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高维数据的两样本检验及其基因集检验应用AI 解读

We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling’s classical T2 test does not work for this “large p, small n” situation. The proposed test does not require explicit conditions in the relationship between the data dimension and sample size. This offers much flexibility in analyzing high-dimensional data. An application of the proposed test is in testing significance for sets of genes…

最大 Lq 似然估计AI 解读

In this paper, the maximum Lq-likelihood estimator (MLqE), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30–35] is introduced. The properties of the MLqE are studied via asymptotic analysis and computer simulations. The behavior of the MLqE is characterized by the degree of distortion q applied to the assumed model. When q is properly chosen for small and moderate sample sizes, the MLqE can successfully trade bias for precision, resulting in a…

广义错误率的均衡控制AI 解读

Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized family-wise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and step-down procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the…

核学习中的正则化AI 解读

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one can use a regularization term that grows significantly slower than the standard quadratic growth in the RKHS norm.

逆问题中的经验风险最小化AI 解读

We study estimation of a multivariate function f : Rd→R when the observations are available from the function Af, where A is a known linear operator. Both the Gaussian white noise model and density estimation are studied. We define an L2-empirical risk functional which is used to define a δ-net minimizer and a dense empirical risk minimizer. Upper bounds for the mean integrated squared error of the estimators are given. The upper bounds show how the difficulty of the…

常微分方程参数广义剖面估计的渐近效率与有限样本性质AI 解读

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop efficient estimation procedures for these parameters. Among the proposed methods in the literature, the generalized profiling estimation method developed by Ramsay and colleagues is particularly promising for its computational efficiency and good…

弱依赖下学生化统计量的 Edgeworth 展开AI 解读

In this paper, we derive valid Edgeworth expansions for studentized versions of a large class of statistics when the data are generated by a strongly mixing process. Under dependence, the asymptotic variance of such a statistic is given by an infinite series of lag-covariances, and therefore, studentizing factors (i.e., estimators of the asymptotic standard error) typically involve an increasing number, say, ℓ of lag-covariance estimators, which are themselves quadratic…

现状观测模型中的最大平滑似然估计与平滑最大似然估计AI 解读

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function in this model is the nonparametric maximum likelihood estimator (MLE). We study two alternative methods for the estimation of the distribution function, assuming some smoothness of the event time distribution. The first estimator is based…

Lévy 过程分数阶参数的谱估计AI 解读

We consider the problem of estimating the fractional order of a Lévy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for…

矩不等式模型的贝叶斯分析AI 解读

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any δ-contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior.…

非线性扩散过程的全局最优参数估计AI 解读

This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed…

谱密度估计与高斯白噪声的渐近等价AI 解读

We consider the statistical experiment given by a sample y(1), …, y(n) of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam’s deficiency Δ-distance, to two Gaussian experiments with simpler structure is established. The first one is given by independent zero mean Gaussians with variance approximately f(ωi), where ωi is a uniform grid of points in (−π, π) (nonparametric Gaussian scale regression). This…

Beta 混合后验的收敛速度与自适应非参数密度估计AI 解读

In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on [0, 1]. We consider a parametrization of Beta distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter, while putting a prior on this scaling parameter. We prove that such Bayesian nonparametric models have good frequentist asymptotic properties. We determine the posterior rate of…

大规模多重检验中零假设密度与非零效应比例估计的最优收敛速率AI 解读

An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several important problems, including the evaluation of the minimax rate of convergence and the construction of rate-optimal estimators, remain open. In this paper, we consider optimal estimation of the null density and the proportion of nonnull…

高维重抽样的若干非渐近结果（二）：多重检验AI 解读

In the context of correlated multiple tests, we aim to nonasymptotically control the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one- and two-sided multiple testing problem for the mean values of its coordinates. We address this problem by using the confidence regions developed in the companion paper [Ann.…

高维重抽样的若干非渐近结果（一）：置信区域AI 解读

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a nonasymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two…

非平稳非线性随机回归模型的条件最小二乘估计AI 解读

Let {Zn} be a real nonstationary stochastic process such that $E(Z_{n}|{\mathcal{F}}_{n-1})\stackrel{\mathrm{a.s.}}<\infty$ and $E(Z_{n}^{2}|{\mathcal{F}}_{n-1})\stackrel{\mathrm{a.s.}}<\infty$, where $\{{\mathcal{F}}_{n}\}$ is an increasing sequence of σ-algebras. Assuming that $E(Z_{n}|{\mathcal{F}}_{n-1})=g_{n}(\theta_{0},\nu_{0})=g_{n}^{(1)}(\theta_{0})+g_{n}^{(2)}(\theta _{0},\nu_{0})$, θ0∈ℝp, p<∞, ν0∈ℝq and q≤∞, we study the asymptotic properties of $\widehat{\theta}_{n}:=\arg\min_{\theta}\sum_{k=1}^{n}(Z_{k}-g_{k}({\theta,\widehat{\nu}}))^{2}\lambda _{k}^{-1}$…

部分线性单指标模型的估计AI 解读

In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component of the model. Asymptotic normality is established for both parametric components. For the index, a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in…

核随机矩阵的谱AI 解读

We place ourselves in the setting of high-dimensional statistical inference where the number of variables p in a dataset of interest is of the same order of magnitude as the number of observations n. We consider the spectrum of certain kernel random matrices, in particular n×n matrices whose (i, j)th entry is f(X'iXj/p) or f(‖Xi−Xj‖2/p) where p is the dimension of the data, and Xi are independent data vectors. Here f is assumed to be a locally smooth function. The study is…

基于 Copula 的半参数马尔可夫模型的有效估计AI 解读

This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications.…

带参数引导的局部拟似然AI 解读

Generalized linear models and quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification and the resulting model is completely determined by the data themselves. However nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models…

隐马尔可夫模型的子空间估计与预测方法AI 解读

Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite set as well. In particular, we study the geometric structure arising from the nonminimality of the linear state space representation of HMMs, and consistency of a subspace algorithm arising from a certain factorization of the singular value…

异方差回归中 c 最优设计的几何刻画AI 解读

We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23 (1952) 255–262] for c-optimal designs. As…

非线性主成分与多元扩散过程的长期含义AI 解读

We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these NPCs. By exploiting the theory of continuous-time, reversible Markov…