On the role of the shrinkage parameter in local linear smoothing

Summary. It has been shown that local linear smoothing possesses a variety of very attractive properties, not least being its mean square performance. However, such results typically refer only to asymptotic mean squared error, meaning the mean squared error of the asymptotic distribution, and in fact, the actual mean squared error is often infinite. See Seifert and Gasser (1996). This difficulty may be overcome by shrinking the local linear estimator towards another estimator with bounded mean square. However, that approach requires information about the size of the shrinkage parameter. From at least a theoretical viewpoint, very little is known about the effects of shrinkage. In particular, it is not clear how small the shrinkage parameter may be chosen without affecting first-order properties, or whether infinitely supported kernels such as the Gaussian require shrinkage in order to achieve first-order optimal performance. In the present paper we provide concise and definitive answers to such questions, in the context of general ridged and shrunken local linear estimators. We produce necessary and sufficient conditions on the size of the shrinkage parameter that ensure the traditional mean squared error formula. We show that a wide variety of infinitely-supported kernels, with tails even lighter than those of the Gaussian kernel, do not require any shrinkage at all in order to achieve traditional first-order optimal mean square performance. Received: 22 May 1995 / In revised form: 23 January 1997     

肝胆胰系统住院病人医疗费用的多因素分析

本文以武汉市某大医院１９９５年肝胆胰系统出院病例为研究样本，采用逐步回归和岭回归方法拟合模型，对医疗费用进行了多病种、多因素研究。研究结果表明，社会学因素、病种因素、病情因素、手术因素、护理因素等对住院费用和住院天数均有不同程度的影响，并且发现ＭＤＣ７疾病与胆囊结石单一疾病的多因素分析效果十分相近。     

Estimating function with asymptotic bias and its estimator

We introduce the estimating function with asymptotic bias and investigate the asymptotic behavior of the estimator based on it by using their relationship. The estimator based on the estimating function with asymptotic bias has the asymptotic normality with asymptotic bias. We show that this theory has several interesting applications in practical statistics.     

多元线性模型中两类预测的最优性判别

在一般多元线性模型中就基于岭估计的预测量与最优线性无偏预测量的最优性判别问题进行了讨论,得到了基于岭估计的预测量在矩阵迹意义下优于最优线性无偏预测量的充要条件.     

采用小波脊系数幅值导数方差质量图的相位展开法

针对小波变换轮廓术中相位无法快速准确展开的问题,提出了一种能有效抑制噪音的相位展开算法.首先,分析了小波脊系数幅值质量图和相位导数方差质量图的特征;然后依据相位值与其数学期望的偏差程度,利用小波脊系数幅值矩阵和导数方差思想构造了"小波脊系数幅值导数方差"质量图;最后分别进行软件仿真和真实模型实验,并将利用新质量图引导的相位展开效果与传统相位展开质量图法和改进的质量图法进行对比.实验结果表明,本文算法提高了相位展开精确度,相位展开误差率降低了2.61%.所提质量图易于构造,在引导相位展开时不仅能得到较准确的绝对相位值,还能有效抑制噪音的影响,从而重建出精确度高的物体三维模型.     

Application of a genomic model for high‐dimensional chemometric analysis

The rapid development of new technologies for large‐scale analysis of genetic variation in the genomes of individuals and populations has presented statistical geneticists with a grand challenge to develop efficient methods for identifying the small proportion of all identified genetic polymorphisms that have effects on traits of interest. To address such a “large p small n” problem, we have developed a heteroscedastic effects model (HEM) that has been shown to be powerful in high‐throughput genetic analyses. Here, we describe how this whole‐genome model can also be utilized in chemometric analysis. As a proof of concept, we use HEM to predict analyte concentrations in silage using Fourier transform infrared spectroscopy signals. The results show that HEM often outperforms the classic methods and in addition to this presents a substantial computational advantage in the analyses of such high‐dimensional data. The results thus show the value of taking an interdisciplinary approach to chemometric analysis and indicate that large‐scale genomic models can be a promising new approach for chemometric analysis that deserve to be evaluated more by experts in the field. The software used for our analyses is freely available as an R package at http://cran.r‐project.org/web/packages/bigRR/ . Copyright © 2014 John Wiley & Sons, Ltd.