论文检索

通过大小变量与形状变量的独立性刻画分布族AI 解读

Let $X_1, \cdots, X_n$ be $n \geqslant 2$ positive random variables and $G(\mathbf{X})$ a positive variable satisfying $G(a\mathbf{X}) = aG(\mathbf{X})$ for all $a > 0$. Then $G$ is a size variable, and $\mathbf{X}/G$ is a shape vector. If $X_1, \cdots, X_n$ are independent, then the independence of shape and the size variable $G(\mathbf{X})$ characterizes (i) the lognormal distribution if $G(\mathbf{X}) = \Pi X^{1/n}_i$, (ii) the generalized gamma distribution if $G(\mathbf{X}) = (\sum X^b_i)^{1/b}$…

逐步贝叶斯程序AI 解读

Ordinarily a Bayesian estimation procedure uses one prior distribution to obtain a unique estimation rule (its Bayes rule). From the decision theoretical point of view, this procedure can be regarded as a convenient way to obtain admissible decision rules. However, many intuitively appealing, admissible estimation rules cannot be obtained directly in this way. We propose a new mechanism, called the Stepwise Bayesian Procedure (SBP). When the parameter space contains only…

协方差矩阵未知时正态均值向量的极小极大估计AI 解读

Let $X$ be an observation from a $p$-variate normal distribution $(p \geqslant 3)$ with mean vector $\theta$ and unknown positive definite covariance matrix $\sum$. We wish to estimate $\theta$ under the quadratic loss $L(\delta; \theta, \sum) = \lbrack\mathrm{tr}(Q\sum)\rbrack^{-1}(\delta - \theta)'Q(\delta - \theta)$, where $Q$ is a known positive definite matrix. Estimators of the following form are considered: $\delta_{k, h}(X, W) = \lbrack I - kh(X'W^{-1}X)\lambda_1(QW/n^\ast)Q^{-1}W^{-1}\rbrack X,$…

多元正态结构化均值与协方差检验中似然比统计量的非零假设渐近分布AI 解读

The multivariate normal patterned mean and covariance matrix testing problem is studied for general one and $k$-population hypotheses. T. W. Anderson's iterative algorithm for finding the maximum likelihood estimates, the forms of the likelihood ratio tests, and asymptotic chi-square distributions of these tests under the null hypothesis are given. The nonnull asymptotic normal distribution is derived using the standard delta method. This derivation involves using several…

基于不精确观测的时间序列预测函数AI 解读

Let $T \subseteq I$ be sets of real numbers. Let $\{Y(t): t\in I\}$ be a real time series whose covariance kernel is assumed known and positive definite. The mean is assumed either to be known or to be an unknown member of a known class of functions on $I$. For each fixed $s\in I, Y(s)$ is predicted by a minimum mean square error unbiased linear predictor $\hat{Y}(s)$ based on $\{Y(t): t\in T\}$. If $\hat{y}(s)$ is the evaluation of $\hat{Y}(s)$ given that the sample path…

独立正态随机变量随机线性组合的收敛定理AI 解读

It is shown that under fairly mild conditions linear combinations of independent normally distributed random variables with random coefficients tend to zero almost everywhere. The result is applied to parameter estimation in linear regression models.

由二元函数加权和导出的置换统计量的渐近正态性AI 解读

Statistics of the form $H_n = \sum d_{ijn}h_n(X_i, X_j)$ are considered, where $X_1, X_2, \cdots$, are independent and identically distributed random variables, the diagonal terms, $d_{iin}$, are equal to zero, and $h_n(x, y)$ is a symmetric real valued function. The asymptotic normality of such statistics is proven and the result then combined with work of Jogdeo on statistics that are weighted sums of bivariate functions of ranks to find sufficient conditions for…

泊松与正态均值的星形序列估计AI 解读

A vector $\mu = (\mu_1, \cdots, \mu_n)$ is said to be upper [lower] starshaped if $\mu_{m + 1} \geqslant 0 \lbrack \leqslant \mu_{m + 1} \leqslant \bar{\mu}_m\rbrack m = 1, \cdots, n - 1$, where $\bar{\mu}_m$ is a weighted average of $\mu_1, \cdots, \mu_m$. Obtained is the maximum likelihood estimate of $\mu$ when the $\mu_i$'s are the means of $n$ Poisson or normal populations and $\mu$ is known to be starshaped. The method is applied to obtain estimators of IHRA…

预测似然AI 解读

The likelihood function is the common basis of all parametric inference. However, with the exception of an ad hoc definition by Fisher, there has been no such unifying basis for prediction of future events, given past observations. This article proposes a definition of predictive likelihood which can help to remove some nonuniqueness problems in sampling-theory predictive inference, and which can produce a simple prediction analog of the Bayesian parametric result, posterior…

Wald–Wolfowitz 与 Smirnov 两样本检验的多元推广AI 解读

Multivariate generalizations of the Wald-Wolfowitz runs statistic and the Smirnov maximum deviation statistic for the two-sample problem are presented. They are based on the minimal spanning tree of the pooled sample points. Some null distribution results are derived and a simulation study of power is reported.

