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广义最小二乘估计量风险上界的一种方法AI 解读

First, an approach to an upper bound for the risk matrix of GLSE's is established when the information on the parameter space of the structural parameter in the covariance matrix of the error can be utilized. Second, this result is applied to regression with (i) serial correlation and (ii) heteroscedastic covariance structure. In the heteroscedastic regression, the problem of estimating the common mean of two normal populations is studied in detail.

额外观测所包含的统计信息AI 解读

Let $\mathscr{E}^n$ be a statistical experiment based on $n$ i.i.d. observations. We compare $\mathscr{E}^n$ with $\mathscr{E}^{n+r_n}$. The gain of information due to the $r_n$ additional observations is measured by the deficiency distance $\Delta (\mathscr{E}^n, \mathscr{E}^{n+r_n})$, i.e., the maximum diminution of the risk functions. We show that under general dimensionality conditions $\Delta(\mathscr{E}^n, \mathscr{E}^{n+r_n})$ is of order $r_n/n$. Further the behavior…

估计量的大偏差AI 解读

The performance of a sequence of estimators $\{T_n\}$ of $g(\theta)$ can be measured by its inaccuracy rate $-\lim \inf_{n\rightarrow\infty} n^{-1} \log \mathbb{P}_\theta(\|T_n - g(\theta)\| > \varepsilon)$. For fixed $\varepsilon > 0$ optimality of consistent estimators $\operatorname{wrt}$ the inaccuracy rate is investigated. It is shown that for exponential families in standard representation with a convex parameter space the maximum likelihood estimator is optimal. If…

条件经验过程AI 解读

We prove a Donsker-type invariance principle for a nearest-neighbor-type conditional empirical process. As an application we show asymptotic normality of conditional quantiles and derive large-sample distribution-free tests and confidence bands for a conditional distribution function.

随机删失下与V统计量相关的经验过程及一类估计量AI 解读

A class of empirical processes associated with $V$-statistics ($V$-empirical process) under random censoring, and a class of nonparametric estimators based on the corresponding quantile process are defined. The $V$-empirical process is the censored data analogue of the $U$-empirical process considered by Silverman (1976, 1983). The class of estimators is the analogue of the class of generalized $L$-statistics introduced by Serfling (1984) and it includes the results of…

随机退出下指数平均寿命的时间序贯估计AI 解读

In the context of lifetesting, an asymptotically risk-efficient procedure for the estimation of the exponential mean lifetime is considered when the survival times of the units are subject to random censorship. The loss function is the sum of squared error due to estimation, cost of recruitment of the units, and cost of total time on test. Asymptotic properties of the sequential estimator and stopping time are described as the per unit cost of total time on test decreases to…

广义加性模型的降维原理AI 解读

Let $(X, Y)$ be a pair of random variables such that $X = (X_1,\cdots, X_J)$ ranges over $C = \lbrack 0, 1\rbrack^J$. The conditional distribution of $Y$ given $X = x$ is assumed to belong to a suitable exponential family having parameter $\eta \in \mathbb{R}$. Let $\eta = f(x)$ denote the dependence of $\eta$ on $x$. Let $f^\ast$ denote the additive approximation to $f$ having the maximum possible expected log-likelihood under the model. Maximum likelihood is used to fit an…

半鞅回归模型的筛法估计AI 解读

Estimation by the method of sieves for a semimartingale regression model introduced by Aalen (1980) is studied. It is of interest to estimate functions which describe the influence of the covariates over time. An estimator for these functions is introduced and conditions which ensure consistency of the estimator in $L^2$-norm are given. Applications to diffusion processes and point processes with censored data are also discussed.

利用传感器阵列数据估计移动信号源参数AI 解读

This paper is concerned with the problem of estimating the variable time delays of a signal arriving at an array of sensors. A procedure to estimate the parameters of a linear time delay model is proposed. The procedure compares the Fourier transforms at different frequencies (thereby taking the Doppler effect into consideration). Under regularity conditions, the estimate obtained is shown to be consistent and asymptotically normal. Simulations were carried out and the…

移动平均过程样本协方差与相关函数的极限理论AI 解读

Let $X_t = \sum^\infty_{j=-\infty} c_jZ_{t-j}$ be a moving average process where the $Z_t$'s are iid and have regularly varying tail probabilities with index $\alpha > 0$. The limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite fourth moment. Furthermore, in the infinite variance case $(0 < \alpha < 2)$, the sample correlation function is shown to converge in distribution to the ratio of two…

单变量时间序列模型识别的贝叶斯程序AI 解读

This paper is concerned with model selection in time series analysis. An identification criterion is presented that is asymptotically equivalent to a Bayes decision rule. The discussion is conducted in the context of a general class of parametric time series models and consideration is given to the special case of order determination in autoregressive moving-average representations. Consistency of the criterion is proved.

