Bootstrap classification and point-based feature selection from age-staged mouse cerebellum tissues of matrix assisted laser desorption/ionization mass spectra using a fuzzy rule-building expert system

A bootstrap method for point-based detection of candidate biomarker peaks has been developed from pattern classifiers. Point-based detection methods are advantageous in comparison to peak-based methods. Peak determination and selection are problematic when spectral peaks are not baseline resolved or on a varying baseline. The benefit of point-based detection is that peaks can be globally determined from the characteristic features of the entire data set (i.e., subsets of candidate points) as opposed to the traditional method of selecting peaks from individual spectra and then combining the peak list into a data set. The point-based method is demonstrated to be more effective and efficient using a synthetic data set when compared to using Mahalanobis distance for feature selection. In addition, probabilities that characterize the uniqueness of the peaks are determined.This method was applied for detecting peaks that characterize age-specific patterns of protein expression of developing and adult mouse cerebella from matrix assisted laser desorption/ionization (MALDI) mass spectrometry (MS) data. The mice comprised three age groups: 42 adults, 19 14-day-old pups, and 16 7-day-old pups. Three sequential spectra were obtained from each tissue section to yield 126, 57 and 48 spectra for adult, 14-day-old pup, and 7-day-old pup spectra, respectively. Each spectrum comprised 71,879 mass measurements in a range of 3.5-50 kDa. A previous study revealed that 846 unique peaks were detected that were consistent for 50% of the mice in each age group (C. Laurent, D.F. Levinson, S.A. Schwartz, P.B. Harrington, S.P. Markey, R.M. Caprioli, P. Levitt, Direct profiling of the cerebellum by MALDI MS: a methodological study in postnatal and adult mouse, J. Neurosci. Res. 81 (2005) 613-621.).A fuzzy rule-building expert system (FuRES) was applied to investigate the correlation of age with features in the MS data. FuRES detected two outlier pup-14 spectra. Prediction was evaluated using 100 bootstrap samples of 2 Latin-partitions (i.e., 50:50 split between training and prediction set) of the mice. The spectra without the outliers yielded classification rates of 99.1 ± 0.1%, 90.1 ± 0.8%, and 97.0 ± 0.6% for adults, 14-day-old pups, and 7-day-old pups, respectively. At a 95% level of significance, 100 bootstrap samples disclosed 35 adult and 21 pup distinguishing peaks for separating adults from pups; and 8 14-day-old and 15 7-day-old predictive peaks for separating 14-day-old pup from 7-day-old pup spectra. A compressed matrix comprising 40,393 points that were outside the 95% confidence intervals of one of the two FuRES discriminants was evaluated and the classification improved significantly for all classes. When peaks that satisfied a quality criterion were integrated, the 55 integrated peak areas furnished significantly improved classification for all classes: the selected peak areas furnished classification rates of 100%, 97.3 ± 0.6%, and 97.4 ± 0.3% for adult, 14-day-old pups, and 7-day-old pups using 100 bootstrap Latin partitions evaluations with the predictions averaged. When the bootstrap size was increased to 1000 samples, the results were not significantly affected. The FuRES predictions were consistent with those obtained by discriminant partial least squares (DPLS) classifications.     

The effect of objective formulation on retirement decision making

For a retiree who must maintain both investment and longevity risks, we consider the impact on decision making of focusing on an objective relating to the terminal wealth at retirement, instead of a more correct objective relating to a retirement income. Both a shortfall and a utility objective are considered; we argue that shortfall objectives may be inappropriate due to distortion in results with non-monotonically correlated economic factors. The modelling undertaken uses a dynamic programming approach in conjunction with Monte-Carlo simulations of future experience of an individual to make optimal choices. We find that the type of objective targetted can have a significant impact on the optimal choices made, with optimal equity allocations being up to 30% higher and contribution amounts also being significantly higher under a retirement income objective as compared to a terminal wealth objective. The result of these differences can have a significant impact on retirement outcomes.     

An Algorithm for Robust Inference for the Cox Model with Frailties

Abstract

This article proposes a robust method of statistical inference for the Cox's proportional hazards model with frailties. We use the Metropolis—Hastings algorithm and the bootstrap method. We present a computationally efficient algorithm with a customized data structure to implement this method and demonstrate this technique with real data.     

