Showing papers on "U-statistic published in 1982"
893 citations
TL;DR: In this article, the problem of estimating the percentage impact of a dummy variable regressor on the level of the dependent variable in a semilogarithmic regression equation is considered and the minimum variance unbiased estimator is introduced and compared with two previously proposed estimators.
135 citations
25 citations
TL;DR: In this paper, the minimum variance unbiased estimators for the functions of scale and truncation parameters as well as the reliability function of the truncated exponential family distribution were derived, and uniformly most powerful unbiased tests of hypotheses were formulated.
Abstract: Blackwell-Rao-Lehmann-Scheffe' theory is used to derive the minimum variance unbiased estimators for the functions of scale and truncation parameters as well as the reliability function of the truncated exponential family distribution. Uniformly most powerful unbiased tests of hypotheses are formulated. Finally, a particular model of this family, viz., the truncated exponential model is discussed.
11 citations
TL;DR: In this paper, the problem of obtaining best linear unbiased estimators of individual response coefficients in a Random Coefficient Linear Regression (RCR) model is considered, comparing alternative estimators for these response vectors through a simulation study.
Abstract: In this paper we consider the problem of obtaining best linear unbiased estimators of individual response coefficients in a Random Coefficient Linear Regression (RCR} Model, comparing alternative estimators for these response vectors through a simulation study We also provide an empirical example that illustrates the estimation procedure proposed here
7 citations
TL;DR: Approximations for the rms error of the maximum likelihood estimator of the direction of a plane wave incident on a random array of independent, identically distributed random vectors are presented.
Abstract: This paper presents approximations for the rms error of the maximum likelihood estimator of the direction of a plane wave incident on a random array. The sensor locations are assumed to be realizations of independent, identically distributed random vectors. The second part of the paper presents an asymptotically unbiased estimator of the noise wavenumber spectrum from random array data.
5 citations
TL;DR: In this article, the authors considered the problem of unbiased estimation for nonparametric families of distributions subject to generalised moment restrictions, and provided necessary and sufficient conditions under which symmetric statistics are unique minimum variance unbiased estimators of their expectations.
Abstract: This paper is concerned with the theory of unbiased estimation for nonparametric families of distributions subject to "generalised moment" restrictions. Necessary and sufficient conditions under which symmetric statistics are unique minimum variance unbiased estimators of their expectations are obtained, and some new boundedly complete families of distributions are exhibited. 1. Introduction. In 1946, Halmos published the first paper which gave formal justification of the heuristic principle that statistics which are symmetric functions of a random sample are to be preferred (in terms of minimum variance and unbiasedness) when estimating parameters of some general families of probability distributions. This was accomplished by showing that if a given parameter 9 admits an unbiased estimator of finite variance, then there exists a unique symmetric unbiased estimator of 9 with smaller variance than all other (asymmetric) unbiased estimators based on the same sample. In essence, Halmos' paper introduced the concept of "completeness" as it pertains to estimators (or more formally, to families of distributions), as it is shown that any symmetric unbiased estimator of zero must be identically zero. Halmos' results were confined to families of discrete distributions comprising all distributions concentrated on finite subsets of a given set X. Subsequently, Fraser (1954, 1957) showed that similar results were true for some general families of continuous distributions (e.g. all distributions on the real line which have probability density functions). Fraser's discussion was in terms of the order statistic of a random sample, since a function which is symmetric in its arguments is a function of the order statistic, and conversely. Thus, for the nonparametric families considered by Halmos and Fraser, the order statistic is a complete sufficient statistic. The uniqueness of symmetric statistics of finite variance as uniform minimum variance unbiased estimators (UMVUE's) is then a consequence of the Rao-Blackwell theorem, and the class of all parameters 9 admitting UMVUE's is obtained by computing the expectations of all the symmetric statistics of finite variance. Fraser's results were extended to general probability measure spaces by Bell, Blackwell and Breiman (1960). Hoeffding (1977a, b) considered situations similar to those studied by Halmos and Fraser, but in which a certain amount of information is (assumed) known about the distributions: each distribution P in the family of interest satisfies the k "generalised moment" conditions
5 citations
4 citations
TL;DR: In this paper, a thorough theoretical analysis of the methods available for estimation from a reverse Fourier neutron time-of-flight experiment is carried out, where independent variables of the correlated observations are found from the frequency domain by means of the discrete Fourier cosine and sine transforms.
4 citations
TL;DR: In this article, a nonparametric test of independence for two quadrantly dependent random variables is suggested, based on the hypothesis of independence, and the distribution of an estimator of monotonic dependence function is derived under the assumption of independence.
Abstract: Asymptotic distribution of an estimator of monotonic dependence function is derived under the hypothesis of independence. Also a nonparametric test of independence for two quadrantly dependent random variables is suggested.
3 citations
TL;DR: In this article, the variance of unknown variate values in a finite population is investigated and the usual unbiased estimator for the variance which is an element of the class considered turns out to be inadmissible.
Abstract: With each unti of a finite population is associated an unknown variate value. We are interested in the variance of these values and consider (1) simple random sampling without replacement. (2) quadratic loss and (3) a one parameter class of estimators. We determine all admissible elements of the class. The usual unbiased estimator for the variance which is an element of the class considered turns out to be inadmissible.
TL;DR: In this article, the authors define the index of performance of unbiased estimators in the sense of Lehmann (L-unbiased), which evaluates the power for the estimators to discriminate any wrong values of a parametric function from a correct one.
