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801.
The standard error of the maximum-likelihood estimator for 1/μ based on a random sample of size N from the normal distribution N(μ,σ2) is infinite. This could be considered to be a disadvantage.Another disadvantage is that the bias of the estimator is undefined if the integral is interpreted in the usual sense as a Lebesgue integral. It is shown here that the integral expression for the bias can be interpreted in the sense given by the Schwartz theory of generalized functions. Furthermore, an explicit closed form expression in terms of the complex error function is derived. It is also proven that unbiased estimation of 1/μ is impossible.Further results on the maximum-likelihood estimator are investigated, including closed form expressions for the generalized moments and corresponding complete asymptotic expansions. It is observed that the problem can be reduced to a one-parameter problem depending only on , and this holds also for more general location-scale problems. The parameter can be interpreted as a shape parameter for the distribution of the maximum-likelihood estimator.An alternative estimator is suggested motivated by the asymptotic expansion for the bias, and it is argued that the suggested estimator is an improvement. The method used for the construction of the estimator is simple and generalizes to other parametric families.The problem leads to a rediscovery of a generalized mathematical expectation introduced originally by Kolmogorov [1933. Foundations of the Theory of Probability, second ed. Chelsea Publishing Company (1956)]. A brief discussion of this, and some related integrals, is provided. It is in particular argued that the principal value expectation provides a reasonable location parameter in cases where it exists. This does not hold generally for expectations interpreted in the sense given by the Schwartz theory of generalized functions. 相似文献
802.
小域估计(Small Area Estimation)是抽样调查领域里一个重要的研究方向,国计民生中的许多重要问题如失业率、传染病的发病率和民意测验等抽样调查都需要采用不同的小域估计方法。本文针对小域估计问题,以估计方法发展脉络为主线,以分层贝叶斯分析的小域估计为重点,对小域估计问题的理论、方法和最新进展进行简述,并利用澳大利亚残疾、老龄化和护理者(SDAC 2003)抽样调查实际数据,从分层贝叶斯分析角度对澳大利亚残疾率进行估计,最后对估计结果进行比较和讨论。 相似文献
803.
Ludovico Piccinato 《Statistical Methods and Applications》1992,1(2):251-274
Summary The main issues which characterize the current inferential paradigms are discussed. Emphasis is given to the kind of probability
that can be used and to the problem of total or partial conditioning. Through classical examples, the major role of conditioning
is stressed. Some trends of the main approaches (frequentist and Bayesian) are illustrated and some comments on the completely
predictive approach are also provided.
Revised version of an invited paper presented at the Meeting of the Italian Statistical Society onMethodological Developments in the Different Approaches to Statistical Inferences, Cagliari, April 3–5, 1991. 相似文献
804.
Qi Li 《Econometric Reviews》1996,15(3):261-274
Based on the kernel integrated square difference and applying a central limit theorem for degenerate V-statistic proposed by Hall (1984), this paper proposes a consistent nonparametric test of closeness between two unknown density functions under quite mild conditions. We only require the unknown density functions to be bounded and continuous. Monte Carlo simulations show that the proposed tests perform well for moderate sample sizes. 相似文献
805.
Partha Deb 《Econometric Reviews》1996,15(1):51-68
In this paper I examine finite sample properties of the maximum likelihood and quasi-maximum likelihood estimators of EGARCH(1,1) processes using Monte Carlo methods. I use response surface methodology to summarize the results of a wide array of experiments which suggest that the maximum likelihood estimator has reasonable finite sample properties. The Gaussian quasi-maximum likelihood estimator has poor finite sample properties when the data generating process has conditional excess kurtosis. Some of these poor properties appear to be asymptotic in nature. 相似文献
806.
Aridaman K. Jain 《Journal of statistical planning and inference》1981,5(1):57-69
A rotation scheme for a stratified multi-stage sample, discussed in this paper, was designed to statisfy the following conditions: (i) there is a constraint on the number of units that can be replaced in each round, and (ii) it is relatively inexpensive to increase the sample size gradually. An example of these conditions was observed in the development of a plan for measuring the accuracy of the billing process of a telephone company. Estimators of the population proportion of elements that possess a specified characteristic are also derived. Each estimator is a weighted average of the corresponding estimates based on the retained units from the original sample and on the new units, where the weight of the estimate based on the new units increases over time. While this rotation scheme is discussed in connection with the billing accuracy of a telephone company, the methodology can be applied to other similar problems. 相似文献
807.
Bent Jørgensen 《Statistical Methods and Applications》1994,3(3):355-384
Summary We consider the ideas of sufficiency and ancillarity for parametric models with nuisance parameters, and more generally Barndorff-Nielsen's
notion of nonformation. The original four definitions of non-formation, namelyB-,S-,G- andM-nonformation, each cover different types of models. We stress the interpretation of nonformation in terms of the idea of
perfect fit. This leads to a new definition of nonformation, calledI-nonformation, which is well suited for inference in exponential families. We also consider Rémon's concept ofL-sufficiency, and a recent extension toL-nonformation, due to Barndorff-Nielsen, which unifies and extendsB-,S- andG- nonformation. We study the relations between these six definitions, and show that they are all special cases ofM-nonformation.
All animals are equal, but some animals are more equal than others. From ‘Animal Farm’, by G. Orwell (1945). 相似文献
808.
In this paper the work of Weier & Basu (1980) is extended to a special case of the trivariate exponential distributions and to the general k-variate case. In the trivariate case several statistics are derived including one based on the likelihood ratio approach and the locally most powerful rank statistic, and power studies are carried out. The general k-variate model is derived, and testing for independence is shown to reduce to a solved problem. 相似文献
809.
Sorana Froda 《Revue canadienne de statistique》1986,14(1):75-79
Scholz (1974) proved that the asymptotic variance of an R-estimator of location is no larger than that of an L-estimator when the observations come from a distribution G different from the distribution F for which the two estimators are efficient. This note extends this result to distributions F whose density has a first but no second derivative. 相似文献
810.
Geoffrey S. Watson 《Journal of statistical planning and inference》1983,8(3):245-256
The Langevin (or von Mises-Fisher) distribution of random vector x on the unit sphere ωq in q has a density proportional to exp κμ'x where μ'x is the scalar product of x with the unit modal vector μ and κ?0 is a concentration parameter. This paper studies estimation and tests for a wide variety of situations when the sample sizes are large. Geometrically simple test statistics are given for many sample problems even when the populations may have unequal concentration parameters. 相似文献