case, which they called Rang-preserving unbiased estimator in Partial Differential Equations.
Abstract: (1989). Rang—preserving unbiased estimators in the poisson case. Communications in Partial Differential Equations: Vol. 14, No. 4, pp. 1029-1030.
03 Oct 2005
TL;DR: This paper considers latent variable models and introduces a new $\mathcal{U}$-likelihood concept for estimating the distribution over hidden variables, which gives an alternative to Bayesian inference when the authors don't want to define a prior over parameters and gives a alternative to the ML method when they want a better estimate of the distributionover hidden variables.
Abstract: In this paper we consider latent variable models and introduce a new $\mathcal{U}$-likelihood concept for estimating the distribution over hidden variables. One can derive an estimate of parameters from this distribution. Our approach differs from the Bayesian and Maximum Likelihood (ML) approaches. It gives an alternative to Bayesian inference when we don't want to define a prior over parameters and gives an alternative to the ML method when we want a better estimate of the distribution over hidden variables. As a practical implementation, we present a $\mathcal{U}$-updating algorithm based on the mean field theory to approximate the distribution over hidden variables from the $\mathcal{U}$-likelihood. This algorithm captures some of the correlations among hidden variables by estimating reaction terms. Those reaction terms are found to penalize the likelihood. We show that the $\mathcal{U}$-updating algorithm becomes the EM algorithm as a special case in the large sample limit. The useful behavior of our method is confirmed for the case of mixture of Gaussians by comparing to the EM algorithm.
TL;DR: In this article, the scale and location parameter is considered in terms of a Lehmann-unbiased estimator, which depends strongly on the form of the loss function, and quadratic and other loss functions are discussed.
Abstract: In this paper Lehmann-unbiased estimation of the scale and location parameter is considered. Lehmann-unbiased estimators depend strongly on the form of the loss function. Therefore quadratic and the other loss functions are discussed. Results of this paper, obtained in the class of linear statistics, can be specified to these obtained byGoodman andKicinska-Slaby [1982a, 1982b].