-混合样本下含附加信息时条件分位数估计的渐近性质(英文)

本文利用经验似然方法构造了含附加信息时条件分位数的一类估计,并证明了估计的渐近正态性且渐近方差不大于通常核估计的渐近方差.     

ψ-混合样本下含附加信息时条件分位数估计的渐近性质

本文利用经验似然方法构造了含附加信息时条件分位数的一类估计,并证明了估计的渐近正态性且渐近方差不大于通常核估计的渐近方差.     

φ-混合样本下含附加信息时条件分位数估计的渐近性质

本文利用经验似然方法构造了含附加信息时条件分位数的一类估计，并证明了估计的渐近正态性且渐近方差不大于通常核估计的渐近方差。     

含际加信息时条件分位数的估计及其渐近性质

本文利用经验似然方法给出了含附另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。     

含附加信息时条件分位数的估计及其渐近性质

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．     

强混合样本情形含附加信息时总体分位数的估计

在强混合样本下,利用分组经验似然方法构造了总体分位数的一类新的估计,证明了估计的渐近正态性,同时证明了含附加信息时估计的渐近方差小于或者等于不含附加信息时估计的渐近方差.     

Panel Count Data模型参数的经验似然推断

对Panel Count Data的处理越来越受到人们的关注,Sun与Wei^([1-2])基于简单的半参数模型,提出了Panel Count Data的回归分析,并且给出了参数的估计方程。本文则基于经验似然的思想,讨论了上述Panel Count Data模型参数的置信域构造问题,特别仅通过经验似然置信区域给出了参数估计的方差阵估计,证明了估计的1/n相合性。基于Sun与Wei所给的数据,给出了参数置信区域的具体构造过程和结果。通过作图比较可以看出经验似然置信域要优于依据渐近正态性所构造的置信域。我们还依据所作出的经验似然置信域对参数估计的方差矩阵进行了估计,与用传统渐近正态性得到的矩阵较为接近。     

纵向数据下部分非线性模型的广义经验似然推断

本文研究了纵向数据下部分非线性模型中未知参数的置信域的构造.利用经验似然方法,构造了非线性函数中未知参数的广义对数经验似然比统计量,证明了其渐近于卡方分布.同时,得到了未知参数的最大经验似然估计,并证明了其渐近正态性.     

截断情况下线性回归模型响应变量均值的经验似然

本文讨论了在带有截断情况的线性回归模型中 ,响应变量均值的估计问题 .将经验似然的方法应用到带有截断情况的回归模型中 ,在估计响应变量的均值时构造了调整的经验似然统计量 ,证明了在一定的条件下 ,该统计量渐近服从 χ2 分布 ,给出了均值的置信区间 ,并与正态下得到的结果进行了比较 ,模拟的结果说明了经验似然的优良性 .     

纵向数据下部分线性模型的经验似然推断

考虑纵向数据下部分线性模型,研究了回归系数和基准函数的经验似然推断,证明了所提出的经验对数似然比渐近于卡方分布,由此构造了相应兴趣参数的置信域和区间. 此外,利用经验似然比函数得到了回归系数和基准函数的最大经验似然估计,并且证明了所得估计量的渐近正态性.模拟研究比较了经验似然与正态逼近方法的有限样本性质,并进行了案例分析.     

Kernel estimators of the ROC Curve with censored data

Receiver operating characteristic (ROC) curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kaplan-Meier estimator. In this paper we propose a smoothed estimator based on kernel techniques for the ROC curve with censored data. The large sample properties of the smoothed estimator are established. Moreover, deficiency is considered in order to compare the proposed smoothed estimator of the ROC curve with the empirical one based on Kaplan-Meier estimator. It is shown that the smoothed estimator outperforms the direct empirical estimator based on the Kaplan-Meier estimator under the criterion of deficiency. A simulation study is also conducted and a real data is analyzed.     

左截断右删失数据分位差估计及其渐近性质

我们研究了左截断右删失数据分位差,基于左截断右删失数据乘积限构造了分位差的经验估计,同时克服经验估计的非光滑性,提出了分位数差的核光滑估计.利用经验过程理论推导出这两个估计的渐近偏差和渐近方差,并且在左截断右删失数据下研究了这两个分位差的大样本性质,获得分位差估计的相合性和渐近正态性.同时给出计算模拟以验证光滑分位差估计的表现,在均方损失的意义下模拟结果表明光滑估计比经验估计具有更好的性质.     

