共查询到20条相似文献,搜索用时 734 毫秒
1.
Suppose we observe a stationary Markov chain with unknown transition distribution. The empirical estimator for the expectation of a function of two successive observations is known to be efficient. For reversible Markov chains, an appropriate symmetrization is efficient. For functions of more than two arguments, these estimators cease to be efficient. We determine the influence function of efficient estimators of expectations of functions of several observations, both for completely unknown and for reversible Markov chains. We construct simple efficient estimators in both cases. 相似文献
2.
Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function
associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all
of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random.
Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator.
All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of
the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection
method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform
relatively well. We illustrate our methods with an analysis of some vascular disease data. 相似文献
3.
We consider the nonparametric regression model with long memory data that are not necessarily Gaussian and provide an asymptotic
expansion for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators. We
show this MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous
expansion for the kernel estimators. However, for the kernel estimators, this MISE expansion generally fails if an additional
smoothness assumption is absent.
Research supported in part by the NSF grant DMS-0103939. 相似文献
4.
Jose M. Vidal-Sanz Miguel A. Delgado 《Annals of the Institute of Statistical Mathematics》2004,56(4):791-818
This paper considers delta estimators of the Radon-Nikodym derivative of a probability function with respect to a σ-finite
measure. We provide sufficient conditions for universal consistency, which are checked for some wide classes of nonparametric
estimators. 相似文献
5.
Properties of nonparametric estimators of autocovariance for stationary random fields 总被引:1,自引:0,他引:1
Summary We introduce nonparametric estimators of the autocovariance of a stationary random field. One of our estimators has the property that it is itself an autocovatiance. This feature enables the estimator to be used as the basis of simulation studies such as those which are necessary when constructing bootstrap confidence intervals for unknown parameters. Unlike estimators proposed recently by other authors, our own do not require assumptions such as isotropy or monotonicity. Indeed, like nonparametric function estimators considered more widely in the context of curve estimation, our approach demands only smoothness and tail conditions on the underlying curve or surface (here, the autocovariance), and moment and mixing conditions on the random field. We show that by imposing the condition that the estimator be a covariance function we actually reduce the numerical value of integrated squared error. 相似文献
6.
Thresholding projection estimators in functional linear models 总被引:1,自引:0,他引:1
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows us to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits us to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove that these estimators are minimax and rates of convergence are given for some particular cases. 相似文献
7.
We focus on nonparametric multivariate regression function estimation by locally weighted least squares. The asymptotic behavior for a sequence of error processes indexed by bandwidth matrices is derived. We discuss feasible data-driven consistent estimators minimizing asymptotic mean squared error or efficient estimators reducing asymptotic bias at points where opposite sign curvatures of the regression function are present in different directions. 相似文献
8.
We establish the consistency, asymptotic normality, and efficiency for estimators derived by minimizing the median of a loss function in a Bayesian context. We contrast this procedure with the behavior of two Frequentist procedures, the least median of squares (LMS) and the least trimmed squares (LTS) estimators, in regression problems. The LMS estimator is the Frequentist version of our estimator, and the LTS estimator approaches a median-based estimator as the trimming approaches 50% on each side. We argue that the Bayesian median-based method is a good tradeoff between the two Frequentist estimators. 相似文献
9.
Recent developments in the production frontier literature include nonparametric estimators with shape constraints. A few of these estimators rely on the Afriat inequalities to provide piecewise linear approximations to the production function/frontier. We show in this paper that these Afriat–Diewert–Parkan (ADP) estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance. We propose new estimators with lower variance and a relatively low bias. We consider such alternative estimators based on (weighted) averages of random hinge functions with parameter restrictions. Small sample properties of the estimators are presented that show our new estimators outperform the existing ADP estimators when moderate to large amounts of noise are present. 相似文献
10.
本文考虑参数空间被限制时有限总体的可容许估计问题,在期望均方误差准则下,获得了有限总体指标值的线性函数之线性估计在线性估计类中为可容许的充要条件. 相似文献
11.