外部贝叶斯意见汇总算子的刻画AI 解读

When a panel of experts is asked to provide some advice in the form of a group probability distribution, the question arises as to whether they should synthesize their opinions before or after they learn the outcome of an experiment. If the group posterior distribution is the same whatever the order in which the pooling and the updating are done, the pooling mechanism is said to be externally Bayesian by Madansky (1964). In this paper, we characterize all externally Bayesian…

球对称误差下线性模型系数的改进置信集AI 解读

Under the assumption of normal errors, confidence spheres for $p(p \geq 3)$ coefficients of a linear model centered at the positive part James-Stein estimators were recently proved, by Hwang and Casella, to dominate the usual confidence set with the same radius. In this paper, the same domination results are established under various spherically symmetric distributions. These distributions include uniform distributions, double exponential distributions, and multivariate $t$ d…

多元分布的置信集合AI 解读

The confidence sets for a $q$-dimensional distribution studied in this paper have several attractive features: affine invariance, correct asymptotic level whatever the actual distribution may be, numerical feasibility, and a local asymptotic minimax optimality property. When dimension $q$ equals one, the confidence sets reduce to the usual Kolmogorov-Smirnov confidence bands, except that critical values are determined by bootstrapping.

共同主成分分析的渐近理论AI 解读

Under the common principal component model $k$ covariance matrices $\mathbf{\Sigma}_1,\cdots,\mathbf{\Sigma}_k$ are simultaneously diagonalizable, i.e., there exists an orthogonal matrix $\mathbf{\beta}$ such that $\mathbf{\beta'\Sigma_i\beta = \Lambda_i}$ is diagonal for $i = 1,\cdots, k$. In this article we give the asymptotic distribution of the maximum likelihood estimates of $\mathbf{\beta}$ and $\mathbf{\Lambda}_i$. Using these results, we derive tests for (a) equality…

多元方差分量模型的极大似然估计与似然比准则AI 解读

Maximum likelihood estimators are obtained for multivariate components of variance models under the condition that the effect covariance matrix is positive semidefinite with a maximum rank. The rank of the estimator is random. The estimation procedure leads to a likelihood ratio test that the rank of the effect matrix is not greater than a given number against the alternative that the rank is not greater than a larger specified number. Linear structural relationship models…

强依赖平稳高斯时间序列参数估计的大样本性质AI 解读

A strongly dependent Gaussian sequence has a spectral density $f(x, \theta)$ satisfying $f(x, \theta) \sim |x|^{-\alpha(\theta)} L_\theta(x)$ as $x \rightarrow 0$, where $0 < \alpha(\theta) < 1$ and $L_\theta(x)$ varies slowly at 0. Here $\theta$ is a vector of unknown parameters. An estimator for $\theta$ is proposed and shown to be consistent and asymptotically normal under appropriate conditions. These conditions are satisfied by fractional Gaussian noise and fractional…

ε 污染先验下的稳健贝叶斯与经验贝叶斯分析AI 解读

For Bayesian analysis, an attractive method of modelling uncertainty in the prior distribution is through use of $\varepsilon$-contamination classes, i.e., classes of distributions which have the form $\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, \pi_0$ being the base elicited prior, $q$ being a "contamination," and $\varepsilon$ reflecting the amount of error in $\pi_0$ that is deemed possible. Classes of contaminations that are considered include (i) all possible…

伪极大似然估计：渐近分布AI 解读

Gong and Samaniego (1981) define pseudo maximum likelihood estimation and derive the asymptotic distribution of the resulting estimates. This note gives a simpler and more elegant expression for the asymptotic variance of a pseudo maximum likelihood estimate.

非对称污染下截尾均值的最大渐近方差AI 解读

We consider the following problem arising in robust estimation theory: Find the maximum asymptotic variance of a trimmed mean used to estimate an unknown location parameter when the error distribution is subject to asymmetric contamination. The model for the error distribution is $F = (1 - \varepsilon)F_0 + \varepsilon G$, where $F_0$ is a known distribution symmetric about $0, \varepsilon$ is fixed proportion of contamination, and $G$ is an unknown and possibly asymmetric…

自回归传递函数准则选阶的渐近效率AI 解读

The autoregressive orders selected by the criterion autoregressive transfer function (CAT) of Parzen (1974), a new version, CAT$^\ast$, of CAT introduced by Parzen (1977), and the CAT$_2$ criterion of Bhansali (1985) are shown to be asymptotically efficient in the sense defined by Shibata (1980, 1981). A generalization of the penalty function considered by Shibata (1980) is introduced. The order selected by the CAT$_\alpha$ criterion of Bhansali (1985), with any fixed $\alpha > 1$…

Bechhofer–Kulkarni伯努利总体选择程序的最优性质AI 解读

In a recent article Bechhofer and Kulkarni proposed a class of closed adaptive sequential procedures for selecting that one of $k \geq 2$ Bernoulli populations with the largest single-trial success probability. These sequential procedures which take no more than $n$ observations from any one of the $k$ populations achieve the same probability of a correct selection as does a single-stage procedure which takes exactly $n$ observations from every one of the $k$ populations. In…

Dirichlet过程下不可回溯序贯抽样的有限停止AI 解读

This paper shows that for sequential sampling without recall from a Dirichlet process, there exists a finite bound beyond which one will cease sampling with probability 1. The result is valid for Dirichlet processes defined on closed bounded intervals of the real line.

临床试验中受限随机化规则下的多处理比较AI 解读

In the course of conducting a clinical trial to compare $K (\geq 2)$ treatments, it is often desirable to balance the trial with respect to the assignments of patients to treatments. On the other hand, some form of randomization of treatment assignments is essential for reducing experimental bias. In this article, the large-sample approximation to the null distribution of $K$-sample randomization tests generated from a broad class of restricted randomization rules is…