Non-parametric estimation of copula based mutual information

Abstract

Mutual information is a measure for investigating the dependence between two random variables. The copula based estimation of mutual information reduces the complexity because it is depend only on the copula density. We propose two estimators and discuss the asymptotic properties. To compare the performance of the estimators a simulation study is carried out. The methods are illustrated using real data sets.     

A generalized ordered Probit model

Abstract

The ordered probit and logit models, based on the normal and logistic distributions, can yield biased and inconsistent estimators when the distributions are misspecified. A generalized ordered response model is introduced which can reduce the impact of distributional misspecification. An empirical exploration of various determinants of life satisfaction suggests possible benefits of allowing for diverse distributional characteristics. These improvements are confirmed using a Monte Carlo study to contrast the performance of the flexible parametric specifications to the probit and logit specifications.     

Infant feeding and post-neonatal mortality in Derbyshire,England, in the early twentieth century

This paper examines influences on post-neonatal mortality in Derbyshire (England) in the early twentieth century, by applying multivariate hazard analysis to a rare individual-level data set. The data allow detailed patterns of breastfeeding and weaning to be examined. The role of feeding is given special attention as a mediator between mortality and the other environmental, social, and demographic factors considered. Twins and illegitimate children were more likely to have been hand-fed, but this could explain only a small fraction of their increased vulnerability. Artificial feeding was associated with increased risks of death from diarrhoea, respiratory disease, and wasting diseases. It is suggested that the link with wasting diseases was predominantly the result of the greater likelihood of congenitally weak children being hand-fed. Most of the variation in post-neonatal mortality, particularly from respiratory disease, was explained by environmental influences - population density, altitude, and the presence of mining.     

Nonparametric Bayes and empirical Bayes estimation of the population median,with application in finite-population sampling

ABSTRACT

Nonparametric Bayes and empirical Bayes estimators of the population median are provided under Dirichlet process priors. The finite-population sampling is used to estimate the finite-population median under Dirichlet process priors. The asymptotic properties of the estimators are obtained from a frequentist perspective.     

中国消费不足背后的人口结构因素——基于省际动态面板的实证研究

本文以生命周期理论为出发点．使用中国1990-2011年的省际面板数据和动态面板GMM估计方法。考察了人口年龄结构变化对我国最终消费的影响。实证结果表明．少儿抚养比对最终消费有正的影响．而老年抚养比对最终消费有负的影响。我国尚处老龄化的初期,预期寿命的延长使得中老年人减少消费并增加储蓄．以保证退休后的生活水平不下降．这直接造成了我国最终消费率伴随老年抚养比的上升而下降的独特现象。在使用不同的计量技术和识别方法之后,以上结果依然稳健。从人口年龄结构角度看,我国低消费、高投资的经济发展特点仍将持续一段时间．这种情况在长期会逐渐反转。     

Robust estimation for finite populations based on a working model

A common scenario in finite population inference is that it is possible to find a working superpopulation model which explains the main features of the population but which may not capture all the fine details. In addition, there are often outliers in the population which do not follow the assumed superpopulation model. In situations like these, it is still advantageous to make use of the working model to estimate finite population quantities, provided that we do it in a robust manner. The approach that we suggest is first to fit the working model to the sample and then to fine-tune for departures from the model assumed by estimating the conditional distribution of the residuals as a function of the auxiliary variable. This is a more direct approach to handling outliers and model misspecification than the Huber approach that is currently being used. Two simple methods, stratification and nearest neighbour smoothing, are used to estimate the conditional distributions of the residuals, which result in two modifications to the standard model-based estimator of the population distribution function. The estimators suggested perform very well in simulation studies involving two types of model departure and have small variances due to their model-based construction as well as acceptable bias. The potential advantage of the proposed robustified model-based approach over direct nonparametric regression is also demonstrated.     