随机环境分枝过程中的估计问题AI 解读

Estimators are given for the two main parameters of the branching process with random environments, namely, the mean of the environmental mean (the average number of offspring per individual) and the mean of the logarithm of the environmental mean. The latter parameter indicates the certain extinction or possible explosion of the process. The consistency and asymptotic normality of the estimators are shown in the context of Smith and Wilkinson. Consistent estimators are also…

马尔可夫转移函数的非参数估计AI 解读

Let $\{X_n\}$ be a Markov chain having a stationary transition function and assume that the state set is an arbitrary set in a Euclidean space. The state transition law of the chain is given by a function $F(y|x) = P\lbrack X_{n+1} \leqslant y|X_n = x\rbrack$, which is assumed defined and continuous for all $x$. In this paper we give a statistical procedure for determining a function $F_n(y\mid x)$ on the basis of the sample $\{X_j\}^n_{j=1}, n = 1, 2,\cdots,$ and prove that…

给定边际分布的回归AI 解读

We consider the class of regression functions $\mathscr{M}(F, G) = \{m(x) = E\lbrack Y\mid X = x\rbrack, (X, Y) \in \Pi(F, G)\}$ where $\Pi(F, G)$ denotes the set of random vectors with marginal distributions $F$ and $G$. A characterization of $\mathscr{M}(F, G)$ is given together with a representation for the projection operator it induces in an appropriate Hilbert space.

发现新物种概率的线性估计AI 解读

A population consisting of an unknown number of distinct species is searched by selecting one member at a time. No a priori information is available concerning the probability that an object selected from this population will represent a particular species. Based on the information available after an $n$-stage search it is desired to predict the conditional probability that the next selection will represent a species not represented in the $n$-stage sample. Properties of a…

多元情形下的筛查函数与单调依赖函数AI 解读

An approach to simultaneous treatment of dependence and screening problems is presented. New characterizations of dependence of a random variable $X$ on a random vector $Y$ are obtained by functions $\nu_{X, Y}: (0, 1)\rightarrow \lbrack 0, 1\rbrack$ and $\mu_{X, Y} : (0, 1) \rightarrow \lbrack -1, 1\rbrack$ called respectively screening and monotonic dependence functions. These functions are shown to be appropriate measures of the intensity of connection and concordance of $X$…

矩阵 von Mises–Fisher 与 Bingham 分布的极大似然估计AI 解读

It has been conjectured by Khatri and Mardia that with probability one MLEs for the parameters of the von Mises-Fisher matrix distribution exist and are unique. We prove that, except for small sample sizes, this conjecture is true, both in the case where the parameter matrix has known rank and in the unrestricted case. The corresponding result for the matrix Bingham distribution is proven also.

多元正态分布似然比检验的渐近最优性AI 解读

In multivariate analysis under normality assumptions, many likelihood ratio criteria $(\lambda^{(n)})$ are distributed as $k\prod^m_{i=1} Z^a_{li}(1 - Z_{li})^{b_i}\prod^{m'}_{j=1} Z^{c_j}_{2j}$ for some constants, $k, m, m', a_i, b_i,$ and $c_j$ when their associated null hypotheses are true, where $Z_{ij}$ are independently distributed beta variates. Let $T^{(n)} = -n^{-1} \ln \lambda^{(n)}$. This paper shows that a sequence $\{T^{(n)}\}$ of this kind is asymptotically…

复合假设贝叶斯序贯检验的近似AI 解读

This paper deals with approximations to Bayesian sequential tests of composite hypotheses. If the distributions of the data form an exponential or truncation family, then such tests may be described by a continuation region in the space of $n$, the sample size, and $M_n$, the sufficient statistics, which are of fixed dimension. In this case Schwarz has been able to describe the asymptotic shape of the continuation region as the sampling cost $c$ approaches zero. We have…

利用狄利克雷过程混合估计二项分布参数AI 解读

The theory of Dirichlet processes is applied to the empirical Bayes estimation problem in the binomial case. The approach is Bayesian rather than being empirical Bayesian. When the prior is a Dirichlet process the posterior is a mixture of Dirichlet processes. Explicit estimators are given for the case of 2 and 3 parameters and compared with other empirical Bayes estimators by way of examples. Since the number of calculations become enormous when the number of parameters…

两个条件极限定理及其应用AI 解读

Let $(X_1, Y_1),\cdots, (X_N, Y_N)$ be i.i.d. rv's where the $X$'s are nonnegative integer-valued. Conditional on $\sigma X_k$ the asymptotic distribution of $\sigma Y_k$ and $\sigma a_k X_k$ are derived by general methods. Some applications are briefly discussed: sampling without replacement, the classical occupancy problem, the Wilcoxon statistic, the Poisson index of dispersion, testing geometric versus Poisson distribution.

具有特定最优性质的 Friedman 检验替代方法AI 解读

R. L. Anderson proposed a $\chi^2$-type rank statistic for the nonparametric analysis of a randomized blocks design. In this paper the asymptotic distribution of the test statistic is derived under a sequence of alternatives contiguous to the null hypothesis. Using Bahadur's concept of local approximate slope, it is shown that the test is optimal within a large class of rank tests including the tests proposed by Friedman and by Page. The results are extended to BIB designs.…

线性过程估计的高阶效率AI 解读

Estimation as a reduction of data is usually accompanied by some loss of information. This paper theoretically compares asymptotically efficient estimation methods for parameters in Gaussian linear processes. By means of the concept of "asymptotic information loss" suitably defined, estimates equivalent to the order of $N^{-\frac{1}{2}}$ are differentiated. This problem was studied by C. R. Rao for multinomial distributions and by K. Takeuchi for the exponential family of…

线性时不变系统的分布滞后近似AI 解读

An infinite distributed lag system is approximated by a truncated one, which can be consistently estimated. We investigate the rate at which the parameter space in the approximate model can be increased as sample size increases, in such a way that these estimates will provide consistent estimates of the underlying system.

平稳向量时间序列参数估计的中心极限定理及含噪信号应用AI 解读

A general finite parameter model for stationary ergodic nondeterministic vector time series is considered. A central limit theorem for parameter estimates, obtained by maximising frequency domain approximations to the Gaussian likelihood, is established. The treatment given extends the central limit theorem of Dunsmuir and Hannan in that the innovations covariance matrix and the linear transfer function need not be separately parameterised. Models for a stationary vector…