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1.
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1996,48(2):365-380
Under suitable regularity conditions, it is shown that a third order asymptotically efficient estimator is fourth order asymptotically efficient in some class of estimators in the sense that the estimator has the most concentration probability in any symmetric interval around the true parameter up to the fourth order in the class. This is a resolution of the conjecture by Ghosh (1994, Higher Order Asymptotics, Institute of Mathematical Statistics, Hayward, California). It is also shown that the bias-adjusted maximum likelihood estimator is fourth order asymptotically efficient in the class. 相似文献
2.
Masafumi Akahira Hyo Gyeong Kim Nao Ohyauchi 《Annals of the Institute of Statistical Mathematics》2012,64(6):1121-1138
In the paper of Akahira (Ann Inst Statist Math 48:349–364, 1996), it was shown that the second order asymptotic loss of information in reducing to a statistic consisting of extreme values and an asymptotically ancillary statistic vanished for a family of non-regular distributions whose densities have the same values and the sum of differential coefficients at the endpoints of the bounded support is equal to zero. In this paper, the result can be shown to be extended to the case of a family of non-regular distributions without the above restriction. 相似文献
3.
Masaflimi Akahira 《Annals of the Institute of Statistical Mathematics》1988,40(2):311-328
We consider i.i.d. samples from a continuous density with finite cusps. Then we obtain the bound for the second order asymptotic distribution of all asymptotically median unbiased estimators. Further we get the second order asymptotic distribution of a bias-adjusted maximum likelihood estimator, and we see that it is not generally second order asymptotically efficient. 相似文献
4.
Suppose thatX 1,X 2, ...,X n , ... is a sequence of i.i.d. random variables with a densityf(x, θ). Letc n be a maximum order of consistency. We consider a solution \(\hat \theta _n \) of the discretized likelihood equation $$\sum\limits_{i = 1}^n {\log f(X_i ,\hat \theta _n + rc_n^{ - 1} ) - } \sum\limits_{i = 1}^n {\log f(X_i ,\hat \theta _n ) = a_n (\hat \theta _n ,r)} $$ wherea n (θ,r) is chosen so that \(\hat \theta _n \) is asymptotically median unbiased (AMU). Then the solution \(\hat \theta _n \) is called a discretized likelihood estimator (DLE). In this paper it is shown in comparison with DLE that a maximum likelihood estimator (MLE) is second order asymptotically efficient but not third order asymptotically efficient in the regular case. Further it is seen that the asymptotic efficiency (including higher order cases) may be systematically discussed by the discretized likelihood methods. 相似文献
5.
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1982,34(1):69-82
Summary The bound of the asymptotic distributions of
for all asymptotically median unbiased (AMU) estimators
is given in non-regular cases. It provides us with a powerful criterion for an AMU estimator to be two-sided asymptotically
efficient and also useful in the cases when there may not exist a two-sided asymptotically efficient estimator since we may
find an AMU estimator whose asymptotic distribution attains at least at a point, or an AMU estimator whose asymptotic distribution
is uniformly “close” to it. Some examples are given.
The results of this paper have been presented at the Meeting on Statistical Theory of Model Analysis at Tsukuba University
in Japan, October 1979. 相似文献
6.
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1987,39(1):25-36
Summary The problem to estimate a common parameter for the pooled sample from the double exponential distributions is discussed in
the presence of nuisance parameters. The maximum likelihood estimator, a weighted median, a weighted mean and others are asymptotically
compared up to the second order, i.e. the ordern
−1/2 with the asymptotic expansions of their distributions.
University of Electro-communications 相似文献
7.
Masafumi Akahira Nao Ohyauchi 《Annals of the Institute of Statistical Mathematics》2002,54(4):806-815
For a family of non-regular distributions with a location parameter including the uniform and truncated distributions, the stochastic expansion of the Bayes estimator is given and the asymptotic lower bound for the Bayes risk is obtained and shown to be sharp. Some examples are also given. 相似文献
8.
9.
Summary The problem to estimate a common parameter for the pooled sample from the uniform distributions is discussed in the presence
of nuisance parameters. The maximum likelihood estimator (MLE) and others are compared and it is shown that the MLE based
on the pooled sample is not (asymptotically) efficient. 相似文献
10.
Hidekazu Tanaka Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》2003,55(2):309-317
A family of distributions for which an unbiased estimator of a functiong(θ) of a real parameter θ can attain the second order Bhattacharyya lower bound is derived. Indeed, we obtain a necessary
and sufficient condition for the attainment of the second order Bhattacharyya bound for a family of mixtures of distributions
which belong to the exponential family. Furthermore, we give an example which does not satisfy this condition, but where the
Bhattacharyya bound is attainable for a non-exponential family of distributions. 相似文献