共查询到20条相似文献,搜索用时 31 毫秒
1.
We provide uniform-in-bandwidth functional limit laws for the increments of the empirical and quantile processes. Our theorems, established in the framework of convergence in probability, imply new sharp uniform-in-bandwidth limit laws for functional estimators. In particular, they yield the explicit value of the asymptotic limiting constant for the uniform-in-bandwidth sup-norm of the random error of kernel density estimators. We allow the bandwidth to vary within the complete range for which the estimators are consistent. 相似文献
2.
The nonparametric estimator of the conditional survival function proposed by Beran is a useful tool to evaluate the effects of covariates in the presence of random right censoring. However, censoring indicators of right censored data may be missing for different reasons in many applications. We propose some estimators of the conditional cumulative hazard and survival functions which allow to handle this situation. We also construct the likelihood ratio confidence bands for them and obtain their asymptotic properties. Simulation studies are used to evaluate the performances of the estimators and their confidence bands. 相似文献
3.
On the strong approximation of bootstrapped empirical copula processes with applications 总被引:3,自引:0,他引:3
S. Bouzebda 《Mathematical Methods of Statistics》2012,21(3):153-188
The purpose of the present paper is to provide a strong invariance principle for the generalized bootstrapped empirical copula processwith the rate of the approximation for multivariate empirical processes. As a by-product, we obtain a uniform-in-bandwidth consistency result for kernel-type estimators of copula derivatives, which is of its own interest. We introduce also the delta-sequence estimators of the copula derivatives. The applications discussed here are change-point detection in multivariate copula models, nonparametric tests of stochastic vectorial independence and the law of iterated logarithm for the generalized bootstrapped empirical copula process. Finally, a general notion of bootstrapped empirical copula process constructed by exchangeably weighting the sample is presented. 相似文献
4.
We establish uniform and non-uniform asymptotic simultaneous confidence bands for functionals of the distribution based on
kernel-type estimators, which include the Nadaraya-Watson kernel estimators of regression functions and the Akaike-Parzen-Rosenblatt
kernel density estimators. Our theorems, based upon functional limit laws derived by modern empirical process theory, allow
data-driven local bandwidths for these statistics.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
We establish uniform-in-bandwidth consistency for kernel-type estimators of the differential entropy. Our proofs rely on the methods of Einmahl and Mason (2005) [10]. 相似文献
6.
Peter Hall 《Probability Theory and Related Fields》1981,56(1):47-61
Summary We establish a law of the iterated logarithm for a triangular array of independent random variables, and apply it to obtain laws for a large class of nonparametric density estimators. We consider the case of Rosenblatt-Parzen kernel estimators, trigonometric series estimators and orthogonal polynomial estimators in detail, and point out that our technique has wider application. 相似文献
7.
随机删失数据下几种风险率函数估计的渐近性质 总被引:1,自引:0,他引:1
文中对于删失数据下几种不同的风险率函数估计进行了研究。使用与以往不同的方法,在较弱的条件下,改进并扩充了现有文献的结果,获得了这几种风险率函数估计的渐近正态性,一致强弱相合收敛速度以及重对数律且进行了数值模拟。 相似文献
8.
Han-Ying Liang Elias Ould Saïd 《Annals of the Institute of Statistical Mathematics》2018,70(1):155-189
Based on empirical likelihood method, we construct new weighted estimators of conditional density and conditional survival functions when the interest random variable is subject to random left-truncation; further, we define a plug-in weighted estimator of the conditional hazard rate. Under strong mixing assumptions, we derive asymptotic normality of the proposed estimators which permit to built a confidence interval for the conditional hazard rate. The finite sample behavior of the estimators is investigated via simulations too. 相似文献
9.
Zacharie Dindar 《Transactions of the American Mathematical Society》2001,353(2):427-440
The author investigates the almost sure behaviour of the increments of the partially observed, uniform empirical process. Some functional laws of the iterated logarithm are obtained for this process. As an application, new laws of the iterated logarithm are established for kernel density estimators.
