Nonparametric Kernel Methods with Errors‐in‐Variables: Constructing Estimators,Computing them,and Avoiding Common Mistakes

Estimating a curve nonparametrically from data measured with error is a difficult problem that has been studied by many authors. Constructing a consistent estimator in this context can sometimes be quite challenging, and in this paper we review some of the tools that have been developed in the literature for kernel‐based approaches, founded on the Fourier transform and a more general unbiased score technique. We use those tools to rederive some of the existing nonparametric density and regression estimators for data contaminated by classical or Berkson errors, and discuss how to compute these estimators in practice. We also review some mistakes made by those working in the area, and highlight a number of problems with an existing R package decon .     

Optimal Bandwidth Selection in Heteroskedasticity–Autocorrelation Robust Testing

This paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors. The studentization is based on robust standard errors with truncation lag M=bT for some constant b∈(0, 1] and sample size T. It is shown that the nonstandard fixed‐b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the finite sample distributions than the standard small‐b limit distribution. We further show that, for typical economic time series, the optimal bandwidth that minimizes a weighted average of type I and type II errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long‐run variance estimator. A plug‐in procedure for implementing this optimal bandwidth is suggested and simulations (not reported here) confirm that the new plug‐in procedure works well in finite samples.     

An evaluation of the performance of kernel estimators for graduating mortality data

In the graduation of the age-specific mortality pattern, recent emphasis has been placed on the use of kernel regression estimators. Three such estimators are the Nadaraya-Watson, Gasser-Muller and kernel weighted local linear estimators. This paper discusses the theoretical background of each estimator and evaluates their accuracy in graduating age-specific mortality using data for France, Japan and Sweden. For comparison, we also fit the Heligman-Pollard model and its nine-parameter variant by Kostaki. The Gasser-Muller estimator is found to be superior to the two other kernel estimators in that it is both more stable and not influenced by boundary effects. Furthermore, compared with the two parametrric models, the Gasser-Muller estimator provides a more satisfactory graduation, especially at older adult ages, in terms both of smoothness and of fidelity between the observed and graduated rates.     

不同带宽ISP 的定价博弈与结盟动因分析

不同带宽的网络接入服务商( ISP) 需要有不同的定价策略. 在消费者的单位时间成本不 同情况下,分析了网络接入商的定价博弈. 通过比较静态和动态的纳什均衡价格与收益,得到 了接入服务商的先动优势,也得到了技术进步对宽带接入的有利性. 然后分析了形成价格联盟 后的最优定价,得出了不同带宽的接入服务商之间具有形成价格联盟的激励的结论,并使窄带 接入退出市场. 最后探讨了结成价格联盟以后社会总福利的变化情况,指出这种结盟对于社会 整体来说是无益的.     

Nonparametric kernel estimation of expected shortfall under negatively associated sequences

Abstract

In this article, Bahadur type expansions of a nonparametric kernel estimator for ES under NA sequences are given. The strong consistency and the uniformly asymptotic normality of the estimator are yielded from the Bahadur type expansions, while the convergence rates of the above asymptotic properties are also obtained. Moreover, the expectation, the variance and the mean squared error (MSE) of the estimator are given. Besides, the optimal bandwidth selection of this estimator is discussed. We point out that all above results are based on the NA sequences. Finally, we conduct numerical simulations and compare performances of some ES estimators.     

一种增益可调CMOS恒带宽单片放大器

基于电流跟随器和负反馈原理，并结合电流镜像与虚地技术，得到了一种具有不依赖于闭环电压增益的１２０ｋＨｚ～８ＭＨｚ恒定带宽，增益０～６０ｄＢ可调，最高稳定工作频率５ＭＨｚ，功耗５．２ｍＷ的高性能ＣＭＯＳ放大器，其ＳＰＩＣＥ模拟表明，该放大器电气性能优越，模拟结果与理论分析比较吻合；可采用３～５μｍ硅栅ＣＭＯＳ工艺技术单片化集成实现，并可望用于宽带视频放大等模拟信号处理领域。     

改善相控阵天线工作带宽的技术途径研究

从空间色散和时间色散两方面讨论了常规相控阵天线的窄带特性。从时域阵列理论出发，着重研究了改善相控阵天线工作带宽的技术途径，分析了这些技术措施对天线辐射特性可能造成的影响，供后续工作参考。     

EPON上行接入算法研究

介绍了以太无源光网络中一种新的光线路终端和光网络单元的上行接入算法,给出了一种新的下行授权帧结构,在授权帧中,通过固定的标示各光网络单元地址,将各光网络单元授权集中于一个下行授权帧中,各光网络单元也参与上行接入计算,提高了上下行带宽利用率,通过仿真比较,该算法同时具有良好的时延特性。     

Partitioned cross-validation

Partitioned cross-validation is proposed as a method for overcoming the large amounts of across sample variability to which ordinary cross-validation is subject. The price for cutting down on the sample noise is that a type of bias is intriduced. A theory is presented for optimal trade-off of this variance and bias. Comparison with other bandwidth selection methods is given.     

Inference after variable selection using restricted permutation methods

When confronted with multiple covariates and a response variable, analysts sometimes apply a variable‐selection algorithm to the covariate‐response data to identify a subset of covariates potentially associated with the response, and then wish to make inferences about parameters in a model for the marginal association between the selected covariates and the response. If an independent data set were available, the parameters of interest could be estimated by using standard inference methods to fit the postulated marginal model to the independent data set. However, when applied to the same data set used by the variable selector, standard (“naive”) methods can lead to distorted inferences. The authors develop testing and interval estimation methods for parameters reflecting the marginal association between the selected covariates and response variable, based on the same data set used for variable selection. They provide theoretical justification for the proposed methods, present results to guide their implementation, and use simulations to assess and compare their performance to a sample‐splitting approach. The methods are illustrated with data from a recent AIDS study. The Canadian Journal of Statistics 37: 625–644; 2009 © 2009 Statistical Society of Canada