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具有先后约束的一类序贯控制问题的最优策略AI 解读

Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each phase, one can pursue the projects in any order. When pursuing the project with one unit of resource, the project state changes according to a Markov chain. The probability distribution of the Markov chain is known up to an unknown…

非线性时间序列的渐近谱理论AI 解读

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear time series.

Kiefer–Wolfowitz–Blum 随机逼近算法的伴随算法AI 解读

A stochastic algorithm for the recursive approximation of the location $θ$ of a maximum of a regression function was introduced by Kiefer and Wolfowitz [Ann. Math. Statist. 23 (1952) 462–466] in the univariate framework, and by Blum [Ann. Math. Statist. 25 (1954) 737–744] in the multivariate case. The aim of this paper is to provide a companion algorithm to the Kiefer–Wolfowitz–Blum algorithm, which allows one to simultaneously recursively approximate the size $μ$ of the…

多变量问题中点扩散函数的非参数估计AI 解读

The removal of blur from a signal, in the presence of noise, is readily accomplished if the blur can be described in precise mathematical terms. However, there is growing interest in problems where the extent of blur is known only approximately, for example in terms of a blur function which depends on unknown parameters that must be computed from data. More challenging still is the case where no parametric assumptions are made about the blur function. There has been a…

“大维度、小样本”范式的边际渐近理论及微阵列应用AI 解读

The “large $p$, small $n$” paradigm arises in microarray studies, image analysis, high throughput molecular screening, astronomy, and in many other high dimensional applications. False discovery rate (FDR) methods are useful for resolving the accompanying multiple testing problems. In cDNA microarray studies, for example, $p$-values may be computed for each of $p$ genes using data from $n$ arrays, where typically $p$ is in the thousands and $n$ is less than 30. For FDR…

含噪向量场积分曲线的核估计与检验：扩散张量成像中的统计问题AI 解读

Let $v$ be a vector field in a bounded open set $G\subset {\mathbb{R}}^d$. Suppose that $v$ is observed with a random noise at random points $X_i,\ i=1,\dots, n$, that are independent and uniformly distributed in $G$. The problem is to estimate the integral curve of the differential equation \[\frac{dx(t)}{dt}=v(x(t)),\qquad t\geq 0,x(0)=x_{0}\in G,\] starting at a given point $x(0)=x_0\in G$ and to develop statistical tests for the hypothesis that the integral curve reaches…

检验大小、功效与错误发现率AI 解读

Modern scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the same time. Microarrays epitomize this type of technology, but similar situations arise in proteomics, spectroscopy, imaging, and social science surveys. This paper uses false discovery rate methods to carry out both size and power calculations on large-scale problems. A simple empirical Bayes approach allows the false…

弱依赖下区块变量和的渐近展开AI 解读

Let {Xi}i=−∞∞ be a sequence of random vectors and $Y_{in}=f_{in}(\mathcal{X}_{i,\ell})$ be zero mean block-variables where $\mathcal{X}_{i,\ell}=(X_{i},\ldots,X_{i+\ell-1})$, i≥1, are overlapping blocks of length ℓ and where fin are Borel measurable functions. This paper establishes valid joint asymptotic expansions of general orders for the joint distribution of the sums ∑i=1nXi and ∑i=1nYin under weak dependence conditions on the sequence {Xi}i=−∞∞ when the block length ℓ…

局部 U 统计过程与多个样本变量函数的密度估计AI 解读

A notion of local U-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U-processes that may be useful in other contexts. This local U-statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer. Statist. Assoc. 89 (1994) 517–525] and, as a consequence, uniform in bandwidth central limit theorems in the sup…

Le Cam定理的一个补充AI 解读

This paper examines asymptotic equivalence in the sense of Le Cam between density estimation experiments and the accompanying Poisson experiments. The significance of asymptotic equivalence is that all asymptotically optimal statistical procedures can be carried over from one experiment to the other. The equivalence given here is established under a weak assumption on the parameter space ℱ. In particular, a sharp Besov smoothness condition is given on ℱ which is sufficient…

单调响应模型的似然推断AI 解读

The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the usual parametric or semiparametric situations in that the MLE of the monotone function at a point converges to the truth at rate n1/3 (slower than the usual $\sqrt{n}$ rate) with a non-Gaussian limit distribution. A framework for…

