论文检索

受贝叶斯思想启发的二水平与四水平最小混杂设计AI 解读

Motivated by a Bayesian framework, we propose a new minimum aberration-type criterion for designing experiments with two- and four-level factors. The Bayesian approach helps in overcoming the ad hoc nature of effect ordering in the existing minimum aberration-type criteria. The approach is also capable of distinguishing between qualitative and quantitative factors. Numerous examples are given to demonstrate its advantages.

q 水平分数因子设计的恒等式及其最小混杂度应用AI 解读

Chen and Hedayat and Tang and Wu studied and characterized minimum aberration $2^{n-m}$ designs in terms of their complemetary designs. Based on a new and more powerful approach, we extend the study to identify minimum aberration $q^{n-m}$ designs through their complementary designs. By using MacWilliams identities and Krawtchouk polynomials in coding theory, we obtain some general and explicit relationships between the wordlength pattern of a $q^{n-m}$ design and that of…

部分因子实验中删失数据的贝叶斯分析AI 解读

Censored data arise naturally in industrial experiments whose observations are failure times or measurements with mixed continuous-categorical outcomes. When censored data are observed from a fractionated experiment, likelihood-based estimates quite often do not exist, especially when the opportunity for improvement is great. To circumvent this problem, we propose a Bayesian analysis strategy that has a straightforward implementation using the data augmentation and Monte…

二元响应数据中 Fieller 区间的准确性AI 解读

Finney proposed the use of a fiducial interval for the median response dose based on Fieller's theorem. An alternative is to use the asymptotic confidence interval. The simulations by Abdelbasit and Plackett suggest that the two intervals have similar coverage probabilities. We compare the two intervals theoretically and in an expanded simulation study. Our results show that Fieller intervals are generally superior. An attempt is made to characterize how and when the two…

样本分位数的平衡重复复制法之渐近性质AI 解读

Inference, including variance estimation, can be made from stratified samples by selecting a balanced set of subsamples. This balanced subsampling method is generically called the balanced repeated replication method in survey data analysis, which includes McCarthy's balanced half-samples method and its extensions for more general stratified designs. We establish the asymptotic consistency of the balanced repeated replication variance estimators when the parameter of…

基于混合正交表的平衡重复复制法AI 解读

For stratified samples with arbitrary numbers of primary sampling units per stratum, one can divide the units in the stratum into two groups and then apply the balanced half-samples method to the two groups thus formed. The efficiency loss of the grouped balanced half-samples variance estimator can be substantial. Use of a mixed orthogonal array, whose numbers of symbols correspond to the numbers of units per stratum, gives a set of balanced subsamples. Unlike that of Gupta…

基于混合正交表的平衡重复复制法AI 解读

For stratified samples with arbitrary numbers of primary sampling units per stratum, one can divide the units in the stratum into two groups and then apply the balanced half-samples method to the two groups thus formed. The efficiency loss of the grouped balanced half-samples variance estimator can be substantial. Use of a mixed orthogonal array, whose numbers of symbols correspond to the numbers of units per stratum, gives a set of balanced subsamples. Unlike that of Gupta…

刀切法直方图的渐近性质AI 解读

We study the asymptotic normality of the jackknife histogram. For one sample mean, it holds if and only if $r$, the number of observations retained, and $d (= n - r)$, the number of observations deleted, both diverge to infinity. The best convergence rate $n^{-1/2}$ is obtained when $r = O(n)$ and $d = O(n)$. For $U$ statistics of degree 2 and nonlinear statistics admitting the expansion (3.1), similar results are obtained under conditions on $r$ and $d$. A second order…

刀切法方差估计的一般理论AI 解读

The delete-1 jackknife is known to give inconsistent variance estimators for nonsmooth estimators such as the sample quantiles. This well-known deficiency can be rectified by using a more general jackknife with $d$, the number of observations deleted, depending on a smoothness measure of the point estimator. Our general theory explains why jackknife works or fails. It also shows that (i) for "sufficiently smooth" estimators, the jackknife variance estimators with bounded $d$…

截断回归问题的非参数方法AI 解读

A description is given of a new method of estimating the regression parameters in the linear regression model from data where the dependent variable is subject to truncation. The residual distribution is allowed to be unspecified. The method is iterative and involves estimation of the residual distribution under the truncated sampling scheme. The technique can be interpreted as an iterative bias adjustment of the observations in order to correct the regression relationship…