A case study of green tree frog population size estimation by repeated capture–mark–recapture method with individual tagging: a parametric bootstrap method vs Jolly–Seber method

This paper deals with estimation of a green tree frog population in an urban setting using repeated capture–mark–recapture (CMR) method over several weeks with an individual tagging system which gives rise to a complicated generalization of the hypergeometric distribution. Based on the maximum likelihood estimation, a parametric bootstrap approach is adopted to obtain interval estimates of the weekly population size which is the main objective of our work. The method is computation-based; and programming intensive to implement the algorithm for re-sampling. This method can be applied to estimate the population size of any species based on repeated CMR method at multiple time points. Further, it has been pointed out that the well-known Jolly–Seber method, which is based on some strong assumptions, produces either unrealistic estimates, or may have situations where its assumptions are not valid for our observed data set.     

On improving convergence rate of Bernstein polynomial density estimator

This paper is concerned with the Bernstein estimator [Vitale, R.A. (1975), ‘A Bernstein Polynomial Approach to Density Function Estimation’, in Statistical Inference and Related Topics, ed. M.L. Puri, 2, New York: Academic Press, pp. 87–99] to estimate a density with support [0, 1]. One of the major contributions of this paper is an application of a multiplicative bias correction [Terrell, G.R., and Scott, D.W. (1980), ‘On Improving Convergence Rates for Nonnegative Kernel Density Estimators’, The Annals of Statistics, 8, 1160–1163], which was originally developed for the standard kernel estimator. Moreover, the renormalised multiplicative bias corrected Bernstein estimator is studied rigorously. The mean squared error (MSE) in the interior and mean integrated squared error of the resulting bias corrected Bernstein estimators as well as the additive bias corrected Bernstein estimator [Leblanc, A. (2010), ‘A Bias-reduced Approach to Density Estimation Using Bernstein Polynomials’, Journal of Nonparametric Statistics, 22, 459–475] are shown to be O(n^?8/9) when the underlying density has a fourth-order derivative, where n is the sample size. The condition under which the MSE near the boundary is O(n^?8/9) is also discussed. Finally, numerical studies based on both simulated and real data sets are presented.     

Local rank estimation and related test for varying-coefficient partially linear models

This paper develops a robust estimation procedure for the varying-coefficient partially linear model via local rank technique. The new procedure provides a highly efficient and robust alternative to the local linear least-squares method. In other words, the proposed method is highly efficient across a wide class of non-normal error distributions and it only loses a small amount of efficiency for normal error. Moreover, a test for the hypothesis of constancy for the nonparametric component is proposed. The test statistic is simple and thus the test procedure can be easily implemented. We conduct Monte Carlo simulation to examine the finite sample performance of the proposed procedures and apply them to analyse the environment data set. Both the theoretical and the numerical results demonstrate that the performance of our approach is at least comparable to those existing competitors.     

Blinded sample size re‐estimation in crossover bioequivalence trials

In drug development, bioequivalence studies are used to indirectly demonstrate clinical equivalence of a test formulation and a reference formulation of a specific drug by establishing their equivalence in bioavailability. These studies are typically run as crossover studies. In the planning phase of such trials, investigators and sponsors are often faced with a high variability in the coefficients of variation of the typical pharmacokinetic endpoints such as the area under the concentration curve or the maximum plasma concentration. Adaptive designs have recently been considered to deal with this uncertainty by adjusting the sample size based on the accumulating data. Because regulators generally favor sample size re‐estimation procedures that maintain the blinding of the treatment allocations throughout the trial, we propose in this paper a blinded sample size re‐estimation strategy and investigate its error rates. We show that the procedure, although blinded, can lead to some inflation of the type I error rate. In the context of an example, we demonstrate how this inflation of the significance level can be adjusted for to achieve control of the type I error rate at a pre‐specified level. Furthermore, some refinements of the re‐estimation procedure are proposed to improve the power properties, in particular in scenarios with small sample sizes. Copyright © 2014 John Wiley & Sons, Ltd.