共查询到19条相似文献,搜索用时 218 毫秒
1.
在线性模型中M-方法可以用于线性假设检验, 其中M检验、Wald检验和Rao的计分型检验是最常用的检验准则. 但是在计算这些检验的临界值时都涉及到未知参数的估计. 在本文中我们利用随机加权的方法来逼近这些检验的原假设分布. 结果表明在原假设和局部对立假设之下随机加权统计量的渐近分布与原检验统计量在原假设之下的渐近分布相同. 因此我们不需要对冗余参数进行估计,利用随机加权的方法就可以得到这些检验的临界值. 而且在局部对立假设之下可以实现对功效的计算. 当取不同的误差分布和不同的随机权时, 我们对本文的方法进行了蒙特卡洛模拟. 结果表明用随机加权方法来逼近原假设分布是非常精确的. 相似文献
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半参数回归模型中随机加权M估计的强逼近 总被引:4,自引:0,他引:4
用随机加权法给出了半参数回归模型中参数的随机加权M估计,在一般的条件下证明了用随机加权统计量的分布逼近原估计量误差的分布的强有效性,并给出了M估计的最优强收敛速度。 相似文献
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本文首先研究了条件密度函数近邻-核估计的误差分布的正态逼近精度,然后利用随机加权法构造了近邻-核估计的随机加权统计量,获得了随机加权逼近精度。 相似文献
5.
序集抽样是一种适用于准确测量花费太高而排序费用可以忽略不记时的一种抽样方法.讨论了序集抽样下的对于一般分布族M估计的相合性和渐近正态性并且通过随机加权的方法来估计M估计的分布. 相似文献
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本文首先了条件密度函数近邻一核估计的误差分布的正态逼近精度,然后利用随机加权法构造了近邻-核估计的随机加权统计量,获得了随机加权逼近精度。 相似文献
8.
涂冬生 《数学物理学报(A辑)》1992,12(2):226-233
本文利用对样本随机加权的思想,构造了线性模型中误差方差估计的抽样分布的一种新的逼近,与传统的Boostrop方法相比,随机加权逼近不需要样本独立同分布的假设,在很广泛的条件下,我们证明了新逼近方法的相合性。 相似文献
9.
方连娣 《数学的实践与认识》2019,(18)
考虑一类带有不完全数据的非线性模型,其协变量带有测量误差且反映变量随机缺失.通过核实数据和借补数据构造了回归参数θ的估计的经验对数似然比统计量,证明了所构造的似然比函数渐近独立标准X_1~2变量的加权和分布.在权未知的情况下,分别采用定义权的相合估计法和构造调整被估计的经验对数似然法构造出θ的渐近置信域.进一步,基于借补方法构造了反映变量均值的调整经验对数似然比统计量,并证明了统计量渐近标准X_1~2分布,所得结果可以用来构造反映均值的置信域. 相似文献
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《数学的实践与认识》2020,(4)
在随机缺失(MAR)机制下利用经验似然方法构造了线性回归模型中误差方差的估计.并在一定条件下,证明了该估计的渐近正态性,由此得出当误差的分布不对称时,该估计的渐近方差比常用估计的渐近方差小. 相似文献
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Xiao-yan WU Ya-ning YANG & Lin-cheng ZHAO Department of Statistics Finance University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2007,50(1):87-99
The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic. It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives. 相似文献
12.
Shuangge Ma Michael R. Kosorok 《Annals of the Institute of Statistical Mathematics》2006,58(3):511-526
Current status data arises when a continuous response is reduced to an indicator of whether the response is greater or less
than a random threshold value. In this article we consider adaptive penalized M-estimators (including the penalized least
squares estimators and the penalized maximum likelihood estimators) for nonparametric and semiparametric models with current
status data, under the assumption that the unknown nonparametric parameters belong to unknown Sobolev spaces. The Cox model
is used as a representative of the semiparametric models. It is shown that the modified penalized M-estimators of the nonparametric
parameters can achieve adaptive convergence rates, even when the degrees of smoothing are not known in advance.
consistency, asymptotic normality and inference based on the weighted bootstrap for the estimators of the regression parameter
in the Cox model are also established. A simulation study is conducted for the Cox model to evaluate the finite sample efficacy
of the proposed approach and to compare it with the ordinary maximum likelihood estimator. It is demonstrated that the proposed
method is computationally superior.We apply the proposed approach to the California Partner Study analysis. 相似文献
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John R. Dixon Michael R. Kosorok Bee Leng Lee 《Annals of the Institute of Statistical Mathematics》2005,57(2):255-277
This paper introduces the “piggyback bootstrap.” Like the weighted bootstrap, this bootstrap procedure can be used to generate
random draws that approximate the joint sampling distribution of the parametric and nonparametric maximum likelihood estimators
in various semiparametric models, but the dimension of the maximization problem for each bootstrapped likelihood is smaller.
