On Asymptotic Deficiency of Estimators

The notion of deficiency was introduced by Hodges and Lehmann. It is known that best asymptotically normal (BAN) estimators are second order asymptotically efficient in the class A₂ of all second order asymptotically median unbiased estimators. In this paper it is shown that the asymptotic deficiency of any two estimators in the restricted class D of the third order asymptotically median unbiased BAN estimators is given by the difference between the coefficients of order n^-1 of the variances of the estimators.     

A NOTE ON PREDICTION SUFFICIENCY (ADEQUACY) AND SUFFICIENCY

Let(X, A) be a measurable space and P a family of probability measures on A. Let B and C be sub -algebras of A and B₀ a sub -algebra of B. It is shown that if B₀ is prediction sufficient (adequate) for B with respect to C and P, and Y is sufficient for B₀^vC with respect to P then Y is sufficient for B^vC with respect to P; that if P is homogeneous and (B₀; B, C) is Markov for P, and B₀^vC is sufficient for B^vc with respect to P, then B₀ is sufficient for B with respect to P; and by example that the Markov property is necessary for the latter proposition to hold.     

Randomized confidence intervals of a parameter for a family of discrete exponential type distributions

For a family of one-parameter discrete exponential type distributions, the higher order approximation of randomized confidence intervals derived from the optimum test is discussed. Indeed, it is shown that they can be asymptotically constructed by means of the Edgeworth expansion. The usefulness is seen from the numerical results in the case of Poisson and binomial distributions.     

ASYMPTOTIC DEFICIENCY OF THE JACKKNIFE ESTIMATOR

In this paper it is shown that the bias-adjusted maximum likelihood estimator (MLE) is asymptotically equivalent to the jackknife estimator in the variance up to the order n^-1 and the asymptotic deficiency of the jackknife estimator relative to the bias-adjusted MLE is equal to zero.     

父亲参与和母亲幸福感关系的中日比较研究

以中日抚养学龄前儿童双收入家庭父母为对象,探讨父亲参与育儿对母亲心理幸福感的影响,结果发现中日父亲参与育儿的影响模式一致,即父亲参与育儿通过母亲对父亲育儿支持的认知,间接影响夫妻关系满意度。但在中日之间在母亲对父亲育儿支持的认知影响健康关联QOL的途径存在差异。中国母亲对父亲育儿支持的认知直接或通过心理健康影响健康关联的QOL。日本母亲对父亲育儿支持的认知通过夫妻关系满意度间接影响健康关联QOL。     

An approximation to the generalized hypergeometric distribution

A generalized hypergeometric (GHG) distribution was defined, and its higher order approximations were given by Takeuchi (1984). In this paper, an improvement on the approximation is considered and examined by the numerical calculation. Several examples including the Poisson, binomial, negative-binomial, hypergeometric and negative-hypergeometric distributions are also given.     

Recurrence relations of coefficients of the generalized hypergeometric function in multivariate analysis

James(1960) defined the zonal polynomials and used it to represent the joint distributions of latent roots of VVisfiart matrix. The zonal polviionnals played an important role to define the generalized hypergeometric function of symmetric matrix argument Since then, many density functions and moments based on Wishart matrix have been expressed in terms of the generalized hy¬pergeometric Function. The purpose of this paper is to get the recurrence relations for the coefficients of it. In Section 1 we derive a partial differen¬tial equations having the generalized hypergeometric function as the unique solution. Then we ubtain the recurrence relations until order 7 in Section 2.     

Confidence intervals for the difference of means: application to the Behrens-Fisher type problem

A systematic method of the construction of a confidence interval for the difference between two means is given in the exponential and gamma cases. The application of a similar method to the Behrens-Fisher type problem is also given. Further, the numerical calculation of coverage probabilities is done and a comparison of the confidence interval proposed in this paper with that based on the Fisher-Welch-Wald similar test is given. As a result, the method is seen to be reasonable. Received: April 23, 1999; revised version: February 22, 2000     

A higher order approximation to a percentage point of the non–central t-distribution

A higher order approximation formula for a percentage point of the noncentral t–distribution with v degrees of freedom is given up to the order o(v^-3), using the Cornish-Fisher expansion for the statistic based on a lin-ear combination of a normal random variable and a chi-random variable. The upper confidence limit and the confidence interval for the non–centrality parameter are given. Numerical results are also obtained.     

LOSS OF INFORMATION ASSOCIATED WITH THE ORDER STATISTICS AND RELATED ESTIMATORS IN THE DOUBLE EXPONENTIAL DISTRIBUTION CASE

Fisher (1934) derived the loss of information of the maximum likelihood estimator (MLE) of the location parameter in the case of the double exponential distribution. Takeuchi & Akahira (1976) showed that the MLE is not second order asymptotically efficient. This paper extends these results by obtaining the (asymptotic) losses of information of order statistics and related estimators, and by comparing them via their asymptotic distributions up to the second order.