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变化前分布含未知参数时的序贯变点检测AI 解读

In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution fθ and tries to minimize the detection delay for every possible post-change distribution gλ. In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for…

Kullback–Leibler 损失下改进的极小极大预测密度AI 解读

Let X|μ∼Np(μ,vxI) and Y|μ∼Np(μ,vyI) be independent p-dimensional multivariate normal vectors with common unknown mean μ. Based on only observing X=x, we consider the problem of obtaining a predictive density p̂(y|x) for Y that is close to p(y|μ) as measured by expected Kullback–Leibler loss. A natural procedure for this problem is the (formal) Bayes predictive density p̂U(y|x) under the uniform prior πU(μ)≡1, which is best invariant and minimax. We show that any Bayes…

对称性下的扩展统计建模及其与量子力学的联系AI 解读

We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group G on the cartesian product Π of the parameter spaces of these experiments. The set of possible parameters is constrained to lie in a subspace of Π, an orbit or a set of orbits of G. Each possible model is then connected to a parametric Hilbert…

球面随机场角双谱的高分辨率渐近理论AI 解读

In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the sample size grows. The results we present are then exploited in a set of procedures aimed at testing non-Gaussianity; for these statistics, we are able to show convergence to functionals of standard Brownian motion under the null hypothesis.…

大量独立检验中错误原假设比例的估计AI 解读

We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a family of methods for establishing lower 100(1−α)% confidence bounds for this proportion, based on the empirical distribution of the p-values of the tests. Methods in this family are then compared in terms of ability to consistently…

自适应非参数置信集AI 解读

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and…

多变量贝叶斯函数估计AI 解读

Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries on the multivariate nonparametric regression function. The Bayesian approach then allows one to incorporate hierarchical Bayesian methods directly into the spectral structure, thus providing a symmetry-adaptive multivariate Bayesian…

紧致黎曼流形上分布拟合优度的 Sobolev 检验AI 解读

Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Giné’s Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group SO(3).

Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate suboptimal. In such cases minimax rate optimal procedures are constructed based on local thresholding. These nonquadratic procedures are sometimes fully efficient even when optimal quadratic rules have slow rates of convergence. Moreover, it is…

存在工具变量时的非参数推断方法AI 解读

We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the “difficulty” of which depends…

Patterson 交叉试验设计的普遍最优性AI 解读

We show that the balanced crossover designs given by Patterson [Biometrika 39 (1952) 32–48] are (a) universally optimal (UO) for the joint estimation of direct and residual effects when the competing class is the class of connected binary designs and (b) UO for the estimation of direct (residual) effects when the competing class of designs is the class of connected designs (which includes the connected binary designs) in which no treatment is given to the same subject in…

模型与设计联合推断的两阶段框架AI 解读

We establish a mathematical framework that formally validates the two-phase “super-population viewpoint” proposed by Hartley and Sielken [Biometrics 31 (1975) 411–422] by defining a product probability space which includes both the design space and the model space. The methodology we develop combines finite population sampling theory and the classical theory of infinite population sampling to account for the underlying processes that produce the data under a unified…

含固定与非正态潜变量的相关样本分析AI 解读

A general structural equation model is fitted on a panel data set that consists of I correlated samples. The correlated samples could be data from correlated populations or correlated observations from occasions of panel data. We consider cases in which the full pseudo-normal likelihood cannot be used, for example, in highly unbalanced data where the participating individuals do not appear in consecutive years. The model is estimated by a partial likelihood that would be the…

非高斯线性混合模型的部分观测信息与推断AI 解读

In mixed linear models with nonnormal data, the Gaussian Fisher information matrix is called a quasi-information matrix (QUIM). The QUIM plays an important role in evaluating the asymptotic covariance matrix of the estimators of the model parameters, including the variance components. Traditionally, there are two ways to estimate the information matrix: the estimated information matrix and the observed one. Because the analytic form of the QUIM involves parameters other than…

多类型分枝过程的识别AI 解读

We solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process. Our approach is based on a central limit theorem associated with a quadratic law of large numbers performed by the maximum likelihood or the multidimensional Lotka–Nagaev estimator of the reproduction law means. The extension of this approach to the least squares…

时变自回归过程的递归估计AI 解读

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong to appropriate smoothness classes. An adequate normalization for the correction term used in the recursive estimation procedure allows for very mild assumptions on the innovations distributions. The rate of convergence of the pointwise…

线性过程的分布无关拟合优度检验AI 解读

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett Tp-process with estimated parameters, which converges in distribution to the standard Brownian motion under the null hypothesis. We discuss tests of different natures such as omnibus, directional…

分数自回归空间过程的参数估计AI 解读

A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular, it is shown that $\hat{d}_{N}-d=O_{P}(\frac{(\operatorname{Log}N)^{3}}{N})$, where d=(d1,d2) denotes the long memory parameter.

线性移动平均模型对门限移动平均模型的检验AI 解读

This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process. Under local alternatives, it is shown that this test has nontrivial asymptotic power. The results are based on a new weak convergence of a linear marked empirical process, which is independently of interest. This paper also gives an…

遍历扩散过程漂移函数的精确自适应估计AI 解读

The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift S(⋅) is supposed to belong to a nonparametric class of smooth functions of order k≥1, but the value of k is not known to the statistician. A fully data-driven procedure of estimating the drift function is proposed, using the estimated risk minimization method. The sharp adaptivity of this procedure is proven up to an optimal constant, when the…

纵向数据的函数型线性回归分析AI 解读

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth random trajectories, and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects. In longitudinal studies, the number of repeated measurements per subject is often small and may…

学生化统计量自助分位数的自助后刀切方差估计一致性AI 解读

Efron [J. Roy. Statist. Soc. Ser. B 54 (1992) 83–111] proposed a computationally efficient method, called the jackknife-after-bootstrap, for estimating the variance of a bootstrap estimator for independent data. For dependent data, a version of the jackknife-after-bootstrap method has been recently proposed by Lahiri [Econometric Theory 18 (2002) 79–98]. In this paper it is shown that the jackknife-after-bootstrap estimators of the variance of a bootstrap quantile are…

自回归过程中同一实现预测的阶数选择AI 解读

Assume that observations are generated from an infinite-order autoregressive [AR(∞)] process. Shibata [Ann. Statist. 8 (1980) 147–164] considered the problem of choosing a finite-order AR model, allowing the order to become infinite as the number of observations does in order to obtain a better approximation. He showed that, for the purpose of predicting the future of an independent replicate, Akaike’s information criterion (AIC) and its variants are asymptotically…

GARCH 模型残差的高阶矩部分和过程及其应用AI 解读

In this paper we construct high moment partial sum processes based on residuals of a GARCH model when the mean is known to be 0. We consider partial sums of kth powers of residuals, CUSUM processes and self-normalized partial sum processes. The kth power partial sum process converges to a Brownian process plus a correction term, where the correction term depends on the kth moment μk of the innovation sequence. If μk=0, then the correction term is 0 and, thus, the kth power…