Abstract: In this paper, we define the index of performance of unbiased estimators in the sense of Lehmann (L-unbiased), which evaluates the power for the estimators to discriminate any wrong values of a parametric function from a correct one. We shall call the indexdiscrimination rate of the estimator. The larger discrimination rate the estimator has, the more desirable it is. An upper bound of discrimination rates is obtained, which is given by thesensitivity of the probability family under consideration. The discrimination rates of several L-unbiased estimators are investigated. Moreover we discuss the conditions under which the L-unbiased estimator is improved in the sense of discrimination rate by the L-unbiased estimator depending only on a sufficient statistic.
TL;DR: In this paper, the authors introduced a new definition of efficiency in the multiparameter case (θ 1,..., θk) when the variance-covariance matrix of the vector estimator (t 1,...t k) exists.
Abstract: The paper introduces a new definition of efficiency in the multiparameter case (θ1,...,θk) when the variance-covariance matrix of the vector estimator (t 1, ...t k) exists. The definition is also applicable to the asymptotically unbiased estimators.
TL;DR: In this paper, a sequential unbiased estimator for the cell probabilities subject to log linear constraints is proposed. But the estimator is not consistent in the sense of Wolfowitz (Ann. Math. Statist. (1947) 18).
Abstract: Classical analysis of contingency tables employs (i) fixed sample sizes and (ii) the maximum likelihood and weighted least squares approach to parameter estimation. It is well-known, however, that certain important parameters, such as the main effect and interaction parameters, can neverbe estimated unbiasedly when the sample size is fixed a priori We introduce a sequential unbiased estimator for the cell probabilities subject to log linear constraints. As a simple consequence, we show how parameters such as those mentioned above may. be estimated unbiasedly. Our unbiased estimator for the vector of cell probabilities is shown to be consistent in the sense of Wolfowitz (Ann. Math. Statist. (1947) 18). We give a sufficient condition on a multinomial stopping rule for the corresponding sufficient statistic to be complete. When this condition holds, we have a unique minimum variance unbiased estimator for the cell probabilities.
TL;DR: In this article, a modification of the Greenwood variance estimator is defined and shown to be free of bias whenever its constituent interval estimators are conditionally unbiased, given the sample size at the start of the interval.
Abstract: A modification of the Greenwood variance estimator is defined and shown to be free of bias whenever its constituent interval estimators are conditionally unbiased, given the sample size at the start of the interval. Using the modified estimator as a standard of comparison, the original Greenwood estimator is seen to have an intrinsic positive bias.Underestimation of variances through the use of Greenwood's formula must be due to bias in the constituent interval estimators and/or, with fixed interval bounds, due to disregarding the random character of the total number of life table intervals to exhaustion of ttje sample. Some easy to prove properties of the modified and the original Greenwood estimators are stated that apply in the absence of censoring. A suggestion is made for reducing the bias of the interval variance estimators.
TL;DR: In this article, the necessary and sufficient conditions for the existence of a minimum variance unbiased estimator for a parametric function of ϑ1 and ϑ2 are given for the class of Bivariate Modified Power Series Distributions.
Abstract: The functional form of the class of Bivariate Modified Power Series Distributions is considered. The probabilities are functions of two unknown parameters ϑ1 and ϑ2. The necessary and sufficient conditions for the existence of a minimum variance unbiased estimator for a parametric function of ϑ1 and ϑ2 are given.
TL;DR: The Cramer-Rao theorem as discussed by the authors states that under regularity conditions on f of standard type, the inverse of the Fisher information matrix I is a lower bound for the covariance matrix V of unbiased estimators μ* and σ* of μ and ε of σ.
Abstract: Let x 1, ..., x n be a random sample from a density σ -1 f((x-μ)/gs, where f is known but μ ∈ iR and σ>0 unknown. A familiar multiparameter version of the Cramer-Rao theorem asserts that under regularity conditions on f of standard type the inverse of the Fisher information matrix I is a lower bound for the covariance matrix V of unbiased estimators μ* and σ* of μ and σ (see Cramer, 1946 and Rao, 1973, pp. 326–328). If for particular unbiased estimators μ* and σ* we find that V is close to I -1, then we know that μ* and σ* are good unbiased estimators and the C-R inequality is very informative.
TL;DR: In this paper, the authors used a complete random sample from a gamma distribution with unknown shape and scale parameters, and obtained a median unbiased point estimator and optimum s-confidence bounds and intervals, for the shape parameter; the uniformly minimum variance unbiased estimator, and a conservative lower s -confidence bound, for reliability.
Abstract: The following inferences are obtained, based on a complete random sample from a gamma distribution with unknown shape and scale parameters: a median unbiased point estimator, and optimum s-confidence bounds and intervals, for the shape parameter; the uniformly minimum variance unbiased estimator, and a conservative lower s-confidence bound, for reliability. Illustrative computations and comparisons with competing techniques are presented.
TL;DR: The notion of discrimination rate of any unbiased estimator in the sense of Lehmann is, as defined by the author (1982,Ann. Inst. Statist. Math.,34, A, 19,37), extended to multi-parameter cases.
Abstract: The notion ofdiscrimination rate of any unbiased estimator in the sense of Lehmann is, as defined by the author (1982,Ann. Inst. Statist. Math.,34, A, 19–37), extended to multi-parameter cases.