不同自变量的变系数模型的估计

讨论具有不同自变量的变系数模型的函数系数的估计及其大样本性质。使用局部线性方法和积分方法,得到函数系数的积分估计;由于该估计有较大的方差,进一步使用回切法改进这一估计,获得了函数系数的改进估计;同时,研究了改进估计的渐近正态性。最后,用模拟例子说明提出的估计方法是有效的。     

Parameter Estimation of Multivariate Regression Model with Fuzzy Random Errors

In many real-world problems, observations are usually described by approximate values due to fuzzy uncertainty, unlikeprobabilistic uncertainty that has nothing to do with experimentation. The combination of statistical model and fuzzy set theory is helpful to improve the identification and analysis of complex systems. As an extension ofstatistical techniques, this study is an investigation of the relationship between fuzzy multiple explanatory variables and fuzzy response with numeric coefficients and the fuzzy random error term. In this work we describe a parameter estimation procedure carrying out the least-squares method in a complete metric space of fuzzy numbers to determine the coefficients based on the extension principle. We demonstrate how the fuzzy least squares estimators present large sample statistical properties, including asymptotic normality, strong consistency and confidence region. The estimators are also examined via asymptotic relative efficiency concerning traditional least squares estimators. Different from the construction of error term in Kim et al.\cite{21}, it is more reasonable in the proposed model since the problems of inconsistency in referring to fuzzy variable and producing the negative spreads may be avoided. The experimental study verifies that the proposed fuzzy least squares estimators achieve the meaning consistent with the theory identification for large sample data set and better generalization regarding one single variable model.     

Partial linear single index models with distortion measurement errors

We study partial linear single index models when the response and the covariates in the parametric part are measured with errors and distorted by unknown functions of commonly observable confounding variables, and propose a semiparametric covariate-adjusted estimation procedure. We apply the minimum average variance estimation method to estimate the parameters of interest. This is different from all existing covariate-adjusted methods in the literature. Asymptotic properties of the proposed estimators are established. Moreover, we also study variable selection by adopting the coordinate-independent sparse estimation to select all relevant but distorted covariates in the parametric part. We show that the resulting sparse estimators can exclude all irrelevant covariates with probability approaching one. A simulation study is conducted to evaluate the performance of the proposed methods and a real data set is analyzed for illustration.     

On the estimation of optimal batch sizes in the analysis of simulation output

The estimation of the variance of point estimators is a classical problem of stochastic simulation. A more specific problem addresses the estimation of the variance of a sample mean from a steady-state autocorrelated process. Many proposed estimators of the variance of the sample mean are parameterized by batch size. A critical problem is to find an appropriate batch size that provides a good tradeoff between bias and variance. This paper proposes a procedure for determining the optimal batch size to minimize the mean squared error of estimators of the variance of the sample mean. This paper also presents the results of empirical studies of the procedure. The experiments involve symmetric two-state Markov chain models, first-order autoregressive processes, seasonal autoregressive processes, and queue-waiting times for several M/M/1 queueing models. The empirical results indicate that the estimation procedure works nearly as well as it would if the parameters of the processes were known.     

变系数模型中的逐元B-Spline估计法

给出了一种用于估计变系数模型中未知函数的逐元B-Spline方法,建立了估计量的局部渐近偏差,方差和渐近正态分布,开发了一种快速选择估计量窗宽的方法,通过Monte Carlo模拟研究了估计量的有限样本性质.     

Efficient estimation of functional-coefficient regression models with different smoothing variables

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.     

Semiparametric analysis based on weighted estimating equations for transformation models with missing covariates

Missing covariate data are very common in regression analysis. In this paper, the weighted estimating equation method (Qi et al., 2005) [25] is used to extend the so-called unified estimation procedure (Chen et al., 2002) [4] for linear transformation models to the case of missing covariates. The non-missingness probability is estimated nonparametrically by the kernel smoothing technique. Under missing at random, the proposed estimators are shown to be consistent and asymptotically normal, with the asymptotic variance estimated consistently by the usual plug-in method. Moreover, the proposed estimators are more efficient than the weighted estimators with the inverse of true non-missingness probability as weight. Finite sample performance of the estimators is examined via simulation and a real dataset is analyzed to illustrate the proposed methods.     

Variable selection for semiparametric varying coefficient partially linear errors-in-variables models

This paper focuses on the variable selections for semiparametric varying coefficient partially linear models when the covariates in the parametric and nonparametric components are all measured with errors. A bias-corrected variable selection procedure is proposed by combining basis function approximations with shrinkage estimations. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the regularized estimators are established. A simulation study and a real data application are undertaken to evaluate the finite sample performance of the proposed method.     

Truncated Estimation of Ratio Statistics with Application to Heavy Tail Distributions

The problem of estimation of the heavy tail index is revisited from the point of view of truncated estimation. A class of novel estimators is introduced having guaranteed accuracy based on a sample of fixed size. The performance of these estimators is quantified both theoretically and in simulations over a host of relevant examples. It is also shown that in several cases the proposed estimators attain — within a logarithmic factor — the optimal parametric rate of convergence. The property of uniform asymptotic normality of the proposed estimators is established.     

竞争风险数据和协变量相依权重下可加可乘的子分布风险率模型

本文在竞争风险数据下提出一种灵活的含变系数的可加可乘的子分布风险率模型.通过对删失时间的风险函数建立Cox比例风险模型,得到调整后的与协变量相依的权重,在新权重下建立估计方程来估计模型参数,并获得了估计的大样本性质,同时提出了模型中协变量的时变效应的检验方法.通过数值模拟验证了所提方法的有限样本性质,结果表明所提方法可以大大降低估计偏差.最后,分析了一组淋巴滤泡细胞的竞争风险数据集来展示所提方法的实际应用效果.     

