The jackknife estimate of a Kaplan--Meier integral

We derive an explicit formula for the jackknife estimate ofa Kaplan-Meier integral. From this the asymptotic analysis ofthe jackknifed Kaplan-Meier process becomes straightforward.In a small simulation study it is demonstrated that jackknifingmay lead to a considerable reduction of the bias.     

Local estimation of age-dependent variance components from longitudinal twin data

In the study of longitudinal twin and family data, interest is often in the covariance structure of the data and the decomposition of this covariance structure into genetic and environmental components rather than in estimating the mean function. Various parametric models for covariance structures have been proposed but, e.g., in studies of children where growth spurts occur at various ages, it is difficult to a priori determine an appropriate parametric model for the covariance structure. In particular, there is a general lack of the visualization procedures, such as lowess, that are invaluable in the initial stages of constructing a parametric model for a mean function. Here we use kernel smoothing to modify a cross-sectional approach based on the sample covariance matrices to obtain smoothed estimates of the genetic and environmental variances and correlations for longitudinal twin data. The methods are proposed to be exploratory as an aid to parametric modeling rather than inferential, although approximate asymptotic standard errors are derived in the Appendix.     

Variance estimation for statistics computed from single recurrent event processes

This article is concerned with variance estimation for statistics that are computed from single recurrent event processes. Such statistics are important in diagnosis for each individual recurrent event process. The proposed method only assumes a semiparametric form for the first-order structure of the processes but not for the second-order (i.e., dependence) structure. The new variance estimator is shown to be consistent for the target parameter under very mild conditions. The estimator can be used in many applications in semiparametric rate regression analysis of recurrent event data such as outlier detection, residual diagnosis, as well as robust regression. A simulation study and application to two real data examples are used to demonstrate the use of the proposed method.     

应用Jackknife技术统计昆虫生命表参数变异的VFP实现

研究昆虫种群的动态,掌握种群增长的潜力是非常重要的。应用生殖力生命表可进行种群增长动态的估计,常用5个主要参数来描述净增殖率、内禀增长率、世代平均周期、种群倍增时间和周限增长率,Jackknife技术可以用来估计内禀增长率等参数的变异程度,利用VFP编程实现了生命表参数变异程度的计算。     

The analysis of the NSW wheat variety database. II. Variance component estimation

The efficiency of various trialling systems for wheat variety evaluation in New South Wales (NSW) is considered. This involved the estimation of the variance components due to genotype, genotype-by-year, genotype-by-location and genotype-by-year-by-location. It is shown that there is a significant reduction in the magnitude of these variance components by the inclusion of the interaction of genotype maturity, winter habit and aluminium tolerance with environment.     

Variance estimation for systematic designs in spatial surveys

Summary In spatial surveys for estimating the density of objects in a survey region, systematic designs will generally yield lower variance than random designs. However, estimating the systematic variance is well known to be a difficult problem. Existing methods tend to overestimate the variance, so although the variance is genuinely reduced, it is over‐reported, and the gain from the more efficient design is lost. The current approaches to estimating a systematic variance for spatial surveys are to approximate the systematic design by a random design, or approximate it by a stratified design. Previous work has shown that approximation by a random design can perform very poorly, while approximation by a stratified design is an improvement but can still be severely biased in some situations. We develop a new estimator based on modeling the encounter process over space. The new “striplet” estimator has negligible bias and excellent precision in a wide range of simulation scenarios, including strip‐sampling, distance‐sampling, and quadrat‐sampling surveys, and including populations that are highly trended or have strong aggregation of objects. We apply the new estimator to survey data for the spotted hyena (Crocuta crocuta) in the Serengeti National Park, Tanzania, and find that the reported coefficient of variation for estimated density is 20% using approximation by a random design, 17% using approximation by a stratified design, and 11% using the new striplet estimator. This large reduction in reported variance is verified by simulation.     

Variance estimation in clinical studies with interim sample size re-estimation

We consider clinical studies with a sample size re-estimation based on the unblinded variance estimation at some interim point of the study. Because the sample size is determined in such a flexible way, the usual variance estimator at the end of the trial is biased. We derive sharp bounds for this bias. These bounds have a quite simple form and can help for the decision if this bias is negligible for the actual study or if a correction should be done. An exact formula for the bias is also provided. We discuss possibilities to get rid of this bias or at least to reduce the bias substantially. For this purpose, we propose a certain additive correction of the bias. We see in an example that the significance level of the test can be controlled when this additive correction is used.     

Variance calculations for identity-by-descent estimation

Nonparametric linkage strategies often involve estimation of identity by descent (IBD) with the use of affected sibling pairs. Methods for IBD estimation are well established and have been successful for mapping complex traits. However, the majority of linkage approaches involving IBD have focused on statistical testing, rather than on the effect estimates themselves. Through a bootstrap procedure developed for linkage-scan data sets, we provide standard errors for the estimated mean IBD that are broadly applicable. Applications that benefit from the availability of standard errors include effect-size estimates and confidence intervals; meta-analyses, including tests for heterogeneity; and discordant-sibling-pair evaluation. We demonstrate the use of estimated mean IBD and its standard errors in the National Institute of Mental Health Human Genetics Initiative linkage samples for bipolar disorder and Alzheimer disease. Mean IBD and its standard errors are valuable tools for the further assessment and evaluation of linkage-scan samples involving complex disease.