日期精度：到日 1012 篇 · 到月 958 篇 · 到年 101 篇
均值 Bootstrap 的必要条件
It is proved that $EX^2 < \infty$ is necessary for a very mild form of the bootstrap of the mean to work a.s. and that $X$ must be in the domain of attraction of the normal law if a.s. is weakened to "in probability."
观察性研究中隐蔽偏差的置换检验：Holley 不等式与 Savage 格
Randomized experiments and observational studies both attempt to estimate the effects produced by a treatment, but in observational studies, subjects are not randomly assigned to treatment or control. A theory of observational studies would closely resemble the theory for randomized experiments in all but one critical respect: In observational studies, the distribution of treatment assignments is not known. The problems that are special to observational studies revolve…
贝叶斯自助法均值的二阶渐近性质
It is shown that the Bayesian bootstrap approximation to the posterior distribution of the unknown mean (with respect to a Dirichlet process prior) is more accurate than both the standard normal approximation and the bootstrap approximation. It is also shown that the Bayesian bootstrap approximation to the sampling distribution of the sample average is not as accurate as the bootstrap approximation.
实现对称性与同方差性的回归变换
This article considers transformations in regression to eliminate skewness and heteroscedasticity of the response. We work with the transform-both-sides model where the relationship between the median response and the independent variables has been identified, at least tentatively. To preserve this relationship, the response and the regression model are transformed in the same way. Extending the work of others for the location parameter case, we propose an estimator that…
维数增长下稳健回归的渐近理论及其 Bootstrap 应用
A stochastic expansion for $M$-estimates in linear models with many parameters is derived under the weak condition $\kappa n^{1/3}(\log n)^{2/3} \rightarrow 0$, where $n$ is the sample size and $\kappa$ the maximal diagonal element of the hat matrix. The expansion is used to study the asymptotic distribution of linear contrasts and the consistency of the bootstrap. In particular, it turns out that bootstrap works in cases where the usual asymptotic approach fails.
Bootstrap与经验Edgeworth展开的二阶及Lᵖ比较
The bootstrap estimate of distribution functions of studentized statistics is shown to be more accurate than even the two-term empirical Edgeworth expansion, thus strengthening the claim of superiority of the bootstrap over the normal approximation method. The two methods are compared not only with respect to bounded bowl-shaped loss functions but also with respect to squared error loss and, more generally, in $L^p$-norms.
若干非参数假设的自助法与随机化检验
In this paper, the asymptotic behavior of some nonparametric tests is studied in situations where both bootstrap tests and randomization tests are applicable. Under fairly general conditions, the tests are asymptotically equivalent in the sense that the resulting critical values and power functions are appropriately close. This implies, among other things, that the difference in the critical functions of the tests, evaluated at the observed data, tends to 0 in probability.…
使用 Bootstrap 构造分布函数置信带
We first discuss the construction of bootstrap confidence bands for the distribution function F of a population for simple random sampling but do not assume that F is continuous. The known alternative approach is to use the quantiles from the tabled Kolmogorov distribution. This approach is known to be conservative. It has already been shown in Bickel and Freedman (1981) that the bootstrap confidence band has the correct coverage probability asymptotically. We show by…
聚类数量的近似置信区间
We consider clustering for the purpose of data reduction. Similar objects are grouped together in clusters so that one can then work with the few cluster descriptors instead of the many data points. The quality of any given clustering is measured by a loss function that takes into account both the parsimony of the clustering and the loss of information due to clustering. An optimal clustering can be obtained by minimizing the theoretical loss function. It is shown that a…
聚类数量的近似置信区间
We consider clustering for the purpose of data reduction. Similar objects are grouped together in clusters so that one can then work with the few cluster descriptors instead of the many data points. The quality of any given clustering is measured by a loss function that takes into account both the parsimony of the clustering and the loss of information due to clustering. An optimal clustering can be obtained by minimizing the theoretical loss function. It is shown that a…
典型变量分析中的置信区域
It is argued that confidence circles as traditionally drawn on canonical variate diagrams are incorrect, because no allowance is made in their construction for the sampling variability of the canonical variate axes. A series of approximations is employed to obtain tractable expressions for the correct regions. Despite the rather broad approximations involved, empirical assessment via bootstrapping shows the new regions to have much more accurate probability content than the…
Bootstrap的对偶重抽样
An antithetic variates method for the bootstrap is proposed and discussed. It is applicable quite generally, to bias estimation, distribution function estimation and quantile estimation, for example. It is based on an ‘antithetic permutation’ of the sample, which amounts to ranking values of a certain function of the data. Once this has been done B uniform resampling operations may be immediately converted into 2B ‘effective’ resampling operations, yielding greater…
核密度估计中平滑参数的Bootstrap选择
Cross-validation based on integrated squared error has already been applied to the choice of smoothing parameter in the kernel method of density estimation. In this paper, an alternative resampling plan, based on the bootstrap, is proposed in an attempt to estimate mean integrated squared error. This leads to a further data-based choice of smoothing parameter. The two methods are compared and some simulations and examples demonstrate the relative merits. For large samples,…
自然指数族的预测拟合
The paper examines predictive distributions, concentrating on measuring their fit to the true distribution by average KulLback–Leibler divergence. The notion of an ‘averaged bootstrap’ predictive distribution is introduced. This predictive distribution is shown to be asymptotically superior to the estimative distribution, in terms of average Kullback–Leibler divergence, when the true distribution is in a natural exponential family. Small-sample results are presented for the…
高效 bootstrap 模拟
It is shown that three new, efficient bootstrap algorithms are asymptotically equivalent. This is done in two ways. First, asymptotic formulae for variances and mean squared errors are derived, and shown to be identical. Secondly, it is demonstrated that two of the methods may be viewed as approximations to the third. The three algorithms considered are the balanced bootstrap and the linear approximation method proposed by Davison, Hinkley & Schechtman (1986), and a centring…
重要性抽样与嵌套自助法
The nested bootstrap is a computer-intensive technique for reducing the statistical error in the ordinary bootstrap. We show how the Monte Carlo technique of importance sampling can be used to substantially reduce the amount of computation needed in a simple double bootstrap confidence limit method.
R 估计量的刀切法方差估计
Sufficient conditions are given for the consistency of the jackknife variance estimator for R-estimators of location in the one- and two-sample problems. In particular, the jackknife is shown to produce strongly consistent estimates of the variance of the Hodges–Lehmann estimator. An efficient algorithm for computing the variance estimator is presented. For the two sample sizes considered in this paper, calculations for the jackknife estimator of the variance of the…
捕获实验的统计分析
A procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture-recapture data when it is possible to model the capture probabilities of individuals in the population using covariates. The results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size. Confidence intervals for…
典型变量分析中的置信区域
It is argued that confidence circles as traditionally drawn on canonical variate diagrams are incorrect, because no allowance is made in their construction for the sampling variability of the canonical variate axes. A series of approximations is employed to obtain tractable expressions for the correct regions. Despite the rather broad approximations involved, empirical assessment via bootstrapping shows the new regions to have much more accurate probability content than the…
病例队列设计的替代方差与效率计算
We define a bootstrap sampling plan for the case-cohort design and present bootstrap variance estimates and confidence intervals for the log relative hazard. The coverages of these confidence intervals are found to be near nominal levels in simulations. A simple null variance calculation, based on a superpopulation model, is shown to provide good estimates of the power and efficiency of the case-cohort design.
自回归中利用 Bootstrap 进行 Edgeworth 修正
We prove that the distribution of least-squares estimates in autoregressions can be bootstrapped with accuracy $o(n^{-1/2})$ a.s., thereby improving the normal approximation error of $O(n^{-1/2})$.
若干非独立同分布模型下的自助法程序
It is shown in this article that the classical i.i.d. bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location, as long as the random observations are independently drawn from distributions with (essentially) a common location. This may be viewed as a robust property of the classical i.i.d. bootstrap. Also included is a study of the second order properties of a different bootstrap procedure proposed by Wu in…
有限总体的贝叶斯自助法
A Bayesian bootstrap for a finite population is introduced; its small-sample distributional properties are discussed and compared with those of the frequentist bootstrap for a finite population. It is also shown that the two are first-order asymptotically equivalent.