复杂调查数据的重采样推断AI 解读

Methods for standard errors and confidence intervals for nonlinear statistics —such as ratios, regression, and correlation coefficients—have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement, in particular, the important special case of two sampled clusters per stratum. These methods include the customary linearization (or Taylor) method and resampling methods based on the jackknife and balanced repeated replication…

两阶段抽样对 F 统计量的影响AI 解读

The assumption of iid observations that underlies many statistical procedures is called into question when analyzing complex survey data. The population structure—particularly the existence of clusters in two-stage samples that usually exhibit positive intracluster correlation—invalidates the independence assumption. Kish and Frankel (1974) investigated the impact of this fact on regression analysis by using the standard sample-survey-theory framework; Campbell (1977) and…

两阶段抽样对 F 统计量的影响AI 解读

The assumption of iid observations that underlies many statistical procedures is called into question when analyzing complex survey data. The population structure-particularly the existence of clusters in two-stage samples that usually exhibit positive intracluster correlation-invalidates the independence assumption. Kish and Frankel (1974) investigated the impact of this fact on regression analysis by using the standard sample-survey-theory framework; Campbell (1977) and…

线性模型中 Jackknife 方差估计量的异方差稳健性AI 解读

The asymptotic unbiasedness and consistency of three types of jackknife variance estimators in the presence of error variance heteroscedasticity in linear models are studied. The results are given in terms of the number of observations deleted and measures of imbalance of the model. The consistency of a class of Wu's weighted jackknife variance estimators for nonlinear parameters is also studied. A necessary and sufficient condition is given for the asymptotic unbiasedness…

回归估计量的方差估计AI 解读

The regression estimator and the ratio estimator are commonly used in survey practice. In the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs. The ratio estimator is appropriate for populations whose regression line passes close to the origin. If the intercept of the regression line is significantly nonzero, however, it is much less efficient than the regression estimator (Deng 1984).…

调查抽样中回归估计量的方差估计AI 解读

The regression estimator and the ratio estimator are commonly used in survey practice. In the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs. The ratio estimator is appropriate for populations whose regression line passes close to the origin. If the intercept of the regression line is significantly nonzero, however, it is much less efficient than the regression estimator (Deng 1984).…

回归分析中的 Jackknife、Bootstrap 与其他重抽样方法AI 解读

Motivated by a representation for the least squares estimator, we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time. They are unbiased for homoscedastic errors and a special case, the delete-one jackknife, is almost unbiased for heteroscedastic errors. The method is extended to cover nonlinear parameters, regression $M$-estimators, nonlinear regression and generalized linear…

非线性情形下序贯设计的渐近推断AI 解读

It is shown that confidence regions for nonlinear parameters constructed by the repeated-sampling principle, are asymptotically valid for sequential designs in general linear models. The related questions of consistency of parameter estimators and convergence of sequential design to an optimal design are answered positively. An empirical finding of Ford & Silvey (1980) is given a theoretical justification.

分层样本推断：非线性统计量三种方法的二阶分析AI 解读

For stratified samples and nonlinear statistics that can be expressed as functions of estimated totals, second-order asymptotic expansions of the linearization, jackknife, and balanced repeated-replication variance estimators are obtained. Based on these, comparisons are made in terms of their biases. Some higher order asymptotic equivalence results are also established. The special case of a combined ratio estimator is investigated in detail. Some results on bias reduction…

非线性情形下序贯设计的渐近推断AI 解读

This document shows that confidence regions constructed by the repeated-sampling principle are asymptotically valid for sequential designs in general linear models and nonlinear parameters. For estimation of parameters in nonlinear models or nonlinear parameters in linear models, sequential design of experiment is often used to best utilize the information. It results in saving the number of runs. After the termination of the experiment with a fixed sample size, inference…

统计推断与序贯设计AI 解读

If an experiment is designed sequentially, repeated-sampling inference may not necessarily be made using distributional results that are valid for fixed designs. A few simple illustrative examples and alternative approaches are given. Sometimes the sequential nature of design can be ignored asymptotically. Links are forged with inference for stochastic processes and missing data problems.

Wu (1980) defined the consistent directions of the least squares estimator in a linear model as the linear combinations of parameter estimates that are asymptotically consistent. For the polynomial regression model, a characterization of the space of consistent directions $S$ was obtained in terms of the convergence rates of the corresponding design sequence to its limit points. By employing a more general and yet simpler approach, we obtain here a similar result for any…