This reduction results in significant computational savings in comparison to the weighted bootstrap. The procedure can be
stated quite simply. First obtain a valid random draw for the parametric component of the model. Then take the draw for the
nonparametric component to be the maximizer of the weighted bootstrap likelihood with the parametric component fixed at the
parametric draw. We prove the procedure is valid for a class of semiparametric models that includes frailty regression models
airsing in survival analysis and biased sampling models that have application to vaccine efficacy trials. Bootstrap confidence
sets from the piggyback, and weighted bootstraps are compared for biased sampling data from simulated vaccine efficacy trials. 相似文献
14.
In this paper we investigate the weighted bootstrap for U-statistics and its properties. Under very general choices of random weights and certain regularity conditions, we show that the weighted bootstrap method with U-statistics provides second-order accurate approximations to the distribution of U-statistics. We shall prove this via one-term Edgeworth expansions of weighted U-statistics. 相似文献
15.
Shuangge Ma 《Journal of multivariate analysis》2005,96(1):190-217
M-estimation is a widely used technique for statistical inference. In this paper, we study properties of ordinary and weighted M-estimators for semiparametric models, especially when there exist parameters that cannot be estimated at the convergence rate. Results on consistency, rates of convergence for all parameters, and consistency and asymptotic normality for the Euclidean parameters are provided. These results, together with a generic paradigm for studying semiparametric M-estimators, provide a valuable extension to previous related research on semiparametric maximum-likelihood estimators (MLEs). Although penalized M-estimation does not in general fit in the framework we discuss here, it is shown for a great variety of models that many of the forgoing results still hold, including the consistency and asymptotic normality of the Euclidean parameters. For semiparametric M-estimators that are not likelihood based, general inference procedures for the Euclidean parameters have not previously been developed. We demonstrate that our paradigm leads naturally to verification of the validity of the weighted bootstrap in this setting. For illustration, several examples are investigated in detail. The new M-estimation framework and accompanying weighted bootstrap technique shed light on a universal way of investigating semiparametric models. 相似文献
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Edgeworth expansions which are local in one coordinate and global in the rest of the coordinates are obtained for sums of independent but not identically distributed random vectors. Expansions for conditional probabilities are deduced from these. Both lattice and continuous conditioning variables are considered. The results are then applied to derive Edgeworth expansions for bootstrap distributions, for Bayesian bootstrap distribution, and for the distributions of statistics based on samples from finite populations. This results in a unified theory of Edgeworth expansions for resampling procedures. The Bayesian bootstrap is shown to be second order correct for smooth positive “priors,” whenever the third cumulant of the “prior” is equal to the third power of its standard deviation. Similar results are established for weighted bootstrap when the weights are constructed from random variables with a lattice distribution. 相似文献
17.
This work assumes that the small area quantities of interest follow a Fay–Herriot model with spatially correlated random area
effects. Under this model, parametric and nonparametric bootstrap procedures are proposed for estimating the mean squared
error of the empirical best linear unbiased predictor (EBLUP). A simulation study based on the Italian Agriculture Census
2000 compares bootstrap and analytical estimates of the MSE and studies their robustness to non-normality. Results indicate
lower bias for the non-parametric bootstrap under specific departures from normality.
相似文献
18.
Summary This paper considers different bootstrap procedures for investigating the estimation of the fractional parameter d in a particular
case of long memory processes, i.e. for ARFIMA models withd in (0.0, 0.5). We propose two bootstrap techniques to deal with semiparametric estimation methods of d. One approach consists
of the local bootstrap method for time frequency initially suggested for the ARMA case by Paparoditis and Politis (1999),
and the other consists of the bootstrapping in the residuals of the frequency-domain regression equation. Through Monte Carlo
simulation, these alternative bootstrap methods are compared, based on the mean and the mean square error of the estimators,
with the well-known parametric and nonparametric bootstrap techniques for time series models. 相似文献
19.
XiaoMingWANG WangZHOU 《数学学报(英文版)》2004,20(1):93-104
The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation,and prove that the approximation is valid in probability 1.A simulation is made to show the effects of bootstrap approximation,randomly weighted approximation and normal approximation. 相似文献