Empirical likelihood inference for error density estimators in first-order autoregression models

In this paper we apply empirical likelihood method to the error density estimators in first-order autoregressive models under some mild conditions. The log-likelihood ratio statistic is shown to be asymptotically chi-squared distributed at a fixed point. In simulation, we show that the empirical likelihood produces confidence intervals having theoretical coverage accuracy which is better than normal approximation.     

具有核化函数的部分线性模型及其应用

本文基于再生核希尔伯特空间中的再生核，将核技巧与高斯-赛责尔迭代算法相结合，提出了具有核化函数的部分线性模型（PLMKF）及其算法收敛性条件等相关内容，具体包括：（1）基于OLS的PLMKF；（2）基于岭估计的PLMKF；（3）基于GLS的PLMKF；（4）基于多核学习的PLMKF。它们构成了PLMKF家族，具有一定的相互转化关系。在数值模拟中，本文验证了各个算法的有效性，比较了基于OLS与GLS、单核与多核的PLMKF模拟结果。实际应用中，在大幅外推情景下，PLMKF仍保持了良好的泛化能力，预测精度高于PLM、GAM和SVR。     

Kernel density estimation for hierarchical data

Abstract

Multistage sampling is a common sampling technique employed in many studies. In this setting, observations are identically distributed but not independent, thus many traditional kernel smoothing techniques, which assume that the data are independent and identically distributed (i.i.d.), may not produce reasonable density estimates. In this paper, we sample repeatedly with replacement from each cluster, create multiple i.i.d. samples containing one observation from each cluster, and then create a kernel density estimate from each i.i.d. sample. These estimates will then be combined to form an estimate of the marginal probability density function of the population.     

Diagnostic measures for kernel ridge regression on reproducing kernel Hilbert space

The aim of this paper is to define and develop diagnostic measures with respect to kernel ridge regression in a reproducing kernel Hilbert space (RKHS). To identify influential observations, we define a particular version of Cook’s distance for the kernel ridge regression model in RKHS, which is conceptually consistent with Cook’s distance in a classical regression model. Then, by using the perturbation formula for the regularized conditional expectation of the outcome in RKHS, we develop an approximate version of Cook”s distance in RKHS because the original definition requires intensive computations. Such an approximated Cook”s distance is represented in terms of basic building blocks such as residuals and leverages of the kernel ridge regression. The results of the simulation and real application demonstrate that our diagnostic measure successfully detects potentially influential observations on estimators in kernel ridge regression.     

Goodness-of-fit test under length-biased sampling

In this article, we study a goodness-of-fit (GOF) test in the presence of length-biased sampling. For this purpose, we introduce a smoothed estimator of distribution function (d.f.) and we investigate its asymptotic behaviors, such as uniform consistency and asymptotic normality. Based on this estimator, we define a one-sample Kolmogorov type of GOF test for length-biased data. We conduct Monte Carlo simulations to evaluate the performance of the proposed test statistic and compare it with the one-sample Kolmogorov type of GOF test obtained by the non smoothed estimator of d.f.     

Rate-optimal nonparametric estimation in classical and Berkson errors-in-variables problems

We consider nonparametric estimation of a regression curve when the data are observed with Berkson errors or with a mixture of classical and Berkson errors. In this context, other existing nonparametric procedures can either estimate the regression curve consistently on a very small interval or require complicated inversion of an estimator of the Fourier transform of a nonparametric regression estimator. We introduce a new estimation procedure which is simpler to implement, and study its asymptotic properties. We derive convergence rates which are faster than those previously obtained in the literature, and we prove that these rates are optimal. We suggest a data-driven bandwidth selector and apply our method to some simulated examples.     

农村居民收入分布的动态演进及趋势

采用核密度估计法和马尔可夫链方法,对我国农村居民人均纯收入分布的动态演进及趋势进行了分析。结果表明:90年代以来,农村居民人均纯收入分布都呈现明显的"双峰"状,一直处于两极分化状态。从其分项收入来看,家庭经营性收入和工资性收入差距不断扩大,而财产性收入和转移性收入由"双峰"演变为"单峰"状,两极分化现象逐渐消失,收入差距缩小。从马尔可夫链的稳态分布来看,各地区的农村居民人均纯收入将仍然保持较大差异,短期内难以实现均衡发展。     

Survival analysis for the inverse Gaussian distribution with the Gibbs sampler

This paper describes a comprehensive survival analysis for the inverse Gaussian distribution employing Bayesian and Fiducial approaches. It focuses on making inferences on the inverse Gaussian (IG) parameters μ and λ and the average remaining time of censored units. A flexible Gibbs sampling approach applicable in the presence of censoring is discussed and illustrations with Type II, progressive Type II, and random rightly censored observations are included. The analyses are performed using both simulated IG data and empirical data examples. Further, the bootstrap comparisons are made between the Bayesian and Fiducial estimates. It is concluded that the shape parameter ( ϕ=λ/μ) of the inverse Gaussian distribution has the most impact on the two analyses, Bayesian vs. Fiducial, and so does the size of censoring in data to a lesser extent. Overall, both these approaches are effective in estimating IG parameters and the average remaining lifetime. The suggested Gibbs sampler allowed a great deal of flexibility in implementation for all types of censoring considered.