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41.
T. A. Ramasubban 《Revue canadienne de statistique》1979,7(2):185-192
This paper deals with the linear, exponential and Gompertz models and compares the bias and variance of a number of estimators of the growth-rate parameters of these models. Some of these estimators have been commonly recommended in the literature and others are most frequently used in empirical practice. The present analysis points to the strengths and weaknesses of the estimators in their usage. 相似文献
42.
Michael G. Akritas Indrani Basak Myung Hwi Lee 《Australian & New Zealand Journal of Statistics》1993,35(3):303-318
The properties of robust M-estimators with type II censored failure time data are considered. The optimal members within two classes of ψ-functions are characterized. The first optimality result is the censored data analogue of the optimality result described in Hampel et al. (1986); the estimators corresponding to the optimal members within this class are referred to as the optimal robust estimators. The second result pertains to a restricted class of ψ-functions which is the analogue of the class of ψ-functions considered in James (1986) for randomly censored data; the estimators corresponding to the optimal members within this restricted class are referred to as the optimal James-type estimators. We examine the usefulness of the two classes of ψ-functions and find that the breakdown point and efficiency of the optimal James-type estimators compare favourably with those of the corresponding optimal robust estimators. From the computational point of view, the optimal James-type ψ-functions are readily obtainable from the optimal ψ-functions in the uncensored case. The ψ-functions for the optimal robust estimators require a separate algorithm which is provided. A data set illustrates the optimal robust estimators for the parameters of the extreme value distribution. 相似文献
43.
In this article, small sample properties of the maximum-likelihood estimator (m.l.e.) for the offspring distribution (pk) and its mean m are considered in the context of the simple branching process. A representation theorem is given for the m.l.e. of (Pk) from which the m.l.e. of m is obtained. The case where p0 + p1 + p2 = 1 is studied in detail: numerical results are given for the exact bias of these estimators as a function of the age of the process; a curve fitting analysis expresses the bias of m? as a function of the mean and the variance of the offspring distribution and finally an “approximate m.l.e.” for (pk) is given. 相似文献
44.
T.F. Móri 《Journal of statistical planning and inference》1983,7(4):353-358
We consider the family of uniform distributions with range of unit length. The main result of this note asserts that the average variance of any unbiased estimator of the midpoint of the range is not less than (2(n+1))(n+2))-1 and this lower bound is sharp. The proof is based upon a nonregular version of the Cramér-Rao inequality. 相似文献
45.
Andrew L. Rukhin 《Journal of statistical planning and inference》1983,8(1):59-74
The estimation problem of a permutation parameter on the basis of a random sample of increasing size is considered. A necessary and sufficient condition for the existence of an estimator, asymptotically fully efficient for two different distributions families, is derived. We also study the application of this result to cyclic groups of order two and three. 相似文献
46.
Theo Stijnen 《Journal of statistical planning and inference》1982,6(4):363-372
In this paper we study empirical Bayes (e.B.) rules from a viewpoint which has not yet got any attention in the literature. Since an e.B. estimator can be seen as an estimate of an unknown function, namely the true Bayes estimator, it is natural to consider e.B. estimators as stochastic processes. In this paper we make a first attempt in the direction of this approach. For a certain class of e.B. estimators for the continuous one-parameter exponential family, we investigate the global behaviour on finite intervals. It is shown that the difference between the e.B. and the true Bayes estimator can be represented as a certain type of Gaussian process plus a remainder which is uniformly of smaller order. Several applications of this result are given. 相似文献
47.
This paper summarizes the literature on estimation and testing of present value relations. Twenty-four test statistics are illustrated and compared in a simulation experiment utilizing six different data generation models. The test statistics are calculated for actual Standard and Poor's 500 annual stock price and dividend data, and the results are interpreted in light of the Monte Carlo experiments. 相似文献
48.
D. Szatmari-Voicu 《统计学通讯:理论与方法》2013,42(11):2037-2048
The median absolute deviation (MAD) is known to be the M-estimator of scale with minimum gross errors sensitivity (GES) when the error distribution is known to be symmetric and strongly unimodal. The problem considered here is to find the Fisher consistent M-estimator with minimum GES when the error distribution is symmetric but not necessarily unimodal. Under some general conditions, the score function χ corresponding to the minimizing M-estimator has the form χ(x) = ?1 when |x| < a; χ(x) = c when a < |x| < b; χ(x) = 1 when |x| > b. An example is given in which the M-estimator with minimum GES does not correspond to the MAD. 相似文献
49.
Marvin H. J. Gruber 《统计学通讯:理论与方法》2013,42(2):180-193
Bayesian statistics is concerned with how prior information influence inferences. This article studies this problem by comparing the value of the Rao distance between prior and posterior normal distributions. Particular cases include the linear Bayes estimator, the mixed estimator, and ridge-type estimators. 相似文献
50.
In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the common scale parameter of several distributions using spacing of the pooled sample of all observations of individual samples. We derived conditions for the non negativity of the scale estimator obtained by the above methods. Further, we obtained necessary and sufficient conditions for the derived estimators to be constant multiples of the pooled sample range. 相似文献