共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator (MQLE) in quasi-likelihood nonlinear models (QLNM) with random regressors. The asymptotic results of generalized linear models (GLM) with random regressors are generalized to QLNM with random regressors. 相似文献
2.
The local asymptotic normality (LAN) property is established for multivariate ARMA models with a linear trend or, equivalently, for multivariate general linear models with ARMA error term. In contrast with earlier univariate results, the central sequence here is correlogram-based, i.e. expressed in terms of a generalized concept of residual cross-covariance function. 相似文献
3.
Yoichi Nishiyama 《Annals of the Institute of Statistical Mathematics》1995,47(2):195-209
This paper deals with statistical inference problems for a special type of marked point processes based on the realization in random time intervals [0,u]. Sufficient conditions to establish the local asymptotic normality (LAN) of the model are presented, and then, certain class of stopping times u satisfying them is proposed. Using these stopping rules, one can treat the processes within the framework of LAN, which yields asymptotic optimalities of various inference procedures. Applications for compound Poisson processes and continuous time Markov branching processes (CMBP) are discussed. Especially, asymptotically uniformly most powerful tests for criticality of CMBP can be obtained. Such tests do not exist in the case of the non-sequential approach. Also, asymptotic normality of the sequential maximum likelihood estimators (MLE) of the Malthusian parameter of CMBP can be derived, although the non-sequential MLE is not asymptotically normal in the supercritical case. 相似文献
4.
The problem of the nonparametric minimax estimation of an infinitely smooth density at a given point, under random censorship, is considered. We establish the exact asymptotics of the local minimax risk and propose the efficient kernel-type estimator based on the well known Kaplan-Meier estimator. 相似文献
5.
We introduce the estimating function with asymptotic bias and investigate the asymptotic behavior of the estimator based on it by using their relationship. The estimator based on the estimating function with asymptotic bias has the asymptotic normality with asymptotic bias. We show that this theory has several interesting applications in practical statistics. 相似文献
6.
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
7.
Si-li Niu 《应用数学学报(英文版)》2012,28(4):781-794
In this paper, we discuss the asymptotic normality of the wavelet estimator of the density function based on censored data, when the survival and the censoring times form a stationary ??-mixing sequence. To simulate the distribution of estimator such that it is easy to perform statistical inference for the density function, a random weighted estimator of the density function is also constructed and investigated. Finite sample behavior of the estimator is investigated via simulations too. 相似文献
8.
Local asymptotic mixed normality (LAMN) of a class of transformed Gaussian models for discretely observed random fields is proved. The original Gaussian random field is assumed to be the product of a deterministic process and a process with independent increments. The transformed process is observed only on discrete lattice points in the unit cube and fixed domain asymptotics is investigated. This model is useful for modeling random fields with non-Gaussian marginal distributions. 相似文献
9.
Song Yang 《Statistics & probability letters》1990,10(5):419-426
For an open set Θ of
k, let \s{Pθ: θ Θ\s} be a parametric family of probabilities modeling the distribution of i.i.d. random variables X1,…, Xn. Suppose Xi's are subject to right censoring and one is only able to observe the pairs (min(Xi, Yi), [Xi Yi]), i = 1,…, n, where [A] denotes the indicator function of the event A, Y1,…, Yn are independent of X1,…, Xn and i.i.d. with unknown distribution Q0. This paper investigates estimation of the value θ that gives a fitted member of the parametric family when the distributions of X1 and Y1 are subject to contamination. The constructed estimators are adaptive under the semi-parametric model and robust against small contaminations: they achieve a lower bound for the local asymptotic minimax risk over Hellinger neighborhoods, in the Hájel—Le Cam sense. The work relies on Beran (1981). The construction employs some results on product-limit estimators. 相似文献
10.
For a stable autoregressive process of order p with unknown vector parameter θ, it is shown that under a sequential sampling scheme with the stopping time defined by the trace of the observed Fisher information matrix, the least-squares estimator of θ is asymptotically normally distributed uniformly in θ belonging to any compact set in the parameter region. 相似文献
11.
12.
The 3/2th and 2nd order asymptotic efficiency of maximum probability estimators in non-regular cases
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1991,43(1):181-195
In this paper we consider the estimation problem on independent and identically distributed observations from a location parameter family generated by a density which is positive and symmetric on a finite interval, with a jump and a nonnegative right differential coefficient at the left endpoit. It is shown that the maximum probability estimator (MPE) is 3/2th order two-sided asymptotically efficient at a point in the sense that it has the most concentration probability around the true parameter at the point in the class of 3/2th order asymptotically median unbiased (AMU) estimators only when the right differential coefficient vanishes at the left endpoint. The second order upper bound for the concentration probability of second order AMU estimators is also given. Further, it is shown that the MPE is second order two-sided asymptotically efficient at a point in the above case only.Research supported by University of Tsukuba Project Research. 相似文献
13.
In this paper,the estimation of joint dlstribution F(y,z)of(Y,Z)and the estimation in thelinear regression model Y=b'Z+εfor complete data are extended to that of the right censored data.Theregression parameter estimates of b and the variance of ε are weighted least square estimates with randomweights. The central limit theorems of the estimators are obtained under very weak conditions and the derivedasymptotic variance has a very simple form. 相似文献
14.
M. Nussbaum 《Journal of multivariate analysis》1984,14(3):300-314
We consider estimation of the parameter B in a multivariate linear functional relationship Xi=ξi+ξ1i, Yi=Bξi+ξ2i, i=1,…,n, where the errors (ζ1i′, ζ2i′) are independent standard normal and (ξi, i
) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n−1/2 is also established. 相似文献
15.
16.
M. Huebner 《Statistical Inference for Stochastic Processes》1999,2(1):57-68
Consider a parabolic stochastic partial differential equation perturbed by small noise observed on a time interval [0,T]. We construct the maximum likelihood estimators of the coefficients of the operators involved in these equations based on partial observations in the form of diffusion processes and show the asymptotic efficiency for loss functions with polynomial majorant as the variance goes to zero. 相似文献
17.
Kentaro Tanaka Akimichi Takemura 《Annals of the Institute of Statistical Mathematics》2005,57(1):1-19
We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator
is strongly consistent, if the scale parameters of the component uniform distributions are restricted from below by exp(−n
d
), 0<d<1, wheren is the sample size. 相似文献
18.
YEERHUA 《高校应用数学学报(英文版)》1995,10(4):379-386
In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator (MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency. 相似文献
19.
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
20.
Magda Peligrad 《Journal of Theoretical Probability》1996,9(3):703-715
The aim of this paper is to investigate the asymptotic normality for strong mixing sequences of random variables in the absense of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences. The class of applications include filters of certain Gaussian sequences.Supported in part by an NSF grant, cost-sharing from the University of Cincinnati, and a Taft research grant. 相似文献