10.
In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators. 相似文献
11.
《数学季刊》2016,(2):178-188
Statistical inference is developed for the analysis of generalized type-II hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size, we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively, and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here. 相似文献
12.
Summary. An extended notion of a local empirical process indexed by functions is introduced, which includes kernel density and regression
function estimators and the conditional empirical process as special cases. Under suitable regularity conditions a central
limit theorem and a strong approximation by a sequence of Gaussian processes are established for such processes. A compact
law of the iterated logarithm (LIL) is then inferred from the corresponding LIL for the approximating sequence of Gaussian
processes. A number of statistical applications of our results are indicated.
Received: 11 January 1995/In revised form: 12 July 1996 相似文献
13.
在左截断右删失数据下,我们基于乘积限估计给出了分位密度估计, 获得了分位密度估计及其导数的重对数律。 相似文献
14.
The main purpose of the present work is to establish the functional asymptotic normality of a class of kernel conditional mode estimates when functional stationary ergodic data are considered. More precisely, consider a random variable (X,Z) taking values in some semi-metric abstract space E × F. For a real function φ defined on F and for each x ∈ E, we consider the conditional mode, say ?φ(x), of the real random variable φ(Z) given the event “X = x”. While estimating the conditional mode function by Θ?φ,n(x), using the kernel-type estimator, we establish the limiting law of the family of processes {Θ?φ(x) - Θφ(x)} (suitably normalized) over Vapnik–Chervonenkis class C of functions φ. Beyond ergodicity, no other assumption is imposed on the data. This paper extends the scope of some previous results established under mixing condition for a fixed function φ. From this result, the asymptotic normality of a class of predictors is derived and confidence bands are constructed. Finally, a general notion of bootstrapped conditional mode constructed by exchangeably weighting samples is presented. The usefulness of this result will be illustrated in the construction of confidence bands. 相似文献
15.
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
16.
Katharina Proksch 《Annals of the Institute of Statistical Mathematics》2016,68(1):209-236
In a multivariate nonparametric regression problem with fixed, deterministic design asymptotic, uniform confidence bands for the regression function are constructed. The construction of the bands is based on the asymptotic distribution of the maximal deviation between a suitable nonparametric estimator and the true regression function which is derived by multivariate strong approximation methods and a limit theorem for the supremum of a stationary Gaussian field over an increasing system of sets. The results are derived for a general class of estimators which includes local polynomial estimators as a special case. The finite sample properties of the proposed asymptotic bands are investigated by means of a small simulation study. 相似文献
17.
《Stochastic Processes and their Applications》2005,115(3):493-537
We establish Chung–Mogulskii type functional laws of the iterated logarithm for medium and large increments of the uniform empirical and quantile processes. This gives the ultimate sup-norm distance between various sets of properly normalized empirical increment processes and a fixed function of the relevant cluster sets. Interestingly, we obtain the exact rates and constants even for most functions of the critical border of Strassen type balls and further introduce minimal entropy conditions on the locations of the increments under which the fastest rates are achieved with probability one. Similar results are derived for the Brownian motion and other related processes. 相似文献
18.
Di Xin ZHANG 《数学学报(英文版)》2006,22(2):339-346
So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions. 相似文献
19.
Sergio Alvarez-Andrade N. Balakrishnan Laurent Bordes 《Annals of the Institute of Statistical Mathematics》2009,61(4):887-903
This paper proposes an inferential method for the semiparametric proportional hazards model for progressively Type-II censored
data. We establish martingale properties of counting processes based on progressively Type-II censored data that allow to
derive the asymptotic behavior of estimators of the regression parameter, the conditional cumulative hazard rate functions,
and the conditional reliability functions. A Monte Carlo study and an example are provided to illustrate the behavior of our
estimators and to compare progressive Type-II censoring sampling plans with classical Type-II right censoring sampling plan. 相似文献
20.
Xia Chen 《Journal of Theoretical Probability》2006,19(3):721-739
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm.
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm. 相似文献