A comparison of robust estimators based on two types of trimming

The least trimmed squares (LTS) estimator and the trimmed mean (TM) are two well-known trimming-based estimators of the location parameter. Both estimates are used in practice, and they are implemented in standard statistical software (e.g., S-PLUS, R, Matlab, SAS). The breakdown point of each of these estimators increases as the trimming proportion increases, while the efficiency decreases. Here we have shown that for a wide range of distributions with exponential and polynomial tails, TM is asymptotically more efficient than LTS as an estimator of the location parameter, when they have equal breakdown points.     

DASSO: connections between the Dantzig selector and lasso

Summary.  We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the least angle regression algorithm that is used to compute the lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to the least angle regression algorithm. Comparison of the two algorithms sheds new light on the question of how the lasso and Dantzig selector are related. In addition, we provide theoretical conditions on the design matrix X under which the lasso and Dantzig selector coefficient estimates will be identical for certain tuning parameters. As a consequence, in many instances, we can extend the powerful non-asymptotic bounds that have been developed for the Dantzig selector to the lasso. Finally, through empirical studies of simulated and real world data sets we show that in practice, when the bounds hold for the Dantzig selector, they almost always also hold for the lasso.     

LSE method using the CHSS model

Testing the reliability at a nominal stress level may lead to extensive test time. Estimations of reliability parameters can be obtained faster thanks to step-stress accelerated life tests (ALT). Usually, a transfer functional defined among a given class of parametric functions is required, but Bagdonavi?ius and Nikulin showed that ALT tests are still possible without any assumption about this functional. When shape and scale parameters of the lifetime distribution change with the stress level, they suggested an ALT method using a model called CHanging Shape and Scale (CHSS). They estimated the lifetime parameters at the nominal stress with maximum likelihood estimation (MLE). However, this method usually requires an initialization of lifetime parameters, which may be difficult when no similar product has been tested before. This paper aims to face this issue by using an iterating least square estimation (LSE) method. It will enable one to initialize the optimization required to carry out the MLE and it will give estimations that can sometimes be better than those given by MLE.     

Asymptotics of cross-validated risk estimation in estimator selection and performance assessment

Risk estimation is an important statistical question for the purposes of selecting a good estimator (i.e., model selection) and assessing its performance (i.e., estimating generalization error). This article introduces a general framework for cross-validation and derives distributional properties of cross-validated risk estimators in the context of estimator selection and performance assessment. Arbitrary classes of estimators are considered, including density estimators and predictors for both continuous and polychotomous outcomes. Results are provided for general full data loss functions (e.g., absolute and squared error, indicator, negative log density). A broad definition of cross-validation is used in order to cover leave-one-out cross-validation, V-fold cross-validation, Monte Carlo cross-validation, and bootstrap procedures. For estimator selection, finite sample risk bounds are derived and applied to establish the asymptotic optimality of cross-validation, in the sense that a selector based on a cross-validated risk estimator performs asymptotically as well as an optimal oracle selector based on the risk under the true, unknown data generating distribution. The asymptotic results are derived under the assumption that the size of the validation sets converges to infinity and hence do not cover leave-one-out cross-validation. For performance assessment, cross-validated risk estimators are shown to be consistent and asymptotically linear for the risk under the true data generating distribution and confidence intervals are derived for this unknown risk. Unlike previously published results, the theorems derived in this and our related articles apply to general data generating distributions, loss functions (i.e., parameters), estimators, and cross-validation procedures.     

主成分估计的应用探讨

本文首次把主成分估计的方法应用于动物性状的多元线性回归模型中复共性线之克服，结果表明由此法所获得的回归参数的估计不但在数值上较最小二乘估计合理，而且还在一定意义上使得被共线性扭曲了的变量间的关系得到恢复，从而提高了模型的预测精度。     

A consistency result in general censoring models

In this paper we prove a consistency result for sieved maximum likelihood estimators of the density in general random censoring models with covariates. The proof is based on the method of functional estimation. The estimation error is decomposed in a deterministic approximation error and the stochastic estimation error. The main part of the proof is to establish a uniform law of large numbers for the conditional log-likelihood functional, by using results and techniques from empirical process theory.     

Weighted Median of the Data in Solving Least Absolute Deviations Problems

We consider the weighted median problem for a given set of data and analyze its main properties. As an illustration, an efficient method for searching for a weighted Least Absolute Deviations (LAD)-line is given, which is used as the basis for solving various linear and nonlinear LAD-problems occurring in applications. Our method is illustrated by an example of hourly natural gas consumption forecast.     

内生结构突变下的突变点确定方法与单位根检验研究 ——基于残差平方和最小值确定突变点的比较分析

 对于内生突变情形下的单位根检验,突变点的确定方法会影响到单位根检验的功效,不同方法在确定突变点位置时的表现也不尽相同。本文首先评述了几种常用的突变点确定方法及相应的单位根检验,然后对基于各类回归式残差平方和最小值确定突变点的方法进行了比较分析,本文所设数据生成过程有别于已有研究,并首次考虑了依据可行广义最小二乘（FGLS）估计来确定突变点。在此基础上,还对比分析了几种不同突变点确定方法下的单位根检验功效和实际检验水平。结论显示,依据FGLS残差平方和最小值得到准确突变点的频率最高,且在AO模型下据此进行Perron检验具有较高的功效且不会发生较大的水平扭曲。     

基于ARFIMA(p, d, q)过程的半参数估计量分布特征及其有偏性研究7737976300

 本文运用蒙特卡罗模拟的方法对小样本下长记忆性的三种半参数估计量的分布特征尤其是有偏性问题进行了深入分析,结果发现,当长记忆和短记忆同时存在时,在大多数情况下,各参数估计量仍然服从正态分布,因此在小样本下仍可以构造t统计量判别参数的显著性,但由于受到短期参数的影响,估计量的分布是有偏的,因此导致参数的估计和检验出现偏差。而当真实数据过程接近非平稳或过度差分时,半参数估计量的分布也会发生改变。     

R 2 Measures Based on Wald and Likelihood Ratio Joint Significance Tests

Two methods are suggested for generating R ² measures for a wide class of models. These measures are linked to the R ² of the standard linear regression model through Wald and likelihood ratio statistics for testing the joint significance of the explanatory variables. Some currently used R ²'s are shown to be special cases of these methods.