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响应依赖的回顾性抽样中的最优估计AI 解读

In more conventional analytic surveys, we sample the response variates y through a sampling design that is dependent on the covariate x. The x values are assumed known for all the units in the population. However, contrary to these situations, there are areas of statistical application when the values of the response variable are known for all the individuals but not the values of covariate (for example, in epidemiology and reliability). Here we sample the x values the…

响应依赖回顾性抽样的最优估计AI 解读

In more conventional analytic surveys, we sample the response variates y through a sampling design that is dependent on the covariate x. The x values are assumed known for all the units in the population. However, contrary to these situations, there are areas of statistical application when the values of the response variable are known for all the individuals but not the values of covariate (for example, in epidemiology and reliability). Here we sample the x values the…

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有偏处理分配下的最优估计AI 解读

This paper provides a semi-parametric solution to a problem proposed by Robbins & Zhang (1991). The solution is obtained utilizing the theory of optimum estimating functions (Godambe & Thompson, 1989). Our solution coincides with maximum likelihood estimation for the parametric model suggested by Robbins & Zhang (1991). Even for alternative models investigated in this paper, the efficiency of our estimation appears very close to that of maximum likelihood estimation.

估计函数的正交性与干扰参数AI 解读

Cox & Reid (1987) proposed the technique of orthogonalizing parameters, to deal with the general problem of nuisance parameters, within fully parametric models. They obtained a large-sample approximation to the conditional likelihood. Along the same lines Davison (1988) studied generalized linear models. In the present paper we deal with the problem of nuisance parameters, within a semiparametric setup which includes the class of distributions associated with generalized…

估计函数的正交性与干扰参数AI 解读

Cox & Reid (1987) proposed the technique of orthogonalizing parameters, to deal with the general problem of nuisance parameters, within fully parametric models. They obtained a large-sample approximation to the conditional likelihood. Along the same lines Davison (1988) studied generalized linear models. In the present paper we deal with the problem of nuisance parameters, within a semiparametric setup which includes the class of distributions associated with generalized…

随机过程有限样本估计的基础AI 解读

The Gauss-Markov theorem on least squares for linear models derives its general applicability because it depends on the underlying distribution only through the first two moments. In this paper, a similar theorem is established within the context of stochastic processes. Various problems of finite sample estimation are solved by application of this theorem.

随机过程有限样本估计的基础AI 解读

The Gauss-Markov theorem on least squares for linear models derives its general applicability because it depends on the underlying distribution only through the first two moments. In this paper, a similar theorem is established within the context of stochastic processes. Various problems of finite sample estimation are solved by application of this theorem.

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通过估计方程实现稳健估计AI 解读

Utilizing the theory of estimating equations (Godambe, 1960; Godambe & Thompson, 1978), this paper develops concepts of parameter defining function and effective parameter. The paper provides theory and techniques for choosing from a given set of robust parameters one that is most effective, or one that can most efficiently be estimated.

通过估计方程实现稳健估计AI 解读

Utilizing the theory of estimating equations (Godambe, 1960; Godambe & Thompson, 1978), this paper develops concepts of parameter defining function and effective parameter. The paper provides theory and techniques for choosing from a given set of robust parameters one that is most effective, or one that can most efficiently be estimated.

调查抽样中的估计：稳健性与最优性AI 解读

It is shown how the criteria of efficiency and robustness can be integrated fruitfully in a single optimality criterion within the framework of the Unified Theory (Godambe 1955). This is achieved by extending the scope of the usual model-based estimation using appropriate sampling designs. Some situations of common occurrence in survey practice are discussed with a numerical study.

存在干扰参数时的充分性与辅助性AI 解读

This paper discusses the definitions of ancillarity and sufficiency in the presence of a nuisance parameter given by Godambe (1976a). Illustrative examples are given and the relation to Fisher information discussed.

存在滋扰参数时的充分性与辅助性AI 解读

This paper discusses the definitions of ancillarity and sufficiency in the presence of a nuisance parameter given by Godambe (1976a). Illustrative examples are given and the relation to Fisher information discussed.

条件似然与无条件最优估计方程AI 解读

Godambe & Thompson (1974) characterized optimum estimating equations for some situations when the underlying frequency function contained a nuisance parameter. In the present paper the nuisance parameter case is related to concepts of conditional likelihood and complete sufficiency. Under suitable conditions it is shown that the maximum conditional likelihood equation provides the optimum estimating equation, the criterion of optimality being independent of conditioning. In…

条件似然与无条件最优估计方程AI 解读

Godambe & Thompson (1974) characterized optimum estimating equations for some situations when the underlying frequency function contained a nuisance parameter. In the present paper the nuisance parameter case is related to concepts of conditional likelihood and complete sufficiency. Under suitable conditions it is shown that the maximum conditional likelihood equation provides the optimum estimating equation, the criterion of optimality being independent of conditioning. In…

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存在干扰参数时的估计方程AI 解读

Estimating equations for a real parameter $\theta$ which indexes a family of densities $p(x, \theta)$ were considered in the note by Godambe (Ann. Math. Statist. 31 (1960) 1208-1211). An optimality property of the equation $\partial \log p/\partial \theta = 0$ among unbiased estimating equations was established. In this paper an analogous result is proved for estimation of a real parameter $\theta_1$ in the presence of a nuisance parameter $\theta_2$.

可交换先验分布下的抽样理论估计AI 解读

Godambe (1955) and Godambe and Joshi (1965) established the joint optimality of the Horvitz-Thompson estimates and the corresponding sampling designs with respect to a class of prior distributions which were "product measures." In the present paper the optimality is established replacing the "product measures" by prior distributions which are exchangeable in appropriately transformed variates. Furthermore, the optimality criterion is justified in terms of Chebychev's…

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调查抽样回归推断的贝叶斯、信赖与频率学派视角AI 解读

Summary In this paper an attempt is made to show how the regression analysis generally used for hypothetical populations can also be validated for the actual populations commonly dealt with in statistical surveys. This validation is based on a frequency distribution generated by randomization. In this context some comments are made on the relationships between Bayes, fiducial and frequency theories of statistical inference.

信赖论证及其在调查抽样中的应用AI 解读

Summary Sprott (1960) proposed certain restrictions on distributions a posteriori in terms of the likelihood function. Hacking (1965) put forward a criterion for irrelevance restricting the choice of the pivots in terms of the likelihoods. This paper presents an extended application of Hacking's criterion to accommodate ancillary statistics. This extension is utilized to obtain the fiducial distribution of the mean of a survey (finite) population based on the given random…

有限总体抽样的新方法（二）：分布无关充分性AI 解读

Summary The idea that in some situations the prior knowledge about the unknown parameters could be formulated as a class of prior distributions, which could be used, not necessarily through Bayes posterior probability, for subsequent inference, is already present in Godambe (1955). In the present paper, the concept of distribution-free linear sufficiency or in short linear sufficiency, originally due to Barnard (1963b) but redefined by the present author (Part I), is…