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马尔可夫链蒙特卡洛中样本均值的渐近效率AI 解读

SUMMARY In many cases, a univariate time series derived from a time reversible stationary Markov chain has the property that there is a distribution function on [–1, 1] ([0, 1]) such that, for all non-negative integers l, its lth moment is the lth lag autocorrelation of the time series. We discuss some consequences of this property. Effects of the asymptotic efficiency of the sample mean on the efficiency of subsampling a stationary Markov chain are discussed. The…

非参数风险率估计中平滑参数的 Bootstrap 选择AI 解读

An asymptotic representation of the mean weighted integrated squared error for the kernel-based estimator of the hazard rate in the presence of right-censored samples is obtained for different bootstrap resampling methods. As a consequence, a new bandwidth selector based on the bootstrap is introduced. Very satisfactory simulations results are obtained in comparison to the cross-validation selector for different models, using WARPed (i.e., binned) versions of the estimators.

方向数据置信域的改进枢轴方法AI 解读

The importance of pivoting is well established in the context of nonparametric confidence regions. It ensures enhanced coverage accuracy. However, pivoting for directional data cannot be achieved simply by rescaling. A somewhat cumbersome pivotal method, which involves passing first into a space of higher dimension, has been developed by Fisher and Hall for samples of unit vectors. Although that method has some advantages over nonpivotal techniques, it does suffer from…

插补调查数据的 Bootstrap 方法AI 解读

Most surveys use imputation to compensate for missing data. However, treating the imputed data set as the complete data set and directly applying existing methods (e.g., the linearization, the jackknife, and the bootstrap) for variance estimation and/or statistical inference does not produce valid results, because these methods do not account for the effect of missing data and/or imputation. In this article we show that correct bootstrap estimates can be obtained by…

摘要暂缺

插补调查数据的自助法AI 解读

Most surveys use imputation to compensate for missing data. However, treating the imputed data set as the complete data set and directly applying existing methods (e.g., the linearization, the jackknife, and the bootstrap) for variance estimation and/or statistical inference does not produce valid results, because these methods do not account for the effect of missing data and/or imputation. In this article we show that correct bootstrap estimates can be obtained by…

利用自助法置信区间改善似不相关回归方程的推断AI 解读

The usual standard errors for the regression coefficients in a seemingly unrelated regression model have a substantial downward bias. Bootstrapping the standard errors does not seem to improve inferences. In this paper, Monte Carlo evidence is reported which indicates that bootstrapping can result in substantially better inferences when applied to t -ratios rather than to standard errors.

预测更新方法及其在贝叶斯分类中的应用AI 解读

SUMMARY We propose algorithms based on random draws from predictive distributions of unknown quantities (missing values, for instance). This procedure can either be iterative, which is a special variation of the Gibbs sampler, or be sequential, which is a variation of sequential imputation. In the latter case one can update the posterior distribution with new observations easily. The methods proposed have intuitive statistical implications and can be generalized to…

基于广义矩估计量的检验的自助法临界值AI 解读

Tests based on generalized-method-of-moments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used. This paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions. Particular attention is given to the case of dependent data. It is shown that, with such data, the bootstrap must sample blocks of data and that…

系统发育树的自助法：大偏差与离散程度效应AI 解读

A large deviation result is established for the bootstrap empirical distribution in a finite sample space, thereby validating both nonparametric and parametric bootstrapping in certain phylogenetic inference problems. The bias previously observed in the bootstrap distribution of the estimated tree topology is shown to stem from dispersion effects in the joint distribution of sample and bootstrap empirical distributions. Both results are examined for maximum likelihood…

非参数密度估计的经验似然置信区间AI 解读

We suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x. This suggestion arises from a simulation study which shows that confidence intervals produced by the kernel-based percentle-t bootstrap do not have the coverage claimed by the theory. This coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by…

线性秩统计量、有限总体抽样、置换检验与缩尾处理AI 解读

Asymptotic normality and a representation of all possible subsequential limiting distributions of a simple linear rank statistic are obtained. This is then applied to finite sampling and permutation tests for slope coefficients. The effects of Winsorizing in these situations are considered carefully. Of particular interest regarding slope coefficients is that either using normal score regression constants or Winsorizing slowly increasing numbers of the population values will…

弱假设下的自相关推断AI 解读

In this article we consider the large-sample behavior of estimates of autocorrelations and autoregressive moving average (ARMA) coefficients, as well as their distributions, under weak conditions. Specifically, the usual text book formulas for variances of these estimates are based on strong assumptions and should not be routinely applied without careful consideration. Such is the case when the time series follows an ARMA process with uncorrelated innovations that may not be…

贝叶斯序贯两阶段抽样AI 解读

We propose a sequential two-phase sample design to accommodate applications where conventional two-phase sampling cannot be used. First, we derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then we compare our procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a…

Bootstrap 模型选择AI 解读

In a regression problem, typically there are p explanatory variables possibly related to a response variable, and we wish to select a subset of the p explanatory variables to fit a model between these variables and the response. A bootstrap variable/model selection procedure is to select the subset of variables by minimizing bootstrap estimates of the prediction error, where the bootstrap estimates are constructed based on a data set of size n. Although the bootstrap…

贝叶斯序贯两阶段抽样AI 解读

We propose a sequential two-phase sample design to accommodate applications where conventional two-phase sampling cannot be used. First, we derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then we compare our procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a…

用加权双重自助矩方法检验调查预期的理性AI 解读

Conventional tests for rationality of survey data on expectations are not valid in the presence of measurement errors. However, if two or more survey measures of expectations are available on the true unobserved expectational variables, we can devise the appropriate FIML estimation methods and Wald tests for rationality. This paper uses this method for survey data on expectations for the 90-day Treasury bill rates. However, the Wald tests would be based on inaccurate…

不完整生存数据中分位数函数的非参数似然比置信带AI 解读

The purpose of this paper is to derive confidence bands for quantile functions using a nonparametric likelihood ratio approach. The method is easy to implement and has several appealing properties. It applies to right-censored and left-truncated data, and it does not involve density estimation or even require the existence of a density. Previous approaches (e.g., bootstrap) have imposed smoothness conditions on the density. The performance of the proposed method is…

删失数据下自助法的近似精度AI 解读

In survival analysis with censored data, we consider three closely related survival function estimators: the Kaplan-Meier, Nelson and moment estimators. We derive the Edgeworth expansions for these three estimators with Studentization. Edgeworth expansions for the corresponding bootstrap statistics are also given. It is found that the bootstrap approximation is better than the normal approximation for the Studentized Kaplan-Meier and Nelson estimators, but not so for the…

含趋势的AR(1)模型中自助t检验的水平与功效AI 解读

This paper considers a first-order autoregressive model which may include an intercept and trend where the innovations are independently and identically distributed. The innovation distribution is assumed unknown. The autoregressive parameter is tested using the conventional t statistic. The paper presents Monte Carlo estimates of the rejection probability of the test with bootstrap-based critical values. The results show that the test with the bootstrap-based critical value…

含趋势 AR(1) 模型中 Bootstrap t 检验的水平与功效AI 解读

This paper considers a first-order autoregressive model which may include an intercept and trend where the innovations are independently and identically distributed. The innovation distribution is assumed unknown. The autoregressive parameter is tested using the conventional t statistic. The paper presents Monte Carlo estimates of the rejection probability of the test with bootstrap-based critical values. The results show that the test with the bootstrap-based critical value…

非线性测量误差模型中 SIMEX 估计量的渐近理论AI 解读

Cook and Stefanski have described a computer-intensive method, the SIMEX method, for approximately consistent estimation in regression problems with additive measurement error. In this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors. These standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis. We also give theoretical justification to some of the phenomena…

刚体运动的 bootstrap 置信域估计AI 解读

This article deals with statistical inference of the motion of rigid bodies using bootstrap methodology. We consider two types of motion: motion in p dimensional Euclidean space, and motion on a p-dimensional sphere. This article is motivated by problems of interest to polar scientists understanding the motion of ice pack at the North Pole and those to geoscientists studying the motion of tectonic plates. In addition to obtaining the point estimates for various parameters…

密度估计带宽选择简述AI 解读

There has been major progress in recent years in data-based bandwidth selection for kernel density estimation. Some “second generation” methods, including plug-in and smoothed bootstrap techniques, have been developed that are far superior to well-known “first generation” methods, such as rules of thumb, least squares cross-validation, and biased cross-validation. We recommend a “solve-the-equation” plug-in bandwidth selector as being most reliable in terms of overall…