Kernel‐based Generalized Cross‐validation in Non‐parametric Mixed‐effect Models

Abstract. Although generalized cross‐validation (GCV) has been frequently applied to select bandwidth when kernel methods are used to estimate non‐parametric mixed‐effect models in which non‐parametric mean functions are used to model covariate effects, and additive random effects are applied to account for overdispersion and correlation, the optimality of the GCV has not yet been explored. In this article, we construct a kernel estimator of the non‐parametric mean function. An equivalence between the kernel estimator and a weighted least square type estimator is provided, and the optimality of the GCV‐based bandwidth is investigated. The theoretical derivations also show that kernel‐based and spline‐based GCV give very similar asymptotic results. This provides us with a solid base to use kernel estimation for mixed‐effect models. Simulation studies are undertaken to investigate the empirical performance of the GCV. A real data example is analysed for illustration.     

以人为本：社会主义核心价值体系的理论前提

以人为本是社会主义核心价值体系区别于以往任何二种价值体系的根本所在，社会主义核心价值体系的四方面内容均蕴涵着以人为本的原则。在当前大力建设这一核心价值体系的过程中，我们还应充分认识和挖掘以人为本在其中的意义和作用。     

Random sequential packing in Rn

We introduce a Monte Carlo method for packing hypercubes in Rⁿ . Rigorous and conceptually simple, it is currently practical for n≥4. Experimental results indicate that Palasti's conjecture is false for R ² and K³ and still undecided for K⁴     

A Simulation Study of the Performance of Five Discriminant Analysis Methods for Mixtures of Continuous and Binary Variables

The present study investigates the performance of fice discrimination methods for data consisting of a mixture of continuous and binary variables. The methods are Fisher’s linear discrimination, logistic discrimination, quadratic discrimination, a kernal model and an independence model. Six-dimensional data, consisting of three binary and three continuous variables, are simulated according to a location model. The results show an almost identical performance for Fisher’s linear discrimination and logistic discrimination. Only in situations with independently distributed variables the independence model does have a reasonable discriminatory ability for the dimensionality considered. If the log likelihood ratio is non-linear ratio is non-linear with respect to its continuous and binary part, the quadratic discrimination method is substantial better than linear and logistic discrimination, followed by the kernel method. A very good performance is obtained when in every situation the better one of linear and quardratic discrimination is used.     

Testing exponentiality using transformed data

In this paper, we introduce a test for uniformity and use it as the second stage of an exact goodness-of-fit test of exponentiality. By simulation, the powers of the proposed test under various alternatives are compared with exponentiality test based on Kullback–Leibler information proposed by Ebrahimi et al. [N. Ebrahimi, M. Habibullah, and E.S. Soofi, Testing exponentiality based on Kullback–Leiber information, J. R. Statist. Soc. Ser. B 54 (1992), pp. 739–748]. The results are impressive, i.e. the proposed test has higher power than the test based on entropy.     

A comparioson of nonparametric unweighited and length-biased density estimation of fibres

Two sampling procedures used to estimate the distribution of the length of textile fibres are studied . Estimators of the density function of fibre length and the asymptotic propertiesof these estimators are discussed. Simulations were undertaken to compare mean square errors of the estimators for various saniple sizes.     

股指期权定价的非参数数值方法研究

扩散过程估计的参数化方法存在先入为主的不足,并且扩散项函数形式的设定十分困难,而非参数方法不需要数据产生过程的先验信息,直接从数据出发估计扩散函数,克服了以上不足。本文提出了一种基于连续时间过程的非参数股指期权定价模型。对于刻画基础资产动态行为特性的扩散函数不加任何函数形式限制,利用离散数据匹配密度函数构造它的非参数估计,进而计算股指期权的均衡价格。论文从理论上论证了扩散项估计的一致性和渐进正态性。实证研究表明,该方法对于实际市场价格具有较高的拟合效果,特别是在市场波动剧烈时期,非参数方法更优于经典B-S方法。     

基于三螺旋理论的大学生机会型创业研究

鉴于机会型创业在拉动经济增长、创造更多就业岗位以及取得更多社会经济收益方面发挥的重要作用,为鼓励大学生从事机会型创业、提高机会型创业的成功率,基于三螺旋理论从大学、产业和政府的互动合作中探索三者的交互作用对大学生机会型创业的影响机制。据此提出促进大学生机会型创业的对策建议：高校应激发大学生的创业意识,提升大学生的创业技能;产业应促进新知识的传播和共享,加强大生科技成果的转化;政府应完善对创业的政策扶持,营造大学生创业的制度环境。     

Computation of the run-length percentiles of CUSUM control charts under changes in variances

In this paper, the run-length distributions of cumulative sum (CUSUM) charts for monitoring mean changes under normal distributions have been investigated thoroughly. However, there are few studies devoted to the analysis of the run-length distributions of CUSUM charts under changes in process variances. Motivated by this, this paper develops a fast and accurate algorithm based on piecewise collocation method for computing the run-length distributions of CUSUM scale charts. It is shown that the proposed method can provide more accurate approximation to the run-length distribution than the conventional Gauss-type quadrature-based methods applied to the CUSUM location charts. Some computational aspects for facilitating computation load are discussed, including the alternative formulation based on matrix decomposition and the geometric approximation to the distribution of large run lengths.     

Reducing data dimension for cluster detection

Clustering high-dimensional data is often a challenging task both because of the computational burden required to run any technique, and because the difficulty in interpreting clusters generally increases with the data dimension. In this work, a method for finding low-dimensional representations of high-dimensional data is discussed, specifically conceived to preserve possible clusters in data. It is based on the critical bandwidth, a nonparametric statistic to test unimodality, related to kernel density estimation. Some useful properties of the aforementioned statistic are enlightened and an adjustment to use it as a basis for reducing dimensionality is suggested. The method is illustrated by simulated and real data examples.