Variable selection for semiparametric varying-coefficient partially linear models with missing response at random

In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

基于轮换样本连续性调查的校准组合估计方法研究

校准估计是抽样调查中比较常用的一种利用辅助信息提高估计量精度的方法。回归组合估计量作为轮换样本连续性调查中使用的一种有效的估计量,是可以通过校准程序得到的。基于回归组合估计量和校准程序之间的关系,本文提出了轮换样本连续性抽样调查条件下的不同校准组合估计量及其方差估计。校准组合估计量的主要思想是在校准估计程序中将拼配样本和非拼配样本的辅助信息进行不同的组合利用。本文利用美国现时人口调查的微观数据进行数值模拟,来比较不同校准组合估计量的估计效率,模拟结果表明两步校准组合估计量和两步校准双组合估计量的表现相似,且估计精度都高于H-T估计量及回归组合估计量;而两步校准组合估计量由于其简便性更适合应用于实践中。最后以我国农村住户连续性抽样调查为例,设计一套符合我国实际的轮换样本连续性调查方案,并将提出的校准组合估计量运用于估计阶段,为中国政府统计调查提供一定的借鉴和参考.     

Weighted composite quantile estimation and variable selection method for censored regression model

This paper considers the weighted composite quantile (WCQ) regression for linear model with random censoring. The adaptive penalized procedure for variable selection in this model is proposed, and the consistency, asymptotic normality and oracle property of the resulting estimators are also derived. The simulation studies and the analysis of an acute myocardial infarction data set are conducted to illustrate the finite sample performance of the proposed method.     

Reducing component estimation for varying coefficient models with longitudinal data

Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.     

Robust estimation for varying index coefficient models

Varying index coefficient models (VICMs) proposed by Ma and Song (J Am Stat Assoc, 2014. doi: 10.1080/01621459.2014.903185) are a new class of semiparametric models, which encompass most of the existing semiparametric models. So far, only the profile least squares method and local linear fitting were developed for the VICM, which are very sensitive to the outliers and will lose efficiency for the heavy tailed error distributions. In this paper, we propose an efficient and robust estimation procedure for the VICM based on modal regression which depends on a bandwidth. We establish the consistency and asymptotic normality of proposed estimators for index coefficients by utilizing profile spline modal regression method. The oracle property of estimators for the nonparametric functions is also established by utilizing a two-step spline backfitted local linear modal regression approach. In addition, we discuss the bandwidth selection for achieving better robustness and efficiency and propose a modified expectation–maximization-type algorithm for the proposed estimation procedure. Finally, simulation studies and a real data analysis are carried out to assess the finite sample performance of the proposed method.     

Testing for small bias of tail index estimators

We determine the joint asymptotic normality of kernel and weighted least-squares estimators of the upper tail index of a regularly varying distribution when each estimator is a bivariate function of two parameters: the tuning parameter is motivated by possible underlying second-order behavior in regular variation, while no such behavior is assumed, and the fraction parameter determines that upper portion of the sample on which the estimator is based. Under the hypothesis that the scaled asymptotic biases of the estimators vanish uniformly in the parameter points considered, these results imply joint asymptotic normality for deviations of ratios of the estimators from 1, which in turn yield asymptotic chi-square tests for checking the small-bias hypothesis, equivalent to the constructibility of asymptotic confidence intervals. The test procedure suggests adaptive choices of the tuning and fraction parameters: data-driven (t)estimators.     

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.     

响应变量随机缺失下变系数模型的变量选择

In this paper,we present a variable selection procedure by combining basis function approximations with penalized estimating equations for varying-coefficient models with missing response at random.With appropriate selection of the tuning parameters,we establish the consistency of the variable selection procedure and the optimal convergence rate of the regularized estimators.A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

Estimation and model selection in a class of semiparametric models for cluster data

Stimulated by a study in Bangladesh about the first birth interval, we propose a semivarying-coefficient model for cluster data analysis. We consider the estimation procedure for the proposed model and establish the asymptotic results of the proposed estimators. Furthermore, we employ the cross-validation (CV) to identify the constant coefficients. The associated asymptotic properties are rigorously examined. Simulation studies are conducted to investigate the performance of the proposed estimation and the CV-based model selection procedure for finite sample size. Finally, our methods are used to analyse the aforementioned data set to explore how several factors affect the first birth interval in Bangladesh.     

部分线性单指标模型的复合分位数回归及变量选择

本文提出复合最小化平均分位数损失估计方法 (composite minimizing average check loss estimation,CMACLE)用于实现部分线性单指标模型(partial linear single-index models,PLSIM)的复合分位数回归(composite quantile regression,CQR).首先基于高维核函数构造参数部分的复合分位数回归意义下的相合估计,在此相合估计的基础上,通过采用指标核函数进一步得到参数和非参数函数的可达最优收敛速度的估计,并建立所得估计的渐近正态性,比较PLSIM的CQR估计和最小平均方差估计(MAVE)的相对渐近效率.进一步地,本文提出CQR框架下PLSIM的变量选择方法,证明所提变量选择方法的oracle性质.随机模拟和实例分析验证了所提方法在有限样本时的表现,证实了所提方法的优良性.