Simple resampling methods of approximating the distribution of LAD estimators for doubly censored regression models

Recently, least absolute deviation (LAD) estimator for median regression models with doubly censored data was proposed and the asymptotic normality of the estimator was established, and the methods based on bootstrap and random weighting were proposed respectively to approximate the distribution of the LAD estimators. But the calculation of the estimators requires solving a non-convex and non-smooth minimization problem, resulting in high computational costs in implementing the bootstrap or random weighting method directly. In this paper, computationally simple resampling methods are proposed to approximate the distribution of the doubly censored LAD estimators. The objective functions in the resampling stage of the new methods are piece-wise linear and convex, and their minimizer can be obtained by the linear programming in the same way as that for the case of uncensored median regression.     

A bootstrap test for symmetry based on ranked set samples

To test the hypothesis of symmetry about an unknown median we propose the maximum of a partial sum process based on ranked set samples. We discuss the properties of the test statistic and investigate a modified bootstrap ranked set sample bootstrap procedure to obtain its sampling distribution. The power of the new test statistic is compared with two existing tests in a simulation study.     

Balanced bootstrap resampling method for neural model selection

Uniform resampling is the easiest to apply and is a general recipe for all problems, but it may require a large replication size B. To save computational effort in uniform resampling, balanced bootstrap resampling is proposed to change the bootstrap resampling plan. This resampling plan is effective for approximating the center of the bootstrap distribution. Therefore, this paper applies it to neural model selection. Numerical experiments indicate that it is possible to considerably reduce the replication size B. Moreover, the efficiency of balanced bootstrap resampling is also discussed in this paper.     

Repeated measures analysis for functional data

Most of the traditional statistical methods are being adapted to the Functional Data Analysis (FDA) context. The repeated measures analysis which deals with the k-sample problem when the data are from the same subjects is investigated. Both the parametric and the nonparametric approaches are considered. Asymptotic, permutation and bootstrap approximations for the statistic distribution are developed. In order to explore the statistical power of the proposed methods in different scenarios, a Monte Carlo simulation study is carried out. The results suggest that the studied methodology can detect small differences between curves even with small sample sizes.     

LS-SVM模型选择的秩准则及其比较

在最小二乘支持向量机的模型选择问题中,基于再抽样技术的模型选择方法,不能从根本上解决计算强度过高的问题。为此,提出基于模型复杂程度进行惩罚的新方法——秩准则,给出估计最小二乘支持向量机调谐参数的快速稳健算法。实例研究表明,该方法不仅能保证模型的预测精度和稳健性,而且在计算速度上优于快速Bootstrap方法。     

Productivity of wastewater treatment plants in the Valencia Region of Spain

This study analyses the evolution of productivity over the 2008–2012 period for a homogenous set of 199 wastewater treatment plants that are located in the Valencia Region of Spain and utilize the same treatment technology, using the smoothed bootstrap Malmquist productivity index based on Data Envelopment Analysis (DEA). The results reveal a negative trend in productivity that is mainly the result of resource management rather than an inappropriate level of innovation or use of new technologies. In addition, the effect of exogenous factors on productivity is analysed using the Kruskal-Wallis (KW) test, finding that productivity levels were affected by the quality of the influent water and the size of the plants, but not by the other factors considered.     

Estimation of uncertainty of percentile values in particle size distribution analysis as a function of number of particles

In the analysis of particle size distribution (PSD), evaluation of the uncertainty of the percentile values is often required. Both theoretical and data processing methods are applicable to estimate standard deviations of percentile values. In this paper, a theory, applicable both in paramedic and non-parametric ways, is introduced. As a practical example, theoretical results based on a lognormal distribution are compared to those obtained by bootstrap method. Excellent agreement is demonstrated between the theory and the direct data processing method.     

Large-sample inference in the general AR(1) model

The situation where the available data arise from a general AR(1) model is discussed, and two new avenues for constructing confidence intervals for the unknown autoregressive root are proposed, one based on a Central Limit Theorem, and the other based on the block-bootstrap. The two new methodologies rely on clever preprocessing of the original series, and are subsequently free of the difficulties present in previous methods that were due to data nonstationarity and/or discontinuity in the limit distribution in the case of a unit root. Some finite-sample simulations are also presented supporting the applicability of the proposed methods, and the problem of bootstrap block size choice is discussed. Research partly supported by NSF Grant DMS-97-03964.     

Bootstrap FDA for counting positives accurately in imprecise environments

Many real-world classification tasks involve discriminations between two unbalanced classes in imprecise environments, in which either the training data do not represent a random sample of the target population or the class distribution may shift over time in the target population. In such situations, in order to minimize the misclassification costs, the class distribution in target population must be known for selecting the optimal threshold. Forman has presented a method, based on the distribution generated on training data and the distribution on unlabeled test data, for estimating the number of positives in target population. However, when the data size is small, it is difficult to reliably generate these distributions for estimating the number of positives. This paper presents a novel algorithm to generate these distributions based on the bootstrap and Fisher discriminant analysis. Experiment results on five UCI data sets demonstrate its effectiveness.     

Nonparametric inference with generalized likelihood ratio tests

The advance of technology facilitates the collection of statistical data. Flexible and refined statistical models are widely sought in a large array of statistical problems. The question arises frequently whether or not a family of parametric or nonparametric models fit adequately the given data. In this paper we give a selective overview on nonparametric inferences using generalized likelihood ratio (GLR) statistics. We introduce generalized likelihood ratio statistics to test various null hypotheses against nonparametric alternatives. The trade-off between the flexibility of alternative models and the power of the statistical tests is emphasized. Well-established Wilks’ phenomena are discussed for a variety of semi- and non-parametric models, which sheds light on other research using GLR tests. A number of open topics worthy of further study are given in a discussion section. This invited paper is discussed in the comments available at: , , , , , , , , . The work was supported by the NSF grants DMS-0354223, DMS-0532370 and DMS-0704337. The paper was initiated when Jiancheng Jiang was a research fellow at Princeton University.