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存在并列与近似并列时总体排名的置信区间AI 解读

Frequentist confidence intervals for population ranks and their statistical justifications are not well established, even though there is a great need for such procedures in practice. How do we assign confidence bounds for the ranks of health care facilities, schools, and financial institutions based on data that do not clearly separate the performance of different entities apart? The commonly used bootstrap-based frequentist confidence intervals and Bayesian intervals for…

高维线性回归中 Lasso 变量选择的稀疏性与偏差AI 解读

Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436–1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of greater order than the sample size. Zhao and Yu [(2006) J. Machine Learning Research 7 2541–2567] formalized the neighborhood stability condition in the context of linear regression as a strong irrepresentable condition. That paper showed…

随机变量函数之和的估计：实例与信息界AI 解读

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit relationship is established between efficient influence functions for the estimation of sums of variables and the estimation of their means. Certain “plug-in” estimators are proved to be asymptotically efficient in finite-dimensional…

用于 cDNA 微阵列归一化与分析的双向半线性模型AI 解读

A basic question in analyzing cDNA microarray data is normalization, the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range. A proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels. We propose a two-way semilinear model (TW–SLM) for normalization and analysis of microarray data. This method does not…

一般经验贝叶斯小波方法与精确自适应极小极大估计AI 解读

In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper, we develop general empirical Bayes methods for the estimation of true signal. Our estimators approximate certain oracle separable rules and achieve adaptation to ideal risks and exact minimax risks in broad collections of classes of signals. In particular, our estimators are uniformly adaptive to the minimum risk of separable estimators and the…

This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models…

复合决策理论与经验贝叶斯方法：特邀论文AI 解读

Introduction.Compound decision theory and empirical Bayes methodology, acclaimed as "two breakthroughs" by Neyman (1962), are the most important contributions of Herbert Robbins to statistics.The purpose of this paper is to provide a brief description of his work in these two intimately connected fields, its impact and a number of important related developments.Robbins introduced compound decision theory in 1950 at the Second Berkeley Symposium on Mathematical Statistics and…

随机设计非参数回归的渐近等价理论AI 解读

This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function. The asymptotic equivalence is established by constructing explicit equivalence mappings between the nonparametric regression and the white-noise experiments, which provide synthetic observations and synthetic asymptotic solutions from any one of the two experiments…

保序回归的风险界AI 解读

Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform $n^{-1/3}$-consistency of the $\ell_p$ risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability distribution of the data, with possibly dependent observations.

单峰回归函数峰值位置的最小二乘估计AI 解读

In this paper, we consider nonparametric least squares estimators of the mode of an unknown unimodal regression function. We establish almost sure convergence of these estimators with nearly optimal convergence rates, under the assumption of the exponential tail for the error distributions.

区间删失数据的线性回归AI 解读

This paper concerns linear regression with interval censored data. $M$-estimators for the regression coefficients are derived. Asymptotic consistency and normality of the $M$-estimators are obtained via an exponential inequality for $U$-statistics. Asymptotically efficient estimators are provided under mild conditions.

光滑性指数为二分之一时非参数实验的渐近不等价性AI 解读

An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is ½

双侧删失数据的线性回归AI 解读

Linear regression with doubly censored responses is considered. Buckley-James-Ritov-type estimators are proposed. Semiparametric information and projective scores are discussed. An expansion of the estimating equations is obtained under fairly general assumptions. Sufficient conditions are given for the asymptotic consistency and normality of the estimators.

离散指数族模型中混合密度的估计AI 解读

This paper concerns estimating a mixing density function $g$ and its derivatives based on iid observations from $f(x) = \int f(x \mid \theta)g(\theta)d\theta$, where $f(x \mid \theta)$ is a known exponential family of density functions with respect to the counting measure on the set of nonnegative integers. Fourier methods are used to derive kernel estimators, upper bounds for their rate of convergence and lower bounds for the optimal rate of convergence. If $f(x \mid \theta_0) \geq \varepsilon^{x + 1} \forall x$…

平均剩余寿命回归模型中的估计AI 解读

SUMMARY The proportional mean residual life model was originally proposed by Oakes and Dasu. This model can be extended to a regression model with explanatory variables. We consider the problem of estimation of the regression parameter in this general model. We investigate two types of estimator, of which one is based on the maximum likelihood equation of the exponential regression model, and the other is based on the underlying proportional hazards structure of the model…

随机乘法删失模型中经验分布的大样本研究AI 解读

Consider an incomplete data problem with the following specifications. There are three independent samples $(X_1, \ldots, X_m), (Z_1, \ldots, Z_n)$ and $(U_1, \ldots, U_n)$. The first two samples are drawn from a common lifetime distribution function $G$, while the third sample is drawn from the uniform distribution over the interval $(0,1)$. In this paper we derive the large sample properties of $\hat{G}_{m,n}$, the nonparametric maximum likelihood estimate of $G$ based on…

两个伯努利总体的渐近有效分配规则AI 解读

SUMMARY Given two Bernoulli populations with unknown means, we consider the problem of sampling x 1, x 2, ... sequentially from these populations such as to maximize the expected value of the sum S n = x 1 + x 2 + ... + x n as n → ∞. We obtain an asymptotically efficient rule. Simulation studies show that it performs well for moderate values of n.

有偏处理分配下乘法处理效应的估计AI 解读

Suppose that, given θ, x is Poisson with mean θ, while, given θ, y is Poisson with mean αθ or βθ according as treatment 1 or treatment 2 is used. Moreover, suppose that treatment 1 is used if x < a, while treatment 2 is used if x≥ a. Under this biased allocation of treatments we give consistent estimators of the two treatment effects α and β. The method also applies when x is binomial and θ is the odds on success, and to other cases.

有偏治疗分配下的乘法治疗效应估计AI 解读

Suppose that, given θ, x is Poisson with mean θ, while, given θ, y is Poisson with mean αθ or βθ according as treatment 1 or treatment 2 is used. Moreover, suppose that treatment 1 is used if x < a, while treatment 2 is used if x≥ a. Under this biased allocation of treatments we give consistent estimators of the two treatment effects α and β. The method also applies when x is binomial and θ is the odds on success, and to other cases.

估计混合密度与混合分布的傅里叶方法AI 解读

Let $X_1, X_2, \cdots$ be iid observations from a mixture density $f(x) = \int f(x \mid \theta)dG(\theta)$, where $f(x \mid \theta)$ is a known parametric family of density functions and $G$ is an unknown distribution function. This paper concerns estimating the mixing density $g = G'$ and the mixing distribution $G$. Fourier methods are used to derive kernel estimators, upper bounds for their rates of convergence and lower bounds for the optimal rate of convergence.…