日期精度：到日 1012 篇 · 到月 958 篇 · 到年 101 篇
模拟功效函数
Tests for a null hypothesis whose specification involves an unknown nuisance parameter may be obtained by inverting a bootstrap confidence region for the parameter being tested or by constructing a simulated null distribution for the test statistic. The power of either test against certain alternatives involving the same unknown nuisance parameter can itself be estimated by simulation.
右删失数据分位数函数的核型估计量
Based on right-censored data from a lifetime distribution F 0, a kernel-type estimator of the quantile function Qo (p) = inf{t: F 0(t) ≧ p}, 0 ≦ p ≦ 1, is proposed. The estimator is defined by , which is smoother than the usual product-limit quantile function , where denotes the product-limit estimator of F 0 from the censored sample. Under the random censorship model and general conditions on hn, K, and F 0, it is shown that Qn (p) is strongly consistent. In addition, an…
交叉验证、刀切法与自助法：前向逻辑回归的超额误差估计
Given a prediction rule based on a set of patients, what is the probability of incorrectly predicting the outcome of a new patient? Call this probability the true error. An optimistic estimate is the apparent error, or the proportion of incorrect predictions on the original set of patients, and it is the goal of this article to study estimates of the excess error, or the difference between the true and apparent errors. I consider three estimates of the excess error:…
高效自助法模拟
Bootstrap methods are simulation methods for assessing sampling properties of statistical estimates. We discuss two ideas for making the simulation more efficient. The first idea is to balance the simulated samples, and the second idea is to make explicit use approximations which do not require simulation. Both ideas are illustrated with three examples.
利用先验信息的自助法
Bayesian analysis is subject to the same kinds of misspeciflcation problems which motivate the robustness and nonparametric literature. We present a method of incorporating prior information which performs well without direct knowledge of the error distribution. This is accomplished by replacing the likelihood in Bayes's formula by a bootstrap estimate of the sampling density of a robust estimator. The flexibility of the method is illustrated by examples, and its performance…
Bootstrap 在功率谱密度估计中的应用
A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on estimated spectral density. The bootstrap method is applied to obtain nonparametric confidence bands and intervals. It is the aim of this paper to indicate how this can be done and to report on the outcome of some Monte Carlo studies of the properties of the resulting procedures. Some asymptotic theory concerning the properties of the…
回归的 Bootstrap 预测区间
Bootstrap prediction intervals provide a nonparametric measure of the probable error of forecasts from a standard linear regression model. These intervals approximate the nominal probability content in small samples without requiring specific assumptions about the sampling distribution. Empirical measures of the prediction error rate motivate the choice of these intervals, which are calculated by an application of the bootstrap. The intervals are contrasted to other…
分位数函数的平滑非参数估计
A smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile function is proposed. The proposed estimator is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sample quantile. The mean squared convergence rate of the proposed estimator is also estimated. Monte Carlo studies are conducted to compare the proposed estimator with the sample quantile and the estimator…
有效得分、方差分解与蒙特卡洛方差缩减
Monte Carlo “swindles” or variance reduction techniques exploit the experimenter's knowledge of the stochastic structure governing the simulated data to construct more precise estimates of unknown parameters. Alternatively, one can reduce the number of replications (and thus the cost) needed to gain a desired level of precision. This article reviews the common case of swindles based on variance decompositions for estimating efficiencies and variances of location and…
方向数据的 Bootstrap 置信锥
Given a sample from a distribution F supported on a p-dimensional sphere, several confidence cones for the ‘mean directional vector’ are proposed. Some methods have been available, but they depend on parametric assumptions. In this paper, nonparametric confidence cones based on the bootstrap are considered, and consistency of these methods is obtained under minimal conditions. We compare the performances of bootstrap methods with the others by Monte Carlo simulations.
消费者价格指数的无应答评估
A household budget survey often suffers from a high nonresponse rate and a selective response. The bias that may be introduced in the estimation of budget shares because of this nonresponse can affect the estimate of a consumer price index, which is a weighted sum of partial price index numbers (weighted with the estimated budget shares). The bias is especially important when related to the standard error of the estimate. Because of the impossibility of subsampling…
方向变量独立性的 Sobolev 检验
Two families of invariant tests for independence of random variables on compact Riemannian manifolds are proposed and studied. The tests are based on Gine's Sobolev norms which are obtained by mapping the manifolds into Hilbert spaces. For general compact manifolds, randomization tests are suggested. For the bivariate circular case, distribution-free tests based on uniform scores are considered.
稳健与准稳健统计方法导论
1. Introduction and Summary.- 1.1. History and main contributions.- 1.2. Why robust estimations?.- 1.3. Summary.- A The Theoretical Background.- 2. Sample spaces, distributions, estimators.- 2.1. Introduction.- 2.2. Example.- 2.3. Metrics for probability distributions.- 2.4. Estimators seen as functionals of distributions.- 3. Robustness, breakdown point and influence function.- 3.1. Definition of robustness.- 3.2. Definition of breakdown point.- 3.3. The influence…
稳健两样本置换检验
A new two-sample randomization test is proposed for testing that the joint distribution of two samples is invariant under permutations. The $p$-value of the test has a finite sample minimaxity property over neighborhoods of completely specified alternative distributions. Asymptotically, the test has minimax Bahadur slope against the neighborhoods, which remain fixed as the sample sizes increase. The proposed test also offers the best compromise between robustness against…
检验分离假设族的一种新方法
Theoretical and empirical evidence are reported showing that the tests given in Cox (1961) and Williams (1970a, b) for the problem of testing separate families of hypotheses suffer from fundamental difficulties. Neither test is guaranteed to be asymptotically level a, even for very smooth problems. A new method proposed here as an alternative works adaptively by repeated application of the parametric bootstrap idea over slowly shrinking confidence regions. Theoretical…
对 Bootstrap 置信区间的疑虑
The percentile method and bias-corrected percentile method of Efron (1981, 1982) are discussed. When these methods are used to construct nonparametric confidence intervals for the variance of a normal distribution, the coverage probabilities are substantially below the nominal level for small to moderate samples. This is due to the inapplicability of assumptions underlying the methods. These assumptions are difficult or impossible to check in the complicated situations for…
聚类分析中正确分配率的估计
A sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations. The mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership. Estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the…
聚类分析中正确分配率的估计
A sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations. The mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership. Estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the…
一类参数问题的 Bootstrap 置信区间
We consider the following class of problems: having observed a multivariate normal data vector y with unknown mean vector η, covariance matrix the identity, find an approximate confidence interval for ø = t(η), a real-valued function of η. A simple geometric construction is given which leads to highly accurate solutions. This construction shows that the standard approximation based on maximum likelihood theory, ø7plusmn;σz(α), can be quite misleading when ø is nonlinear in…
经 Edgeworth 校正的枢轴统计量与 Bootstrap
A general procedure for multistage modification of pivotal statistics is developed to improve the normal approximation. Bootstrapping a first stage modified statistic is shown to be equivalent, in terms of asymptotic order, to the normal approximation of a second stage modification. Explicit formulae are given for some basic cases involving independent random samples and samples drawn without replacement. The Hodges-Lehmann deficiency is calculated to compare the regular $t$-…
协方差矩阵函数的自助检验与置信域
Bootstrap tests and confidence regions for functions of the population covariance matrix have the desired asymptotic levels, provided model restrictions, such as multiple eigenvalues in the covariance matrix, are taken into account in designing the bootstrap algorithm.
复杂抽样下的刀切法卡方检验
Complex sample designs typically invalidate the direct application of the familiar Pearson or likelihood-ratio chi-squared statistics for testing the fit of a model to a cross-classified table of counts. This article discusses the adjustment of these statistics through a jackknifing approach. The technique may generally be applied whenever a standard replication method, such as the jackknife, bootstrap, or repeated half-samples, provides a consistent estimate of the…
Given a sample from a distribution F supported on a p-dimensional sphere, several confidence cones for the ‘mean directional vector’ are proposed. Some methods have been available, but they depend on parametric assumptions. In this paper, nonparametric confidence cones based on the bootstrap are considered, and consistency of these methods is obtained under minimal conditions. We compare the performances of bootstrap methods with the others by Monte Carlo simulations.
We consider the following class of problems: having observed a multivariate normal data vector y with unknown mean vector η, covariance matrix the identity, find an approximate confidence interval for ø = t(η), a real-valued function of η. A simple geometric construction is given which leads to highly accurate solutions. This construction shows that the standard approximation based on maximum likelihood theory, ø7plusmn;σz(α), can be quite misleading when ø is nonlinear in…