On the modal resolution of kernel density estimators

The ability of a kernel density estimator to resolve modes of the underlying density is investigated. For various bimodal densities and three different kernels, the smallest sample size required for the expectation of an optimally smoothed kernel estimator to be bimodal is determined. The optimality criterion employed is equivalent to asymptotic mean integrated squared error for sufficiently smooth densities.     

金融风险管理中VaR度量的光滑估计效率

本文研究了金融风险管理理论中风险价值(VaR)的非参数核光滑估计和经验估计的效率问题.对非独立的时间序列损失/收益样本,在均方误差(MSE)准则的意义下引入亏量的概念,亏量越大表明估计效率越低.并利用亏量对VaR模型的核光滑估计和基于样本分位数的经验估计进行了比较,在理论上证明了VaR模型的核光滑估计优于经验估计.同时,通过计算机模拟证实了理论获得的结论.本文还对国内沪深两市上的证券投资基金进行了实证分析,计算了样本基金的VaR风险度量的经验估计和核光滑估计,并计算了样本基金基于周收益率和VaR估计的风险调整收益(RAROC)值,以此对样本基金的业绩做出了有用的评价.     

纵向数据非参数混合效应模型的一个局部不变估计

非参数核回归方法近年来已被用于纵向数据的分析(Lin和Carroll,2000)．一个颇具争议性的问题是在非参数核回归中是否需要考虑纵向数据间的相关性．Lin和Carroll (2000)证明了基于独立性(即忽略相关性)的核估计在一类核GEE估计量中是(渐近)最有效的．基于混合效应模型方法作者提出了一个不同的核估计类,它自然而有效地结合了纵向数据的相关结构．估计量达到了与Lin和Carroll的估计量相同的渐近有效性,且在有限样本情形下表现更好．由此方法可以很容易地获得对于总体和个体的非参数曲线估计．所提出的估计量具有较好的统计性质,且实施方便,从而对实际工作者具有较大的吸引力．     

Probability density estimation with surrogate data and validation sample

The probability density estimation problem with surrogate data and validation sample is considered. A regression calibration kernel density estimator is defined to incorporate the information contained in both surrogate variates and validation sample. Also, we define two weighted estimators which have less asymptotic variances but have bigger biases than the regression calibration kernel density estimator. All the proposed estimators are proved to be asymptotically normal. And the asymptotic representations for the mean squared error and mean integrated square error of the proposed estimators are established, respectively. A simulation study is conducted to compare the finite sample behaviors of the proposed estimators.     

Stahel-Donoho kernel estimation for fixed design nonparametric regression models

This paper reports a robust kernel estimation for fixed design nonparametric regression models. A Stahel-Donoho kernel estimation is introduced, in which the weight functions depend on both the depths of data and the distances between the design points and the estimation points. Based on a local approximation, a computational technique is given to approximate to the incomputable depths of the errors. As a result the new estimator is computationally efficient. The proposed estimator attains a high breakdown point and has perfect asymptotic behaviors such as the asymptotic normality and convergence in the mean squared error. Unlike the depth-weighted estimator for parametric regression models, this depth-weighted nonparametric estimator has a simple variance structure and then we can compare its efficiency with the original one. Some simulations show that the new method can smooth the regression estimation and achieve some desirable balances between robustness and efficiency.     

Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters

We study a test statistic based on the integrated squared difference between a kernel estimator of the copula density and a kernel smoothed estimator of the parametric copula density. We show for fixed smoothing parameters that the test is consistent and that the asymptotic properties are driven by a U-statistic of order 4 with degeneracy of order 1. For practical implementation we suggest to compute the critical values through a semiparametric bootstrap. Monte Carlo results show that the bootstrap procedure performs well in small samples. In particular, size and power are less sensitive to smoothing parameter choice than they are under the asymptotic approximation obtained for a vanishing bandwidth.     

Estimating spot volatility in the presence of infinite variation jumps

We propose a kernel estimator for the spot volatility of a semi-martingale at a given time point by using high frequency data, where the underlying process accommodates a jump part of infinite variation. The estimator is based on the representation of the characteristic function of Lévy processes. The consistency of the proposed estimator is established under some mild assumptions. By assuming that the jump part of the underlying process behaves like a symmetric stable Lévy process around 0, we establish the asymptotic normality of the proposed estimator. In particular, with a specific kernel function, the estimator is variance efficient. We conduct Monte Carlo simulation studies to assess our theoretical results and compare our estimator with existing ones.     

光滑分布函数分位数估计的注记(英)

文中通过光滑经验分布函数构造了分位数估计，建立该估计的Bahadu－强弱表示定理，并由Bahadur表示定理证明了该分估计估的重对数律和渐近正态性等深刻结果．