摘要:

Suppose that a sample of size n from a continuous and symmetric population with an unknown parameter is given. We consider a fictitious random subsample of sizekdrawn from the original sample and construct the best linear estimator based on the subsample. Applying the Rao-Blackwell type argument, we get an estimator which uses the information contained in the whole sample and is supposed to be uniformly efficient for a wide class of distributions. Monte Carlo experiments established that this estimator is highly efficient for small samples of size 10 to 20.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482258

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Efficiency-robust linear estimation as outlined in Birnbaum and Laska (JASA, 62 (1967) pp. 1230–1240) is applied, determining maximin-efficient linear unbiased estimators (MLUEs), and their efficiencies, for ordered samples of sizes 5 (5) 20 from a family of nine distributions. The results are compactly summarized because of the tendency of these distributions to admit simple orderings such that the MLUE over any subset of the distributions is just the MLUE over the extreme pair in the ordered subset. Relations to other methods are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482259

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The problem of choosing the optimal design to estimate a regression function which can be well-approximated by a polynomial is considered, and two new optimality criteria are presented and discussed. Use of these criteria is illustrated by a detailed discussion of the case that the regression function can be assumed approximately linear. These criteria, which can be considered as compromises between the incompatible goals of inference about the regression function under an assumed model and of checking the model's adequacy, are found to yield designs superior in certain respects to others which have been proposed to deal with this problem, including minimum bias designs.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482260

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

When an experimenter is interested in more than one parameter in the regression model and tries to obtain a design that minimizes the maximum variance of the individual regression coefficients, he is looking for a minimax design with respect to the single parameter. In this article we explicitly present the minimax s.p. designs for the ordinary polynomial regression, when the degree is ≤4. For 5≤n ≤12 we present the minimax s.p. designs obtained through a computer. These are very good approximations to the actual designs. Finally based on these results, a conjecture for constructing a minimax s.p. design for any degree is advanced.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482261

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Independent groups, each of N independent observations on a random variable Z, are taken sequentially with signed ranks obtained within groups. Two tests of symmetry of the parent cdf F about the origin are developed, one based on the within-group configurations of signed ranks and the other based on the within-group sums of positive signed ranks. Some properties of F are F+(z) = 1 - [1-F-(z)]k, x≥0, k>0, and F(0) = k/(k+1) where F+and F-are respectively the conditional cdf's of non-negative and absolute negative values of Z. Properties and examples of the two procedures are given.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482262

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In this article, Bayesian and non-Bayesian methods for estimating parameters of the log-normal distribution and of log-normal regression processes are considered. Posterior distributions for parameters of interest are derived and their properties are described. With respect to point estimation, a rather broad class of estimators is defined and, relative to this class, new minimal mean square error (MSE) estimators for the median and mean of the log-normal distribution and for the median and mean of the dependent variable in log-normal regressions are derived.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482263

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Building on results of an earlier article [6], estimators are suggested for the scale parameter and characteristic exponent of symmetric stable distributions, and Monte Carlo studies of these estimators are reported. The powers of various goodness-of-fit tests of a Gaussian null hypothesis against non-Gaussian stable alternatives are also investigated. Finally, a test of the stability property of symmetric stable variables is suggested and demonstrated.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482264

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482265

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Most results on the asymptotic properties of maximum likelihood estimators are for the standard cases where we observe independent and identically distributed random variables, whose distribution satisfies certain regularity conditions. In this article, similar properties are shown to hold for a class of cases where the observed random variables are not necessarily independent and identically distributed.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482266

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the unique solution of the resulting likelihood equation regardless of the starting value chosen provided that the sample is not concentrated entirely in either or both the first and last groups.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482267

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor