Multiple Hypotheses Testing with Weights

In this paper we offer a multiplicity of approaches and procedures for multiple testing problems with weights. Some rationale for incorporating weights in multiple hypotheses testing are discussed. Various type-I error-rates and different possible formulations are considered, for both the intersection hypothesis testing and the multiple hypotheses testing problems. An optimal per family weighted error-rate controlling procedure a la Spjotvoll (1972) is obtained. This model serves as a vehicle for demonstrating the different implications of the approaches to weighting. Alternative approach es to that of Holm (1979) for family-wise error-rate control with weights are discussed, one involving an alternative procedure for family-wise error-rate control, and the other involving the control of a weighted family-wise error-rate. Extensions and modifications of the procedures based on Simes (1986) are given. These include a test of the overall intersec tion hypothesis with general weights, and weighted sequentially rejective procedures for testing the individual hypotheses. The false discovery rate controlling approach and procedure of Benjamini & Hochberg (1995) are extended to allow for different weights.     

Optimal Weight Functions for Marginal Proportional Hazards Analysis of Clustered Failure Time Data

The choice of weights in estimating equations for multivariate survival data is considered. Specifically, we consider families of weight functions which are constant on fixed time intervals, including the special case of time-constant weights. For a fixed set of time intervals, the optimal weights are identified as the solution to a system of linear equations. The optimal weights are computed for several scenarios. It is found that for the scenarios examined, the gains in efficiency using the optimal weights are quite small relative to simpler approaches except under extreme dependence, and that a simple estimator of an exchangeable approximation to the weights also performs well.     

Importance of sampling weights in multilevel modeling of international large-scale assessment data

Multilevel modeling is an important tool for analyzing large-scale assessment data. However, the standard multilevel modeling will typically give biased results for such complex survey data. This bias can be eliminated by introducing design weights which must be used carefully as they can affect the results. The aim of this paper is to examine different approaches and to give recommendations concerning handling design weights in multilevel models when analyzing large-scale assessments such as TIMSS (The Trends in International Mathematics and Science Study). To achieve the goal of the paper, we examined real data from two countries and included a simulation study. The analyses in the empirical study showed that using no weights or only level 1 weights sometimes could lead to misleading conclusions. The simulation study only showed small differences in estimation of the weighted and unweighted models when informative design weights were used. The use of unscaled or not rescaled weights however caused significant differences in some parameter estimates.     

An empirical investigation into the effect of childbearing on economic wellbeing in Europe

This paper investigates the extent childbearing among couples in Europe affects their level of economic well being. We do so by implementing a propensity score matching procedure in combination with a difference-in-difference estimator. Using data from European Community Household Panel Survey (ECHP), we compare how the impact of childbearing on wellbeing varies among countries. We use several measures for wellbeing, including poverty status and various deprivation indices that take into account the multidimensionality of individuals‘ assessment of wellbeing. Not unexpected we find childbearing tend to worsen the economic wellbeing of households, but with important differences in magnitude across countries. In Scandinavian countries the effect is small and rarely significant, it is strong in the UK and also significant in Mediterranean countries. Depending on the measure of wellbeing, we find important differences among countries that are similar in terms of welfare provision.     

A global optimisation approach to range-restricted survey calibration

Survey calibration methods modify minimally sample weights to satisfy domain-level benchmark constraints (BC), e.g. census totals. This allows exploitation of auxiliary information to improve the representativeness of sample data (addressing coverage limitations, non-response) and the quality of sample-based estimates of population parameters. Calibration methods may fail with samples presenting small/zero counts for some benchmark groups or when range restrictions (RR), such as positivity, are imposed to avoid unrealistic or extreme weights. User-defined modifications of BC/RR performed after encountering non-convergence allow little control on the solution, and penalisation approaches modelling infeasibility may not guarantee convergence. Paradoxically, this has led to underuse in calibration of highly disaggregated information, when available. We present an always-convergent flexible two-step global optimisation (GO) survey calibration approach. The feasibility of the calibration problem is assessed, and automatically controlled minimum errors in BC or changes in RR are allowed to guarantee convergence in advance, while preserving the good properties of calibration estimators. Modelling alternatives under different scenarios using various error/change and distance measures are formulated and discussed. The GO approach is validated by calibrating the weights of the 2012 Health Survey for England to a fine age–gender–region cross-tabulation (378 counts) from the 2011 Census in England and Wales.     

变权重组合预测模型的局部加权最小二乘解法

随着科学技术的不断进步，预测方法也得到了很大的发展，常见的预测方法就有数十种之多。而组合预测是将不同的预测方法组合起来，综合利用各个方法所提供的信息，其效果往往优于单一的预测方法，故得到了广泛的应用。而基于变系数模型的思想研究了组合预测模型，将变权重的求取转化为变系数模型中系数函数的估计问题，从而可以基于局部加权最小二乘方法求解，利用交叉证实法选取光滑参数。其结果表明所提方法预测精度很高，效果优于其他方法。     

Adaptive power priors with empirical Bayes for clinical trials

Incorporating historical information into the design and analysis of a new clinical trial has been the subject of much discussion as a way to increase the feasibility of trials in situations where patients are difficult to recruit. The best method to include this data is not yet clear, especially in the case when few historical studies are available. This paper looks at the power prior technique afresh in a binomial setting and examines some previously unexamined properties, such as Box P values, bias, and coverage. Additionally, it proposes an empirical Bayes‐type approach to estimating the prior weight parameter by marginal likelihood. This estimate has advantages over previously criticised methods in that it varies commensurably with differences in the historical and current data and can choose weights near 1 when the data are similar enough. Fully Bayesian approaches are also considered. An analysis of the operating characteristics shows that the adaptive methods work well and that the various approaches have different strengths and weaknesses.     

A weighted linear quantile regression

In this article, we introduce a new weighted quantile regression method. Traditionally, the estimation of the parameters involved in quantile regression is obtained by minimizing a loss function based on absolute distances with weights independent of explanatory variables. Specifically, we study a new estimation method using a weighted loss function with the weights associated with explanatory variables so that the performance of the resulting estimation can be improved. In full generality, we derive the asymptotic distribution of the weighted quantile regression estimators for any uniformly bounded positive weight function independent of the response. Two practical weighting schemes are proposed, each for a certain type of data. Monte Carlo simulations are carried out for comparing our proposed methods with the classical approaches. We also demonstrate the proposed methods using two real-life data sets from the literature. Both our simulation study and the results from these examples show that our proposed method outperforms the classical approaches when the relative efficiency is measured by the mean-squared errors of the estimators.     

Focused Information Criterion for Capture–Recapture Models for Closed Populations

Abstract. We propose a criterion for selecting a capture–recapture model for closed populations, which follows the basic idea of the focused information criterion (FIC) of Claeskens and Hjort. The proposed criterion aims at selecting the model which, among the available models, leads to the smallest mean‐squared error (MSE) of the resulting estimator of the population size and is based on an index which, up to a constant term, is equal to the asymptotic MSE of the estimator. Two alternative approaches to estimate this FIC index are proposed. We also deal with multimodel inference; in this case, the population size is estimated by using a weighted average of the estimates coming from different models, with weights chosen so as to minimize the MSE of the resulting estimator. The proposed model selection approach is compared with more common approaches through a series of simulations. It is also illustrated by an application based on a dataset coming from a live‐trapping experiment.     

环境“二维化”视角下的居民幸福感量化研究：来自中国CGSS数据的新证据

幸福不仅是影响人们行为的重要因素,更是人们生活追求的最终目标。本文基于中国综合社会调查（CGSS）数据,创新性地从环境“二维化”这一研究视角,将环境因素划分为两个维度,即客观存在的环境污染因素与居民主观的环境行为,采用优化的两阶段有序Probit回归模型,沿着“客观存在的环境污染因素——居民幸福感”和“居民幸福感——居民主观的环境行为”两条研究思路展开实证分析,在实证过程中引入控制变量及工具变量,同时对经济因素及地区因素可能导致的组群差异进行考量和比较。结果显示,无论是环境污染对居民幸福感,还是居民幸福感对居民环境行为,其影响均是显著的,且具有异质性;环境污染通过影响居民的身体健康、生活质量和社会活动对居民幸福感产生影响,而居民环境行为则因个体收入和居民幸福感程度的不同产生差异。本文对环境与居民幸福感之间的作用机制展开深入分析,为政府出台环境政策的制定、提升居民幸福感及居民环境行为贡献度奠定理论基础。     

Robust weighted generalized estimating equations based on statistical depth

Most of the longitudinal data contain influential points and for analyzing them generalized and weighted generalized estimating equations (GEEs and WGEEs) are highly influenced by these points. An approach for dealing with outliers is having weight functions. In this article, we propose some new weights based on the statistical depth. These weights express centrality of points with respect to the whole sample with a smaller depth (larger depth) for the point far from the center (for the point near the center). The proposed approach leads to robust WGEE. These approaches are applied on two real datasets and some simulation studies.     

Shrinkage averaging estimation

We discuss the impact of tuning parameter selection uncertainty in the context of shrinkage estimation and propose a methodology to account for problems arising from this issue: Transferring established concepts from model averaging to shrinkage estimation yields the concept of shrinkage averaging estimation (SAE) which reflects the idea of using weighted combinations of shrinkage estimators with different tuning parameters to improve overall stability, predictive performance and standard errors of shrinkage estimators. Two distinct approaches for an appropriate weight choice, both of which are inspired by concepts from the recent literature of model averaging, are presented: The first approach relates to an optimal weight choice with regard to the predictive performance of the final weighted estimator and its implementation can be realized via quadratic programming. The second approach has a fairly different motivation and considers the construction of weights via a resampling experiment. Focusing on Ridge, Lasso and Random Lasso estimators, the properties of the proposed shrinkage averaging estimators resulting from these strategies are explored by means of Monte-Carlo studies and are compared to traditional approaches where the tuning parameter is simply selected via cross validation criteria. The results show that the proposed SAE methodology can improve an estimators’ overall performance and reveal and incorporate tuning parameter uncertainty. As an illustration, selected methods are applied to some recent data from a study on leadership behavior in life science companies.     

Institutions and Economic Outcomes: A Dominance-Based Analysis

An important issue in both welfare and development economics is the interaction between institutions and economic outcomes. While welfarists are typically concerned with how these variables contribute to overall wellbeing, empirical assessments of their joint contribution are limited. Development economists, on the other hand, have focused extensively on whether institutions cause or are caused by growth yet the relevant literature is still rife with debate. In this article, we use a notion of distributional dominance to tackle both the measurement of multivariate welfare and the evaluation of inter-temporal dependence without hindrance from the mix of discrete (political) and continuous (economic) variables in our data set. On the causality front, our results support the view that institutions promote growth more than growth promotes institutions. On the welfare front, we find that economic growth had a positive impact from 1960 to 2000 but declines in institutional quality over the earlier part of this period were sufficient to produce a decline in overall wellbeing until the mid-1970s. Subsequent improvements in institutions then reversed the trend and, ultimately, wellbeing in 2000 was higher than that in 1960.     

Sequential monitoring of minimum variance portfolio

This paper evaluates the economic effect of monitoring the minimum variance portfolio weights, which depend solely on the covariance matrix of returns. The investor decides whether the portfolio composition providing the smallest portfolio variance remains optimal at the beginning of every new investment period. For this purpose changes in the optimal weights are sequentially detected by means of EWMA control charts. Signals obtained from monitoring are used for improvement of the covariance matrix estimation procedure. The investment strategy exploiting signals from control charts is compared with a number of alternative approaches in the empirical study.     

The Use of Sample Weights in Hot Deck Imputation

A common strategy for handling item nonresponse in survey sampling is hot deck imputation, where each missing value is replaced with an observed response from a "similar" unit. We discuss here the use of sampling weights in the hot deck. The naive approach is to ignore sample weights in creation of adjustment cells, which effectively imputes the unweighted sample distribution of respondents in an adjustment cell, potentially causing bias. Alternative approaches have been proposed that use weights in the imputation by incorporating them into the probabilities of selection for each donor. We show by simulation that these weighted hot decks do not correct for bias when the outcome is related to the sampling weight and the response propensity. The correct approach is to use the sampling weight as a stratifying variable alongside additional adjustment variables when forming adjustment cells.     

Ensemble Approaches to Estimating the Population Mean with Missing Response

We propose new ensemble approaches to estimate the population mean for missing response data with fully observed auxiliary variables. We first compress the working models according to their categories through a weighted average, where the weights are proportional to the square of the least‐squares coefficients of model refitting. Based on the compressed values, we develop two ensemble frameworks, under which one is to adjust weights in the inverse probability weighting procedure and the other is built upon an additive structure by reformulating the augmented inverse probability weighting function. The asymptotic normality property is established for the proposed estimators through the theory of estimating functions with plugged‐in nuisance parameter estimates. Simulation studies show that the new proposals have substantial advantages over existing ones for small sample sizes, and an acquired immune deficiency syndrome data example is used for illustration.     

Measuring the Precision of Statistical Cost Allocations

This article examines the use of regression analysis for allocating indirect costs. When multiple regression is used to estimate the weights of several allocation factors, conventional standard errors and correlation coefficients can be misleading with respect to the statistical precision of the cost allocations. This article develops alternative allocation approaches and measures of precision that use linear prediction theory and Bayesian inference. The proposed methods are illustrated using a university indirect cost study.     

Improved nearest neighbor classifiers by weighting and selection of predictors

Nearest neighborhood classification is a flexible classification method that works under weak assumptions. The basic concept is to use the weighted or un-weighted sums over class indicators of observations in the neighborhood of the target value. Two modifications that improve the performance are considered here. Firstly, instead of using weights that are solely determined by the distances we estimate the weights by use of a logit model. By using a selection procedure like lasso or boosting the relevant nearest neighbors are automatically selected. Based on the concept of estimation and selection, in the second step, we extend the predictor space. We include nearest neighborhood counts, but also the original predictors themselves and nearest neighborhood counts that use distances in sub dimensions of the predictor space. The resulting classifiers combine the strength of nearest neighbor methods with parametric approaches and by use of sub dimensions are able to select the relevant features. Simulations and real data sets demonstrate that the method yields better misclassification rates than currently available nearest neighborhood methods and is a strong and flexible competitor in classification problems.     

Considerations for optimal nonparametric regression under a generalizederror structure

Nonparametric smoothing, such as kernel or spline estimation, has been examined extensively under the assumption of uncorrelated errors. This paper addresses the effects of potential correlation on consistency and other asymptotic properties in a repeated-measures model, using directly optimized linear smoothers of the replicate means. Unrestricted optimal weights, with respect to squared error loss, are used to confirm a lack of consistency for all linear estimators in an autocorrelated errors model. The results indicate kernel methods that work well for an uncorrelated errors model may not have the ability to perform satisfactorily when correlation is introduced, due to an asymmetry in the optimal weights, which disappears for an uncorrelated errors model. These would include data-driven bandwidth selection methods, adjustments of the bandwidth to accommodate correlation, higher-order kernels, and related bias reduction techniques. The analytic results suggest alternative approaches, not considered here in detail, which have shown merit.