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151.
In this paper, the beta-binomial model is introduced as a Markov chain. It is shown that the correlated binomial model of Kupper and Haseman (1978) is identical to the additive binomial model of AItham(1978) and both are a first order approximation of the beta-binomial model. For small γ, the local efficiency of the moment estimators for the mean ρ and the extra-binomial variation γ is examined analytically. It is shown that, locally, the moment estimator for p is efficient up to the second order of y. Exact formulae for the relative efficiency are obtained for both the cases with γ known and unknown. Generalization to the unequal sample size case is also carried out. In particular, the gain in efficiency by using the quasi-likelihood estimator instead of the ratio estimator for p is studied when γ is known. These results are in agreement with the Monte Carlo results of Kleinman(1973) and Crowder(1985). 相似文献
152.
A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished. 相似文献
153.
《统计学通讯:理论与方法》2013,42(5):997-1008
Abstract In this article, we consider the problem of estimating regression coefficients for a linear model with censored and truncated data based on regression depth. Any line can be given a rank using regression depth and the deepest regression line is the line with the maximum regression depth. We propose a method to define the regression depth of a line in the presence of censoring and truncation. We show how the proposed regression performs through analyzing Stanford heart transplant data and AIDS incubation data. 相似文献
154.
The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income
level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators
are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function.
This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population
are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized
for the doubly truncated gamma prior distribution.
Now deceased. 相似文献
155.
Assume independent random samples are drawn from two populations which are exponentially distributed with unknown location parameters and a common known scale parameter. We want to estimate the maximum and the minimum of the unknowo location paremeters. In this paper several estimators are proposed which are better than the natural estimations in terms of absolute bias and /or meaqn squared error. 相似文献
156.
Hidekazu Takeuchi 《统计学通讯:理论与方法》2013,42(11):2645-2669
A multivariate linear calibration problem, in which response variable is multivariate and explanatory variable is univariate, is considered. In this paper a class of generalized inverse regression estimators is proposed in multi-univariate linear calibration. It includes the classical estimator and the inverse regression one (or Krutchkoff estimator). For the proposed estimator we derive the expressions of bias and mean square error (MSE). Furthermore the behavior of these characteristics is investigated through an analytical method. In addition through a numerical study we confirm the existence of a generalized inverse regression estimator to improve both the classical and the inverse regression estimators on the MSE criterion. 相似文献
157.
M.S. Ahmed 《Australian & New Zealand Journal of Statistics》1998,40(3):373-376
Kiregyera (1984), Mukerjee, Rao & Vijayan (1987), and Tripathi & Ahmed (1995) considered a number of regression-type estimators where information on two auxiliary variables related to study variable is available at different levels. Mukerjee et al . (1987) suggested three estimators and computed their mean square errors, but the computations seem to be incorrect. This note corrects them, and finds their estimators are no better than that of Kiregyera (1984). The estimator suggested by Tripathi & Ahmed (1995) is the best in the sense of having the smallest mean square error. 相似文献
158.
We derive an identity for nonparametric maximum likelihood estimators (NPMLE) and regularized MLEs in censored data models
which expresses the standardized maximum likelihood estimator in terms of the standardized empirical process. This identity
provides an effective starting point in proving both consistency and efficiency of NPMLE and regularized MLE. The identity
and corresponding method for proving efficiency is illustrated for the NPMLE in the univariate right-censored data model,
the regularized MLE in the current status data model and for an implicit NPMLE based on a mixture of right-censored and current
status data. Furthermore, a general algorithm for estimation of the limiting variance of the NPMLE is provided.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
159.
MONTSERRAT GUILLEN JENS P. NIELSEN ANA M. PEREZ-MARIN 《Scandinavian Journal of Statistics》2007,34(2):419-431
Abstract. The Nelson–Aalen estimator is well known to be an asymptotically efficient estimator of the cumulative hazard function, see Andersen et al. ( Statistical models based on counting processes , Springer-Verlag, New York, 1993) among many others. In this paper, we show that the efficiency of the Nelson–Aalen estimator can be considerably improved by using more information in the estimation process than the traditional Nelson–Aalen estimator uses. While our approach results in a biased estimator, the variance improvement is substantial. By optimizing the balance between the bias loss and the variance improvement, we obtain results on the efficiency gain. Several examples for known failure time distributions are used to illustrate these ideas. 相似文献
160.
The differential geometric framework of Amari (1982a, 1985) is applied to the study of some second order asymptotics related to the curvatures for exponential family nonlinear regression models, in which the observations are independent but not necessarily identically distributed. This paper presents a set of reasonable regularity conditions which are needed to study asymptotics from a geometric point of view in regression models. A new stochastic expansion of a first order efficient estimator is derived and used to study several asymptotic problems related to Fisher information in terms of curvatures. The bias and the covariance of the first order efficient estimator are also calculated according to the expansion. 相似文献