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动态条件独立模型与Markov链Monte Carlo方法AI 解读

In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, patients and data arrive sequentially, and new patient-specific parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for continuous updating of the evolving posterior distribution, but would need to be restarted from…

随机删失下累积风险与生存函数的精确Bootstrap置信限AI 解读

In clinical trials and other settings, confidence intervals for survival probabilities at a fixed point in time are often required. Typically, such intervals are constructed on the cumulative hazard scale; the quantiles required for computing these intervals are generally obtained using a first-order normal theory approximation. The appropriateness of such intervals for small sample sizes or under moderate to heavy censoring is suspect. We demonstrate that significant…

复杂调查中有限总体均值的经验贝叶斯估计AI 解读

Estimation of finite population means is considered when samples are collected using a stratified sampling design. Finite populations for different strata are assumed to be realizations from different superpopulations. The true means of the observations lie on a regression surface with random intercepts for different strata. The true sampling variances are also different and random for different strata. The strata are connected through two common prior distributions, one for…

随机删失下累计风险与生存函数的准确自助置信限AI 解读

In clinical trials and other settings, confidence intervals for survival probabilities at a fixed point in time are often required. Typically, such intervals are constructed on the cumulative hazard scale; the quantiles required for computing these intervals are generally obtained using a first-order normal theory approximation. The appropriateness of such intervals for small sample sizes or under moderate to heavy censoring is suspect. We demonstrate that significant…

摘要暂缺

异方差时间序列的子抽样推断AI 解读

In this article, a general theory for the construction of confidence intervals or regions in the context of heteroskedastic-dependent data is presented. The basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data. This method was first proposed by Politis and Romano (1994b) for stationary observations. We extend their results to heteroskedastic observations, and prove a general…

利用核平滑改善自助法置信区间AI 解读

Summary Some studies of the bootstrap have assessed the effect of smoothing the estimated distribution that is resampled, a process usually known as the smoothed bootstrap. Generally, the smoothed distribution for resampling is a kernel estimate and is often rescaled to retain certain characteristics of the empirical distribution. Typically the effect of such smoothing has been measured in terms of the mean-squared error of bootstrap point estimates. The reports of these…

观测 Fisher 信息的二阶最优性AI 解读

The realized error of an estimate is determined not only by the efficiency of the estimator, but also by chance. For example, suppose that we have observed a bivariate normal vector whose expectation is known to be on a circle. Then, intuitively, the longer that vector happens to be, the more accurately its angle is likely to be estimated. Yet this chance, though its information is contained in the data, cannot be accounted for by the variance of the estimate. One way to…

在对偶空间中用蒙特卡洛抽样近似经验半空间距离AI 解读

The Kolmogorov-Smirnov distance is an important tool for constructing confidence sets and tests in univariate problems. In multivariate settings, an analogous role is played by the halfspace distance, which has the merit of being invariant under linear transformations. However, the evaluation of the halfspace distance between two samples is a computationally very intensive combinatorial problem even in moderate dimensions, which severely restricts the use of the halfspace…

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预定工具变量下的面板有效估计：矩条件估计量的实证比较AI 解读

The author examines the empirical performance of instrumental variables estimators with predetermined instruments in an application to life-cycle labor supply under uncertainty. The estimators studied are two stage least squares, generalized method-of-moments (GMM), forward filter, independently weighted GMM, and split-sample instrumental variables. The author compares the bias/efficiency trade-off for the estimators using bootstrap algorithms suggested by D. A. Freedman…

半参数加性风险模型的拟合优度检验AI 解读

Kolmogorov-Smirnov and Cramér-von Mises type test statistics based on the standardised cumulative hazard process are proposed. It is very difficult to evaluate their asymptotic distributions, but they can be approximated by the use of the bootstrap. The advantages of the goodness-of-fit test are that arbitrary partitions of the time axis and covariate spaces are not needed for evaluating test statistics and that it has excellent consistency properties. The test is applied to…

基于病例—对照数据的 Logistic 回归拟合优度检验AI 解读

We test the logistic regression assumption under a case-control sampling plan. After reparameterisation, the assumed logistic regression model is equivalent to a two-sample semiparametric model in which the log ratio of two density functions is linear in data. By identifying this model with a biased sampling model, we propose a Kolmogorov-Smirnov-type statistic to test the validity of the logistic link function. Moreover, we point out that this test statistic can also be…