累积预测误差、信息准则与自回归时间序列的最优预测AI 解读

The predictive capability of a modification of Rissanen’s accumulated prediction error (APE) criterion, APEδn, is investigated in infinite-order autoregressive (AR(∞)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APEδn is obtained by summing these squared errors from stage nδn, where n is the sample size and 1/n≤δn≤1−(1/n) may depend on n. Under certain regularity conditions, an asymptotic expression is derived for the…

分数随机微积分的统计学问题AI 解读

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by a fractional Brownian motion with any level of Hölder-regularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear…

长度与表面积估计的非参数方法AI 解读

The Minkowski content L0(G) of a body G⊂ℝd represents the boundary length (for d=2) or the surface area (for d=3) of G. A method for estimating L0(G) is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing G) in which we are able to identify whether every point is inside or outside G. Some theoretical properties concerning strong consistency, L1-error and convergence rates are obtained. A…

时间序列模型的变点检验与近历依赖序列的极限定理AI 解读

This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald test for change points in a general class of time series models under the no change-point hypothesis. As an application, we verify our assumptions for the long-memory fractional ARIMA model.

单调性约束估计量的 Lp 误差AI 解读

We aim at estimating a function λ:[0,1]→ℝ, subject to the constraint that it is decreasing (or increasing). We provide a unified approach for studying the $\mathbb {L}_{p}$-loss of an estimator defined as the slope of a concave (or convex) approximation of an estimator of a primitive of λ, based on n observations. Our main task is to prove that the $\mathbb {L}_{p}$-loss is asymptotically Gaussian with explicit (though unknown) asymptotic mean and variance. We also prove…

协变量调整的响应自适应设计的渐近性质AI 解读

Response-adaptive designs have been extensively studied and used in clinical trials. However, there is a lack of a comprehensive study of response-adaptive designs that include covariates, despite their importance in clinical trials. Because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates, covariate-adjusted response-adaptive (CARA) designs are very complex to formulate. In this paper, we overcome the technical…

缺失数据模型的蒙特卡洛似然推断AI 解读

We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observed data. Our Monte Carlo approximation to the MLE is a consistent and asymptotically normal estimate of the minimizer θ* of the Kullback–Leibler information, as both Monte Carlo…

右删失下具有协变量阈值变点的变换模型推断AI 解读

We consider linear transformation models applied to right censored survival data with a change-point in the regression coefficient based on a covariate threshold. We establish consistency and weak convergence of the nonparametric maximum likelihood estimators. The change-point parameter is shown to be n-consistent, while the remaining parameters are shown to have the expected root-n consistency. We show that the procedure is adaptive in the sense that the nonthreshold…

可分解图上的 Wishart 分布AI 解读

When considering a graphical Gaussian model ${\mathcal{N}}_{G}$ Markov with respect to a decomposable graph G, the parameter space of interest for the precision parameter is the cone PG of positive definite matrices with fixed zeros corresponding to the missing edges of G. The parameter space for the scale parameter of ${\mathcal{N}}_{G}$ is the cone QG, dual to PG, of incomplete matrices with submatrices corresponding to the cliques of G being positive definite. In this…

函数型数据的统计推断AI 解读

With modern technology development, functional data are being observed frequently in many scientific fields. A popular method for analyzing such functional data is “smoothing first, then estimation.” That is, statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another. However, little is known about…

含噪量子零差层析中 Wigner 函数的极小极大与自适应估计AI 解读

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on ℝ2 which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The effect of the losses due to detection inefficiencies, which are always present in a real experiment, is the addition to the…

决策树分割点的置信集AI 解读

We investigate the problem of finding confidence sets for split points in decision trees (CART). Our main results establish the asymptotic distribution of the least squares estimators and some associated residual sum of squares statistics in a binary decision tree approximation to a smooth regression curve. Cube-root asymptotics with nonnormal limit distributions are involved. We study various confidence sets for the split point, one calibrated using the subsampling…

一元平滑估计中的方差降低AI 解读

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While the new estimator retains many advantages of the local linear estimator, it has…