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21.
Representation theorem and local asymptotic minimax theorem are derived for nonparametric estimators of the distribution function on the basis of randomly truncated data. The convolution-type representation theorem asserts that the limiting process of any regular estimator of the distribution function is at least as dispersed as the limiting process of the product-limit estimator. The theorems are similar to those results for the complete data case due to Beran (1977, Ann. Statist., 5, 400–404) and for the censored data case due to Wellner (1982, Ann. Statist., 10, 595–602). Both likelihood and functional approaches are considered and the proofs rely on the method of Begun et al. (1983, Ann. Statist., 11, 432–452) with slight modifications.Division of Biostatistics, School of Public Health, Columbia Univ. 相似文献
22.
刘金山 《纯粹数学与应用数学》1997,13(1):30-37
考虑相依回归方程系统yi=Xiβi+εi(i=1,2),E(εi)=0,Cov(εi,εj)=σijIn。记βi为βi的协方差改进估计^[1]。σij未知时,记βi为用非限定估计σij代替βi中的σij得到的两步估计,并记βi为用限定估计σij代替βi中的σij得到的两步估计,这两种两步估计的协方差中含有未知参数σij代替βi中的σij得到的两步估计,这两种两步估计的协方差中含有未知参数σij。本 相似文献
23.
Let {Xt} be a Gaussian ARMA process with spectral density fθ(λ), where θ is an unknown parameter. The problem considered is that of testing a simple hypothesis H:θ = θ0 against the alternative A:θ ≠ θ0. For this problem we propose a class of tests
, which contains the likelihood ratio (LR), Wald (W), modified Wald (MW) and Rao (R) tests as special cases. Then we derive the χ2 type asymptotic expansion of the distribution of T
up to order n−1, where n is the sample size. Also we derive the χ2 type asymptotic expansion of the distribution of T under the sequence of alternatives An: θ = θ0 + /√n, ε > 0. Then we compare the local powers of the LR, W, MW, and R tests on the basis of their asymptotic expansions. 相似文献
24.
Robert Hable 《International Journal of Approximate Reasoning》2010,51(9):1114-1128
The article considers estimating a parameter θ in an imprecise probability model which consists of coherent upper previsions . After the definition of a minimum distance estimator in this setup and a summarization of its main properties, the focus lies on applications. It is shown that approximate minimum distances on the discretized sample space can be calculated by linear programming. After a discussion of some computational aspects, the estimator is applied in a simulation study consisting of two different models. Finally, the estimator is applied on a real data set in a linear regression model. 相似文献
25.
Wulf Rehder 《Annals of the Institute of Statistical Mathematics》1980,32(1):179-185
Summary Linear unbiased estimation of the mean of a random variable in Hilbert space is treated in the typical case where the mean
belongs to a known subspace.
The best linear estimate depends on the underlying covariance operatorB
0 of the random variable. This operatorB
0, however, is rarely completely known, so that an auxiliary operatorB is used to compute a “pseudo-best” estimate. It is shown that the best and the pseudo-best estimates coincide, if and only
ifB
0
B
−1 leavesM invariant. Applications to linear regression are to be found in the references. 相似文献
26.
本文考虑损失函数的估计问题,分别对于球对称分布和均匀分布情形给出了其参数的J-S型估计量的损失之估计,它们满足[1]中提出的条件(Ⅰ)和(Ⅱ). 相似文献
27.
In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions, that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases. 相似文献
28.
29.
Chin-Tsang Chiang Mei-Cheng Wang 《Annals of the Institute of Statistical Mathematics》2004,56(1):87-100
This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring.
An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process
and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model,
we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically
biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared
risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function
of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological
example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence
rate functions for inpatient cares over time. 相似文献
30.
ρ混合、φ混合、ψ混合线性模型M估计的强相合性 总被引:2,自引:3,他引:2
研究了 ρ混合、φ混合、ψ混合样本线性模型中回归参数M估计的强相合性 ,在条件不变的情况下 ,获得与独立情形一样的M估计是强相合的充分条件 ,推广了文 [1 ]定理 2 . 相似文献