基于图基深度与自助法的平衡置信区域AI 解读

Summary We propose and study the bootstrap confidence regions for multivariate parameters based on Tukey’s depth. The bootstrap is based on the normalized or Studentized statistic formed from an independent and identically distributed random sample obtained from some unknown distribution in R q. The bootstrap points are deleted on the basis of Tukey’s depth until the desired confidence level is reached. The proposed confidence regions are shown to be second order balanced in…

协变量匹配的函数均值差单侧检验AI 解读

When testing hypotheses about the effects of different treatments, variation among covariates can become confounded with that between treatments unless the treatments are applied using paired covariates. In the context of unpaired covariates, we propose implicit covariate-matching methods for testing the hypothesis that one treatment effect is greater than another. The methods are founded on the assumption that the mean treatment effect, conditional on the covariate, is a…

删失数据非参数最大似然估计的混合计算算法AI 解读

We present a hybrid algorithm for nonparametric maximum likelihood estimation from censored data when the log-likelihood is concave. The hybrid algorithm uses a composite algorithmic mapping combining the expectation-maximization (EM) algorithm and the (modified) iterative convex minorant (ICM) algorithm. Global convergence of the hybrid algorithm is proven; the iterates generated by the hybrid algorithm are shown to converge to the nonparametric maximum likelihood estimator…

非线性回归的统计工具：含 S-PLUS 示例的实用指南AI 解读

Presenting methods for analysing data using parametric nonlinear regression models, this text uses examples from experiments in agronomy and biochemistry, and shows how to apply the methods. The book includes methods based on classical nonlinear regression theory, as well as more modern ones such as the bootstrap. The examples are analysed with the software program nls2 implemented in S-PLUS. Examples in biology and agriculture are emphasized.

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条件柯尔莫哥洛夫检验AI 解读

This paper introduces a conditional Kolmogorov test of model specification for parametric models with covariates (regressors). The test is an extension of the Kolmogorov test of goodness-of-fit for distribution functions. The test is shown to have power against 1/[square root of n] local alternatives and all fixed alternatives to the null hypothesis. A parametric bootstrap procedure is used to obtain critical values for the test.

删失数据的一类加权自助法研究AI 解读

Edgeworth expansions are derived for a class of weighted bootstrap methods for the Kaplan-Meier and Nelson-Aalen estimates using the methods contained in the monograph by Barbe and Bertail. Von Mises representations up to the third order are established for the weighted bootstrap versions of these estimators. It is shown that there exists weights which outperform Efron's bootstrap method in terms of coverage accuracy. Moreover, it is shown that this holds for a particular…

标准化统计量分布函数的估计AI 解读

Summary For estimating the distribution of a standardized statistic, the bootstrap estimate is known to be local asymptotic minimax. Various computational techniques have been developed to improve on the simulation efficiency of uniform resampling, the standard Monte Carlo approach to approximating the bootstrap estimate. Two new approaches are proposed which give accurate yet simple approximations to the bootstrap estimate. The second of the approaches even improves the…

非参数回归的一致显著性检验AI 解读

This article presents a framework for individual and joint tests of significance employing nonparametric estimation procedures. The proposed test is based on nonparametric estimates of partial derivatives, is robust to functional misspecification for general classes of models, and employs nested pivotal bootstrapping procedures. Two simulations and one application are considered to examine size and power relative to misspecified parametric models and to test for the linear…

极端尾部概率的估计AI 解读

Applications of extreme value theory to problems of statistical inference typically involve estimating tail probabilities well beyond the range of the data, without the benefit of a concise mathematical model for the sampling distribution. The available model is generally only an asymptotic one. That is, an approximation to probabilities of extreme deviation is supposed, which is assumed to become increasingly accurate as one moves further from the range of the data, but…

两阶段抽样中回归估计量的方差估计AI 解读

Many techniques in survey sampling depend on the possession of information about an auxiliary variable x, or a vector of auxiliary variables, available for the entire population. Regression estimates require , the population mean. If such information is unavailable, then one can sometimes obtain a large preliminary sample of xi relatively cheaply and use this to obtain a good estimate, say , of A smaller subsample can then be taken and the characteristic of interest, yi ,…