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固定域渐近下具有 Matérn 协方差的各向同性高斯随机场参数估计AI 解读

A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on Rd with isotropic Matérn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under…

利用高阶二次变差从不规则间距数据估计高斯随机场光滑度AI 解读

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of the corresponding fixed-domain asymptotic theory. In particular, we consider: (i) higher-order quadratic variations using nonequispaced line transect data, (ii) second-order quadratic variations from a sample of Gaussian random field…

计算机实验中随机正交表抽样设计的多元中心极限定理AI 解读

Let f : [0, 1)d→ℝ be an integrable function. An objective of many computer experiments is to estimate ∫[0, 1)d f(x) dx by evaluating f at a finite number of points in [0, 1)d. There is a design issue in the choice of these points and a popular choice is via the use of randomized orthogonal arrays. This article proves a multivariate central limit theorem for a class of randomized orthogonal array sampling designs [Owen Statist. Sinica 2 (1992a) 439–452] as well as for a class…

神经脉冲序列概率模型的若干理论结果AI 解读

This article contains two main theoretical results on neural spike train models, using the counting or point process on the real line as a model for the spike train. The first part of this article considers template matching of multiple spike trains. P-values for the occurrences of a given template or pattern in a set of spike trains are computed using a general scoring system. By identifying the pattern with an experimental stimulus, multiple spike trains can be deciphered…

一类 Matérn 型高斯随机场的固定域渐近理论AI 解读

Stein [Statist. Sci. 4 (1989) 432–433] proposed the Matérn-type Gaussian random fields as a very flexible class of models for computer experiments. This article considers a subclass of these models that are exactly once mean square differentiable. In particular, the likelihood function is determined in closed form, and under mild conditions the sieve maximum likelihood estimators for the parameters of the covariance function are shown to be weakly consistent with respect to…

扰乱网数值积分的渐近分布AI 解读

Recently, in a series of articles, Owen proposed the use of scrambled (t.m.s) nets and (t.s) sequences in high-dimensional numerical integration. These scrambled nets and sequences achieve the superior accuracy of equidistribution methods while allowing for the simpler error estimation techniques of Monte Carlo methods. The main aim of this article is to use Stein's method to study the asymptotic distribution of the scrambled (0.m.s) net integral estimate. In particular, it…

光滑高斯随机场模型中结构化相关矩阵的估计AI 解读

This article considers the estimation of structured correlation matrices in infinitely differentiable Gaussian random field models.The problem is essentially motivated by the stochastic modeling of smooth deterministic responses in computer experiments.In particular, the log-likelihood function is determined explicitly in closed-form and the sieve maximum likelihood estimators are shown to be strongly consistent under mild conditions.

论拉丁超立方抽样AI 解读

This paper contains a collection of results on Latin hypercube sampling. The first result is a Berry-Esseen-type bound for the multivariate central limit theorem of the sample mean $\hat{\mu}_n$ based on a Latin hypercube sample. The second establishes sufficient conditions on the convergence rate in the strong law for $\hat{\mu}_n$. Finally motivated by the concept of empirical likelihood, a way of constructing nonparametric confidence regions based on Latin hypercube…

随机化正交表抽样设计的组合中心极限定理AI 解读

Let X be a random vector uniformly distributed on the unit cube and $f: [0, 1]^3 \to \mathsf{R}$ be a measurable function. An objective of many computer experiments is to estimate $\mu = E(f \circ X)$ by computing f at a set of points in $[0, 1]^3$. There is a design issue in choosing these points. Recently Owen and Tang independently suggested using randomized orthogonal arrays in the choice of such a set. This paper investigates the convergence rate to normality of the…

两个多元正态分布共同均值的估计AI 解读

Let $X_1, X_2$ be two $p \times 1$ multivariate normal random vectors and $S_1, S_2$ be two $p \times p$ Wishart matrices, where $X_1 \sim N_p(\xi, \sum_1), X_2 \sim N_p(\xi, \sum_2), S_1 \sim W_p(\sum_1, n)$ and $S_2 \sim W_p(\sum_2, n)$. We further assume that $X_1, X_2, S_1, S_2$ are stochastically independent. We wish to estimate the common mean $\xi$ with respect to the loss function $L = (\hat{\xi} - \xi)'(\sum^{-1}_1 + \sum^{-1}_2)(\hat{\xi} - \xi)$. By extending the…

协方差矩阵估计AI 解读

Let $S_1$ and $S_2$ be two independent $p \times p$ Wishart matrices with $S_1 \sim W_p(\sum_1, n_1)$ and $S_2 \sim W_p(\sum_2, n_2)$. We wish to estimate $(\sum_1, \sum_2)$ under the loss function $L(\hat{\sum}_1, \hat{\sum}_2; \sum_1, \sum_2) = \sum_i\{\operatorname{tr}(\sum^{-1}_i \hat{\sum}_i) - \log|\sum^{-1}_i\hat{\sum}_i| - p\}$. Our approach is to first utilize the principle of invariance to narrow the class of estimators under consideration to the equivariant ones.…