完全与截尾样本时回归函数的核估计

本文得到了完全与截尾样本时回归函数核估计的强相合性．接着，构造了截尾样本的改良核估计，在Ｅ｜Ｙ｜＜∞下，得到了其强相合性．     

NA样本密度函数估计一致渐近正态性的收敛速度

在平稳NA样本下,讨论了未知密度函数估计的一致渐近正态性.在适当的条件下给出了该密度函数估计一致渐近正态性的收敛速度.这个速度几乎达到n^{-1/6}     

负相协平均剩余寿命函数和有效函数的一类非参数估计

本文在 NA 样本下,讨论了平均剩余寿命函数和有效函数的非参数递归型估计的相合性和渐近正态性．     

在一类特殊的随机截断下分布函数的估计

本文讨论了在一类特殊的随机截断下分布函数的估计及其渐近正态性.     

NA样本下截断型分布族参数的经验Bayes估计

运用NA样本密度函数核估计构造了一类截断型分布族参数的经验Bayes估计，建立了它的收敛速度，证明了在适当条件下该收敛速度可以任意接近于1，文中还给出了适合定理条件的例子。     

删失指标随机缺失下一类非参数函数的加权局部多项式估计及其应用

本文在右删失数据中删失指标部分随机缺失下,构造了一类非参数函数的校准加权局部多项式估计以及插值加权局部多项式估计,并建立了这些估计的渐近正态性;作为该方法的应用,导出了条件分布函数、条件密度函数以及条件分位数的加权局部线性双核估计和插值加权局部线性双核估计,并且得到了这些估计的渐近正态性;最后,在有限样本下对这些估计进行了模拟.     

相协样本分布函数光滑估计的正态逼近速度

在平稳相协样本下,讨论分布函数光滑估计的一致渐近正态性.在较合理的条件下给出了分布函数光滑估计的一致渐近正态性的收敛速度,这个速度几乎达到n~(-1/4).     

Linex损失及PA样本下单边截断型分布族参数函数的EB估计

在Linex损失函数下,运用同分布PA样本密度函数的核估计方法,构造了一类单边截断型分布族参数函数的EB估计,并建立了它的收敛速度.在一定条件下,证明了这个收敛速度可充分接近1.     

非参数回归函数估计的渐近正态性

本文研究了独立或相依样本时非参数回归函数的Ｎａｄａｒａｙａ-Ｗａｔｓｏｎ估计，在简洁合理的条件下，证明了估计量的渐近正态性．获得的结论可在时间序列分析中得到应用．     

相依样本分布函数和回归函数核估计的强收敛性及其速度

本文讨论样本为φ-混合和α-混合时分布函数核估计的强相合性.在α-混合时讨论其收敛速度,我们的结果与i.i.d.情况相一致,从而改进了[2]中的结论。同时,本文还在ρ-混合下,讨论回归函数核估计的强收敛性及收敛速度,其结果接近于独立情形。     

A functional limit theorem for tapered empirical spectral functions

Using convolution properties of frequency-kernels and their upper bounds we obtain some new upper bounds for the cumulants of time series statistics. From these results we derive the asymptotic normality of some spectral estimates and the tightness of tapered empirical spectral functions in the space of Lipschitz-continuous functions. It follows that tapering increases the asymptotic variance of the estimates by a constant factor. All results are proved under integrability conditions on the spectra. A functional limit theorem for the empirical spectral function is also given without assuming all moments of the underlying process to exist.     

Asymptotic Normality of Cross-correlogram Estimates of the Response Function

The problem of estimation of an unknown response function of a time-invariant continuous linear system is considered. Discrete-time sample input–output cross-correlograms are taken as estimates of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes close, in some sense, to a white noise. Both asymptotic normality of finite-dimensional distributions of the estimates and their asymptotic normality in spaces of continuous functions are studied. Our basic tool is a new integral representation for cumulants of the estimate as a finite sum of integrals involving cyclic products of kernels. Some inequalities for these integrals are obtained and their asymptotic behaviour is studied.     

Spectral asymptotics for Laplacians on self-similar sets

Given a self-similar Dirichlet form on a self-similar set, we first give an estimate on the asymptotic order of the associated eigenvalue counting function in terms of a ‘geometric counting function’ defined through a family of coverings of the self-similar set naturally associated with the Dirichlet space. Secondly, under (sub-)Gaussian heat kernel upper bound, we prove a detailed short time asymptotic behavior of the partition function, which is the Laplace-Stieltjes transform of the eigenvalue counting function associated with the Dirichlet form. This result can be applicable to a class of infinitely ramified self-similar sets including generalized Sierpinski carpets, and is an extension of the result given recently by B.M. Hambly for the Brownian motion on generalized Sierpinski carpets. Moreover, we also provide a sharp remainder estimate for the short time asymptotic behavior of the partition function.     

Smoothing estimation of rate function for recurrent event data with informative censoring

This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring. An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model, we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence rate functions for inpatient cares over time.     

删失数据中删失指标随机缺失下回归函数的非参数估计

本文在删失数据中删失指标随机缺失的情况下,运用非参数方法给出了回归函数的两种估计量,给出了估计量的一致收敛速度以及渐近分布,并进一步通过数值模拟验证了所提方法在有限样本下的性质.     

Propriétés asymptotiques d'estimateurs convergents des quantiles conditionnels

We state sufficient conditions for asymptotic normality of convergent estimates of the conditional quantiles, irrespective of data dependence, and give an application to α-mixing stationary processes, under optimal conditions. As an application, we use asymptotic normality to construct confidence bands for predictors based on nonparametric estimates of the conditional median.     

回归函数改良核估计的渐近分布

设(X1,Y1),…,(Xn,Yn)是来自二元总体(X,Y)的样本,若EY＜∞,则回归函数m(x)＝E(Y｜X＝x)存在。在本文中,考虑m(x)的改良核估计     

Local asymptotic normality and mixed normality for Markov statistical models

Summary We prove local asymptotic normality (resp. local asymptotic mixed normality) of a statistical experiment, when the observation is a positive-recurrent (resp. null-recurrent, with an additional technical assumption) Markov chain or Markov step process, under rather mild regularity assumptions on the transition kernel for Markov chains, on the infinitesimal generator for Markov processes. The proof makes intensive use of Hellinger processes, thus avoiding almost completely to study the more complicated structure of the likelihoods themselves.     

Local asymptotic mixed normality for semimartingale experiments

Summary We give conditions for local asymptotic mixed normality of experiments when the observed process is a semimartingale and the observation time increases to infinity. As a consequence we obtain asymptotic efficiency of various estimators. Several special models for counting process,s, diffusion processes and diffusions with jumps are studied.Research supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft