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蒙特卡洛近似对双重 Bootstrap 置信区间覆盖误差的影响AI 解读

Summary A double-bootstrap confidence interval must usually be approximated by a Monte Carlo simulation, consisting of two nested levels of bootstrap sampling. We provide an analysis of the coverage accuracy of the interval which takes account of both the inherent bootstrap and Monte Carlo errors. The analysis shows that, by a suitable choice of the number of resamples drawn at the inner level of bootstrap sampling, we can reduce the order of coverage error. We consider also…

两个伽马总体均值之比的概率误差AI 解读

The two-sample Student's t-interval can be derived by parametric bootstrap coverage calibration of the naive, plug-in interval that fails to account for the estimation of the common variance parameter. The same technique results in an essentially exact confidence interval for the ratio of two means based on independent samples from gamma distributions. The gamma problem is more difficult computationally because an exact pivot is not available. However, the computational…

以目标估计降低偏差与均方误差AI 解读

Given a statistical functional T and a parametric family of distributions, a bias reduced functional $\tilde{T}$ is defined by setting the expected value of the statistic equal to the observed value. Under certain regularity conditions this new statistic, called the target estimator, will have smaller bias and mean square error than the original estimator. The theoretical aspects are analyzed by using higher order von Mises expansions. Several examples are given, including $M$…

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重尾实用指南：统计技术与应用AI 解读

Part 1 Applications: heavy tailed probability distributions in the World Wide Web, M.E. Crovella et al self-similarity and heavy tails - structural modelling of network traffic, W. Willinger et al heavy tails in high-frequency financial data, U.A. Muller et al stable paretian modelling in finance - some empirical and theoretical aspects, S. Mittnik et al risk management and quantile estimation, F. Bassi et al. Part 2 Time series: analyzing stable time series, R.J. Adler et…

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Bootstrap 检验的检验水平失真AI 解读

We provide a theoretical framework in which to study the accuracy of bootstrap P values, which may be based on a parametric or nonparametric bootstrap. In the parametric case, the accuracy of a bootstrap test will depend on the shape of what we call the critical value function. We show that, in many circumstances, the error in rejection probability of a bootstrap test will be one whole order of magnitude smaller than that of the corresponding asymptotic test. We also propose…

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可变长度马尔可夫链AI 解读

We study estimation in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary high-order Markov chains. From an algorithmic view, the VLMC model class has attracted interest in information theory and machine learning, but statistical properties have not yet been explored.…

非参数似然比置信区间AI 解读

We consider construction of two-sided nonparametric confidence intervals in a smooth function model setting. A nonparametric likelihood approach based on Stein's least favourable family is proposed as an alternative to empirical likelihood. The approach enjoys the same asymptotic properties as empirical likelihood, but is analytically and computationally less cumbersome. The simplicity of the method allows us to propose and analyse asymptotic and bootstrapping techniques as…

高维列联表中的交互作用：对数线性模型的自助法替代方法AI 解读

Based on a revised Lancaster-type representation of the additive interactions associated with a probability measure, a new approach for the analysis of high-dimensional contingency tables is proposed. The approach is essentially model-free because the additive interaction tensor is merely a convenient reparameterization of the given table. Single interaction terms are investigated using the bootstrap method whose first-order asymptotic validity is immediate. The global…

区块自助法的理论比较AI 解读

In this paper, we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths. It is shown that, asymptotically, bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order. However, the variances of these bootstrap estimators may be different even in the first order. Expansions for the bias, the variance and the mean-squared error of different…

利用子抽样预测空间累积分布函数AI 解读

The spatial cumulative distribution function (SCDF) is a random function that provides a statistical summary of a random field over a spatial domain of interest. In this article we develop a spatial subsampling method for predicting an SCDF based on observations made on a hexagonal grid, similar to the one used in the Environmental Monitoring and Assessment Program of the U.S. Environmental Protection Agency. We show that under quite general conditions, the proposed…

通过检验反演构造自助法置信区间AI 解读

Summary In this paper we explore the theoretical and practical implications of using bootstrap test inversion to construct confidence intervals. In the presence of nuisance parameters, we show that the coverage error of such intervals is O(n −1/2) which may be reduced to O(n −1) if a Studentized statistic is used. We present three simulation studies and compare the performance of test inversion methods with established methods on the problem of estimating a confidence…

有意偏置的 Bootstrap 方法AI 解读

Summary A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is introduced. It is motivated by the need to adjust empirical methods, such as the ‘uniform’ bootstrap, in a surgical way to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduce variance or to render some characteristic equal to a predetermined quantity. Examples of the…

经验鞍点与自助法尾部近似的小相对误差概率界AI 解读

To obtain test probabilities based on empirical approximations to the distribution of a Studentized function of a mean, we need the approximations to be accurate with sufficiently high probability. In particular, when these test probabilities are small it is best to consider relative errors. Here we show that in the case of univariate standardized means and in the general case of tests based on smooth functions of means, the empirical approximations have asymptotically small…

多维均值泛函的贝叶斯自助法可信集AI 解读

This paper shows that the Bayesian bootstrap (BB) distribution of a multidimensional mean functional based on i.i.d. observations has a strongly unimodal Lebesgue density provided the convex hull of the data has a nonempty interior. This result is then used to construct the finite sample BB credible sets. The influence of an outlier on these credible sets is studied in detail and a comparison is made with the empirical likelihood ratio confidence sets in this context.

利用平滑 ROC 曲线概括和比较诊断系统AI 解读

Receiver operating characteristic (ROC) curves are used for summarizing the performance of imperfect diagnostic systems, especially in biomedical research. These curves are also appropriate for summarizing the performance of a discriminant analysis but are under-utilized by statisticians. This article is illustrates the use of these curves for comparing competing diagnostic systems, develops new estimation methods based on kernel density estimation, and studies the…

广义线性模型中参数与半参数设定的检验AI 解读

We consider a generalized partially linear model E(Y|X, T) = G{X T β + m(T)}, where G is a known function, β is an unknown parameter vector, and m is an unknown function. We introduce a test statistic that allows one to decide between a parametric and a semiparametric model: (a) m is linear (i.e., m(t) = t T γ for a parameter vector γ), and (b) m is a smooth (nonlinear) function. Under linearity (a), we show that the test statistic is asymptotically normal. Moreover, we…

随机曲线分布众数的非参数估计AI 解读

Summary Motivated by the need to develop meaningful empirical approximations to a ‘typical’ data value, we introduce methods for density and mode estimation when data are in the form of random curves. Our approach is based on finite dimensional approximations via generalized Fourier expansions on an empirically chosen basis. The mode estimation problem is reduced to a problem of kernel-type multivariate estimation from vector data and is solved using a new recursive…

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中位数回归模型的自助法AI 解读

The least-absolute-deviations (LAD) estimator for a median-regression or censored median-regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the LAD objective function is not smooth. This paper overcomes this problem by smoothing the objective function. The smoothed estimator is asymptotically equivalent to the ordinary LAD estimator. With bootstrap critical values, the rejection probabilities of…

用独立观测密度估计量强逼近弱依赖观测密度估计量AI 解读

We derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors. We construct, on a sufficiently rich probability space, such a pairing of the random variables of both experiments that the set of observations $X_1,\ldots,X_n}$ from the time series model is nearly the same as the set of observations $Y_1,\ldots,Y_n}$ from the i.i.d. model. With a high probability, all sets of the form $({X_1,\ldots,X_n}\\Delta{Y_1,\ldots,Y_n})\bigcap([a_1,b_1]\times\ldots\times[a_d,b_d])$…

Bootstrap 分位数的崩溃理论AI 解读

A general formula for computing the breakdown point in robustness for the $t$th bootstrap quantile of a statistic $T_n$ is obtained. The answer depends on $t$ and the breakdown point of $T_n$. Since the bootstrap quantiles are vital ingredients of bootstrap confidence intervals, the theory has implications pertaining to robustness of bootstrap confidence intervals. For certain $L$ and $M$ estimators, a robustification of bootstrap is suggested via the notion of Winsorization.