非参数回归函数的稳健Bootstrap

在有异常值的数据中,Bootstrap样本可能比原有样本含有更高的“污染”,这会降低所要做的统计推断的有效性.本文讨论在非参数回归N-W估计中,如何利用影响函数得到重新抽样的概率,使用倾斜的Bootstrap方法得到曲线的拟合,从而达到有效地抵制异常值对回归函数影响的目的,数值模拟的结果表明这种处理方式的有效性.     

Sensitivity analysis of efficiency and Malmquist productivity indices: An application to Spanish savings banks

Hypothesis testing and statistical precision in the context of non-parametric efficiency and productivity measurement have been investigated since the early 1990s. Recent contributions focus on this matter through the use of resampling methods—i.e., bootstrapping techniques. However, empirical evidence is still practically non-existent. This gap is more noticeable in the case of banking efficiency studies, where the literature is immense. In this work, we explore productivity growth and productive efficiency for Spanish savings banks over the (initial) post-deregulation period 1992–1998 using Data Envelopment Analysis (DEA) and bootstrapping techniques. Results show that productivity growth has occurred, mainly due to improvement in production possibilities, and that mean efficiency has remained fairly constant over time. The bootstrap analysis yields further evidence, as for many firms productivity growth, or decline, is not statistically significant. With regard to efficiency measurement, the bootstrap reveals that the disparities in the original efficiency scores of some firms are lessened to a great extent.     

ALTERNATIVE MEASURES OF THE EXPLANATORY POWER OF GENERAL MULTIVARIATE REGRESSION MODELS

In this paper R ²-type measures of the explanatory power of multivariate linear and categorical probit models proposed in the literature are reviewed and their deficiencies discussed. It is argued that a measure of the explanatory power should take into account the components which are explicitly modelled when a regression model is estimated while it should be indifferent to components not explicitly modelled. Based on this view three different measures for multivariate probit models are proposed. Results of a simulation study are presented, designed to compare two measures in various situations, to evaluate the BC _a bootstrap technique for testing the hypothesis that the corresponding measure is zero, and to calculate approximate confidence intervals. The BC _a bootstrap technique turned out to work quite well for a wide range of situations, but may lead to misleading results if the true values of the corresponding measure are close to zero.     

A bootstrap-based aggregate classifier for model-based clustering

In model-based clustering, a situation in which true class labels are unknown and that is therefore also referred to as unsupervised learning, observations are typically classified by the Bayes modal rule. In this study, we assess whether alternative classifiers from the classification or supervised-learning literature—developed for situations in which class labels are known—can improve the Bayes rule. More specifically, we investigate the performance of bootstrap-based aggregate (bagging) rules after adapting these to the model-based clustering context. It is argued that specific issues, such as the label-switching problem, have to be carefully addressed when using bootstrap methods in model-based clustering. Our two Monte Carlo studies show that classification based on the Bayes rule is rather stable and difficult to improve by bootstrap-based aggregate rules, even for sparse data. An empirical example illustrates the various approaches described in this paper.     

改进的Bootstrap方法对比及应用研究

本文针对小样本情形,在不改变原样本的情况下,对原样本的最大(最小)次序统计量进行领域上的扩充,以克服原来自助样本生成范围上的限制.这将在尽可能保持分布特性一致的情形下,大大降低其与原观测样本的相似性,同时也将数据分布的特性拓展至非观测点,它是一种近似,在尽可能少的偏离真实分布的前提下,实现了对真实分布的自助探索.本文针对样本量在10到30之间的时候所做的改进.最后,将改进的Bootstrap方法应用于工程可靠性指标的计算,从而检验方法的可行性.     

On bootstrap estimation of the distribution of the studentized mean

It is shown that bootstrap methods for estimating the distribution of the Studentized mean produce consistent estimators in quite general contexts, demanding not a lot more than existence of finite mean. In particular, neither the sample mean (suitably normalized) nor the Studentized mean need converge in distribution. It is unnecessary to assume that the sampling distribution is in the domain of attraction of any limit law.Now at Michigan State University