On inference for Kendall's τ within a longitudinal data setting

Kendall's τ is a non-parametric measure of correlation based on ranks and is used in a wide range of research disciplines. Although methods are available for making inference about Kendall's τ, none has been extended to modeling multiple Kendall's τs arising in longitudinal data analysis. Compounding this problem is the pervasive issue of missing data in such study designs. In this article, we develop a novel approach to provide inference about Kendall's τ within a longitudinal study setting under both complete and missing data. The proposed approach is illustrated with simulated data and applied to an HIV prevention study.     

Record-breaking data: a parametric comparison of the inverse-sampling and the random-sampling schemes

In many industrial quality control experiments and destructive stress testing, the only available data are successive minima (or maxima)i.e., record-breaking data. There are two sampling schemes used to collect record-breaking data: random sampling and inverse sampling. For random sampling, the total sample size is predetermined and the number of records is a random variable while in inverse-sampling the number of records to be observed is predetermined; thus the sample size is a random variable. The purpose of this papper is to determinevia simulations, which of the two schemes, if any, is more efficient. Since the two schemes are equivalent asymptotically, the simulations were carried out for small to moderate sized record-breaking samples. Simulated biases and mean square errors of the maximum likelihood estimators of the parameters using the two sampling schemes were compared. In general, it was found that if the estimators were well behaved, then there was no significant difference between the mean square errors of the estimates for the two schemes. However, for certain distributions described by both a shape and a scale parameter, random sampling led to estimators that were inconsistent. On the other hand, the estimated obtained from inverse sampling were always consistent. Moreover, for moderated sized record-breaking samples, the total sample size that needs to be observed is smaller for inverse sampling than for random sampling.     

Adjusted empirical likelihood models with estimating equations for accelerated life tests

This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology.     

D- and V-optimal population designs for the quadratic regression model with a random intercept term

In this paper D- and V-optimal population designs for the quadratic regression model with a random intercept term and with values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. D-optimal population designs based on single-point individual designs were readily found but the derivation of explicit expressions for designs based on two-point individual designs was not straightforward and was complicated by the fact that the designs now depend on ratio of the variance components. Further algebraic results pertaining to d-point D-optimal population designs where d≥3 and to V-optimal population designs proved elusive. The requisite designs can be calculated by careful programming and this is illustrated by means of a simple example.     

Aggregation of isotropic autoregressive fields

This note constitutes a corrigendum to the article of Azomahou [2009, Memory properties and aggregation of spatial autoregressive models. J. Statist. Plann. Inference, 139, 2581-2597]. The aggregation of isotropic four nearest neighbors autoregressive models on the lattice Z², with random coefficient, is investigated. The spectral density of the resulting random field is studied in details for a large class of law of the AR coefficient. Depending on this law, the aggregated field may exhibit short memory or isotropic long memory.     

Reporting cumulative proportion of subjects with an adverse event based on data from multiple studies

Experience has shown us that when data are pooled from multiple studies to create an integrated summary, an analysis based on naïvely‐pooled data is vulnerable to the mischief of Simpson's Paradox. Using the proportions of patients with a target adverse event (AE) as an example, we demonstrate the Paradox's effect on both the comparison and the estimation of the proportions. While meta analytic approaches have been recommended and increasingly used for comparing safety data between treatments, reporting proportions of subjects experiencing a target AE based on data from multiple studies has received little attention. In this paper, we suggest two possible approaches to report these cumulative proportions. In addition, we urge that regulatory guidelines on reporting such proportions be established so that risks can be communicated in a scientifically defensible and balanced manner. Copyright © 2010 John Wiley & Sons, Ltd.     

随机系数离散值时间序列模型

 本文建立了q阶随机系数整值滑动平均模型。研究发现：固定指标t,该过程服从泊松分布;求得该过程的期望、方差、协方差;证明了该过程是宽平稳过程,均值与协方差均是遍历的;得到了特殊情况下模型参数的矩法估计,该估计是相合估计。通过Monte Calro模拟来验证估计结量的优劣。     

A Bayesian predictive inference for small area means incorporating covariates and sampling weights

The main goal in small area estimation is to use models to ‘borrow strength’ from the ensemble because the direct estimates of small area parameters are generally unreliable. However, model-based estimates from the small areas do not usually match the value of the single estimate for the large area. Benchmarking is done by applying a constraint, internally or externally, to ensure that the ‘total’ of the small areas matches the ‘grand total’. This is particularly useful because it is difficult to check model assumptions owing to the sparseness of the data. We use a Bayesian nested error regression model, which incorporates unit-level covariates and sampling weights, to develop a method to internally benchmark the finite population means of small areas. We use two examples to illustrate our method. We also perform a simulation study to further assess the properties of our method.     

Empirical likelihood confidence bands for distribution functions with missing responses

Distribution function estimation plays a significant role of foundation in statistics since the population distribution is always involved in statistical inference and is usually unknown. In this paper, we consider the estimation of the distribution function of a response variable Y with missing responses in the regression problems. It is proved that the augmented inverse probability weighted estimator converges weakly to a zero mean Gaussian process. A augmented inverse probability weighted empirical log-likelihood function is also defined. It is shown that the empirical log-likelihood converges weakly to the square of a Gaussian process with mean zero and variance one. We apply these results to the construction of Gaussian process approximation based confidence bands and empirical likelihood based confidence bands of the distribution function of Y. A simulation is conducted to evaluate the confidence bands.     

Estimation of parameters in heavy-tailed distribution when its second order tail parameter is known

Estimating parameters in heavy-tailed distribution plays a central role in extreme value theory. It is well known that classical estimators based on the first order asymptotics such as the Hill, rank-based and QQ estimators are seriously biased under finer second order regular variation framework. To reduce the bias, many authors proposed the so-called second order reduced bias estimators for both first and second order tail parameters. In this work, estimation of parameters in heavy-tailed distributions are studied under the second order regular variation framework when the second order parameter in the distribution tail is known. This is motivated in large part by a recent work by the authors showing that the second order tail parameter is known for a large class of popular random difference equations (for example, ARCH models). The focus is on least squares estimators that generalize rank-based and QQ estimators. Though other possible estimators are also briefly discussed, the least squares estimators are most simple to use and perform best for finite samples in Monte Carlo simulations.