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含附加信息时条件分位数的估计及其渐近性质 总被引:3,自引:0,他引:3
本文利用经验似然方法给出了含附加信息时条件分位数的一类新估计,在一定的正则条件下证明了估计的渐近正态性且渐近方差小于或等于通常的条件分位数核估计的渐近方差. 相似文献
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周期异方差时间序列的季节单位根检验 总被引:1,自引:1,他引:0
为检验带异方差的季节时间序列中的单位根,提出基于最小二乘估计的统计量.在原假设下得到检验统计量的极限分布.用M on te C arlo方法计算同方差下的经验分位数并考虑异方差对检验水平的影响.实例分析表明了用该方法检验季节单位根的有效性. 相似文献
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为了更好地理解和应用样本分位数的极限分布,利用Slutsky定理,推导了样本分位数的极限分布. 相似文献
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随着大数据时代的到来,我们面临的数据越来越复杂,其中待估系数为矩阵的模型亟待构造和求解.无论在统计还是优化领域,许多专家学者都致力于矩阵模型的统计性质分析及寻找其最优解的算法设计.当随机误差期望为0且同方差时,采用基于最小二乘的模型可以很好地解决问题.当随机误差异方差,分布为重尾分布(如双指数分布,t-分布等)或数据含有异常值时,需要考虑稳健的方法来求解问题.常用的稳健方法有最小一乘,分位数,Huber等.目前稳健方法的研究大多集中于线性回归问题,对于矩阵回归问题的研究比较缺乏.本文从最小二乘模型讲起,对矩阵回归问题进行了总结和评述,同时列出了一些文献和简要介绍了我们的近期的部分工作.最后对于稳健矩阵回归,我们提出了一些展望和设想. 相似文献
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论文基于响应数据,应用鞍点近似方法,给出构造Logistic响应分布分位数的近似置信区间的方法. 论文还对这种置信区间进行了模拟,并将该方法应用于QD8电雷管. 模拟和实例结果表明,当样本量较小时,该方法能够较好地推断Logistic响应分布的分位数 相似文献
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本文研究线性模型中关于误差Markov链齐次性的假设检验问题.利用关于未知参数的拟极大似然估计和鞅差方法,获得了似然比检验统计量的极限分布. 相似文献
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In this paper, two new tests for heteroscedasticity in nonparametric regression are presented and compared. The first of these
tests consists in first estimating nonparametrically the unknown conditional variance function and then using a classical
least-squares test for a general linear model to test whether this function is a constant. The second test is based on using
an overall distance between a nonparametric estimator of the conditional variance function and a parametric estimator of the
variance of the model under the assumption of homoscedasticity. A bootstrap algorithm is used to approximate the distribution
of this test statistic. Extended versions of both procedures in two directions, first, in the context of dependent data, and
second, in the case of testing if the variance function is a polynomial of a certain degree, are also described. A broad simulation
study is carried out to illustrate the finite sample performance of both tests when the observations are independent and when
they are dependent. 相似文献
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Modal regression based on nonparametric quantile estimator is given. Unlike the traditional mean and median regression, modal regression uses mode but not mean or median to represent the center of a conditional distribution, which helps the model to be more robust for outliers, asymmetric or heavy-taileddistribution. Most of solutions for modal regression are based on kernel estimation of density. This paper studies a new solution for modal regression by means of nonparametric quantile estimator. This method builds on the fact that the distribution function is the inverse of the quantile function, then the flexibility of nonparametric quantile estimator is utilized to improve the estimation of modal function. The simulations and application show that the new model outperforms the modal regression model via linear quantile function estimation. 相似文献
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A new kernel-type estimator of the conditional density is proposed. It is based on an efficient quantile transformation of the data. The proposed estimator, which is based on the copula representation, turns out to have a remarkable product form. Its large-sample properties are considered and comparisons in terms of bias and variance are made with competitors based on nonparametric regression. A comparative simulation study is also provided. 相似文献
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Stephan Derbort Holger Dette Axel Munk 《Annals of the Institute of Statistical Mathematics》2002,54(1):60-82
A simple consistent test of additivity in a multiple nonparametric regression model is proposed, where data are observed on a lattice. The new test is based on an estimator of the L
2-distance between the (unknown) nonparametric regression function and its best approximation by an additive nonparametric regression model. The corresponding test-statistic is the difference of a classical ANOVA style statistic in a two-way layout with one observation per cell and a variance estimator in a homoscedastic nonparametric regression model. Under the null hypothesis of additivity asymptotic normality is established with a limiting variance which involves only the variance of the error of measurements. The results are extended to models with an approximate lattice structure, a heteroscedastic error structure and the finite sample behaviour of the proposed procedure is investigated by means of a simulation study. 相似文献
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In many medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease.In nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods directly.With the censored data,we construct a new response variable which has the same conditional expectation as the original one.Based on the new variable,we get a nearest neighbor estimator of the regression function.It is established that the estimator has strong consistency and asymptotic normality.The relevant simulation reports are given. 相似文献
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Natalie Neumeyer 《Journal of multivariate analysis》2009,100(7):1551-1566
We propose a new test for independence of error and covariate in a nonparametric regression model. The test statistic is based on a kernel estimator for the L2-distance between the conditional distribution and the unconditional distribution of the covariates. In contrast to tests so far available in literature, the test can be applied in the important case of multivariate covariates. It can also be adjusted for models with heteroscedastic variance. Asymptotic normality of the test statistic is shown. Simulation results and a real data example are presented. 相似文献
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Toshio Honda 《Annals of the Institute of Statistical Mathematics》2010,62(6):995-1021
We consider nonparametric estimation of conditional medians for time series data. The time series data are generated from two mutually independent linear processes. The linear processes may show long-range dependence. The estimator of the conditional medians is based on minimizing the locally weighted sum of absolute deviations for local linear regression. We present the asymptotic distribution of the estimator. The rate of convergence is independent of regressors in our setting. The result of a simulation study is also given. 相似文献
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Yong Zhou Dao-ji Li 《应用数学学报(英文版)》2006,22(3):353-368
In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models (GLMs), when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the (conditional) variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the (conditional) variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance. 相似文献
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This paper is concerned with the conditional bias and variance of local quadratic regression to the multivariate predictor variables. Data sharpening methods of nonparametric regression were first proposed by Choi, Hall, Roussion. Recently, a data sharpening estimator of local linear regression was discussed by Naito and Yoshizaki. In this paper, to improve mainly the fitting precision, we extend their results on the asymptotic bias and variance. Using the data sharpening estimator of multivariate local quadratic regression, we are able to derive higher fitting precision. In particular, our approach is simple to implement, since it has an explicit form, and is convenient when analyzing the asymptotic conditional bias and variance of the estimator at the interior and boundary points of the support of the density function. 相似文献
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Ingrid Van Keilegom Noël Veraverbeke 《Annals of the Institute of Statistical Mathematics》2001,53(4):730-745
Consider a regression model in which the responses are subject to random right censoring. In this model, Beran studied the nonparametric estimation of the conditional cumulative hazard function and the corresponding cumulative distribution function. The main idea is to use smoothing in the covariates. Here we study asymptotic properties of the corresponding hazard function estimator obtained by convolution smoothing of Beran's cumulative hazard estimator. We establish asymptotic expressions for the bias and the variance of the estimator, which together with an asymptotic representation lead to a weak convergence result. Also, the uniform strong consistency of the estimator is obtained. 相似文献