The problem of estimating parameters of a Pareto distribution is investigated under a general scale invariant loss function when the scale parameter is restricted to the interval (0, 1]. We consider the estimation of shape parameter when the scale parameter is unknown. Techniques for improving equivariant estimators developed by Stein, Brewster–Zidek and Kubokawa are applied to derive improved estimators. In particular improved classes of estimators are obtained for the entropy loss and a symmetric loss. Risk functions of various estimators are compared numerically using simulations. It is also shown that the technique of Kubokawa produces improved estimators for estimating the scale parameter when the shape parameter is known. 相似文献
12.
??In this paper, semiparametric estimation of a regression function in the third order partially linear autoregressive model with first order autoregressive errors is mainly studied. We suppose that the regression function has a parametric framework, and use the conditional least squares method to obtain the parameter estimators. Then semiparametric estimators of the regression function can be given by combining with the nonparametric kernel function adjustment. Furthermore, under certain conditions, the consistency of the estimators is proved. Finally, simulation research is presented to evaluate the
effectiveness of the proposed method. 相似文献
13.
Lyudmyla Sakhno 《Lithuanian Mathematical Journal》2012,52(4):400-419
We present a class of minimum contrast estimators based on the objective function that is composed using the squared periodogram. We prove the consistency and asymptotic normality of the proposed estimators. 相似文献
14.
David M. Mason 《Statistical Inference for Stochastic Processes》2012,15(2):151-176
We develop general methods based upon empirical process techniques to prove uniform in bandwidth consistency of a class of non-standard kernel-type function estimators. Examples include projection pursuit regression and conditional distribution estimation. Our results are especially useful to establish uniform consistency of data-driven bandwidth kernel-type function estimators. 相似文献
15.
This paper considers the problem of estimating the finite-population distribution function and quantiles with the use of auxiliary
information at the estimation stage of a survey. We propose the families of estimators of the distribution function of the
study variate y using the knowledge of the distribution function of the auxiliary variate x. In addition to ratio, product and difference type estimators, many other estimators are identified as members of the proposed
families. For these families the approximate variances are derived, and in addition, the optimum estimator is identified along
with its approximate variance. Estimators based on the estimated optimum values of the unknown parameters used to minimize
the variance are also given with their properties. Further, the family of estimators of a finite-population distribution function
using two-phase sampling is given, and its properties are investigated.
相似文献
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18.
Christopher C. Chang Dimitris N. Politis 《Journal of computational and graphical statistics》2016,25(1):144-166
In this article, we introduce a new class of robust autocorrelation estimators based on interpreting the sample autocorrelation function as a linear regression. We investigate the efficiency and robustness properties of the estimators that result from employing three common robust regression techniques. We discuss the construction of robust autocovariance and positive definite autocorrelation estimates, and their application to AR model fitting. We perform simulation studies with various outlier configurations to compare the different estimators. 相似文献
19.
Guo Hua Zou 《数学学报(英文版)》2002,18(1):37-46
This paper considers the admissibility of the estimators for finite population when the parameter space is restricted. We
obtain all admissible linear estimators of an arbitrary linear function of characteristic values of a finite population in
the class of linear estimators under the criterion of the expectation of mean squared error.
Received February 12, 1999, Revised October 8, 1999, Accepted January 14, 2000 相似文献
20.
This paper deals with nonparametric estimation of the boundary curve of the support of a bivariate density function. This estimation problem arises in various contexts, such as for example scatterpoint image analysis and frontier estimation in econometrics. The setup in this paper is a general one, allowing the bivariate density function to be infinite, bounded away from zero or zero at the boundary. Two estimators for the boundary curve are introduced, both based on order statistics. The asymptotic distribution of the estimators and their rate of convergence are established. Via a comparison of the rates of convergence we recommend which estimator to use in a particular situation. Both estimators can be used as an initial estimator in a two-stage procedure, designed for getting a better estimation. Simulation studies demonstrate the finite-sample behavior of the estimators and the proposed two-stage procedure. We illustrate the procedure on a data set on American electric utility companies. 相似文献