日期精度：到日 2575 篇 · 到月 3 篇 · 到年 0 篇
具有半空间形状的置信集
SUMMARY For the problem of estimating the mean of a p-dimensional normal distribution, p > 1, confidence regions based on half-spaces bounded by a hyperplane having the vector of observations as normal are proposed. Confidence regions with exact probability of coverage are constructed. Tables are provided.
半参数加性回归
SUMMARY A simple estimator for β is proposed for the model y = x'β + g(t)+ error, g smooth but unknown. The approach is to approximate the estimating equation obtained from a ***semiparametric likelihood and in the simplest case reduces to minimizing the distance between the 'pseudoresiduals' y - x'β and a local linear cross-validated estimate of them. When the errors are independent with finite variance, the bias and variance of the estimate are computed and compared…
相关误差空间回归模型的一种新预测方法
SUMMARY This paper deals with minimum mean-squared error, unbiased linear interpolation of a continuous domain spatial process based on a sparse set of irregularly spaced observations. The process is assumed to be governed by a linear regression model with errors that follow a second-order stationary Gaussian random field. A new method of prediction is developed that is compatible with the parameter estimation procedures of Vecchia. The result is a new likelihood-based…
利用部分指数模型估计多元均值参数
SUMMARY A class of partly exponential models is proposed for the regression analysis of multivariate response data. The class is parameterized in terms of the response mean and a general shape parameter. It includes the generalized linear error model and exponential dispersion models as special cases. Maximum likelihood equations for mean parameters are shown to be of the same form as certain generalized estimating equations, and maximum likelihood estimates of mean and…
正态位置参数后验矩的精确与近似表达
SUMMARY The forms of first and second posterior moments for a normal location parameter are identified for a rather general class of prior distributions. Exact and approximate illustrations are given where the prior distribution is double exponential or Student t respectively.
非参数回归中方差估计量的比较
SUMMARY We compare two estimators of error variance, both based on quadratic forms in the residuals about smoothing spline fits to data. The estimators are compared over the whole range of values of the smoothing parameter as well as for data-based choices of the smoothing parameter. We show that the commonly used estimator of variance has the serious drawback of underestimating the error variance for small choices of the smoothing parameter. This drawback is not shared by a…
长程相依时间序列的拟合优度检验
SUMMARY We propose a test statistic for goodness of fit in time series with slowly decaying serial correlations. The asymptotic distribution of the test statistic, originally proposed by Milhoj for time series with smooth spectra, turns out to be the same, under the null hypothesis, even if the spectrum has a pole at 0. In particular, the test is suitable to detect lack of independence in the observations, or estimated residuals, if the first few correlations are small but…
多参数指数族中高阶渐近方法的实践应用
SUMMARY Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often…
依赖数据的受约束Monte Carlo最大似然估计
SUMMARY Maximum likelihood estimates (MLEs) in autologistic models and other exponential family models for dependent data can be calculated with Markov chain Monte Carlo methods (the Metropolis algorithm or the Gibbs sampler), which simulate ergodic Markov chains having equilibrium distributions in the model. From one realization of such a Markov chain, a Monte Carlo approximant to the whole likelihood function can be constructed. The parameter value (if any) maximizing this…
异方差线性模型中的参数估计
SUMMARY This paper deals with linear regression models with non-homogeneous error variances. The common situation where the error variance is a smooth function of the values of the regressor variables is considered. The error variance function is represented by a function of known form, but its expression involves the vector of unknown regression coefficients β and an additional vector parameter θ. Estimation of β by iterative weighted least squares (IWLS) therefore also…
基于相关成分的最大似然回归
SUMMARY Most regression methods for multicollinear data are only based on assumptions about the conditional distribution of the dependent variable, given the explanatory variables. Here we propose a new prediction method taking a joint multinomial distribution for all the variables as the starting point. A hypothesis is formulated stating that only a fixed small number of components constructed from the explanatory variables is relevant for prediction, and…
嵌套回归模型族中条件风险比的信息界
SUMMARY Information bounds are obtained for a parametric treatment effect in a nested family of models for the conditional distribution of survival given confounding variables. The family extends from the fully parametric Weibull model to a completely nonparametric model for right-censored data and includes the Cox model and the stratified version of it. It is shown that, in certain special cases, there is no loss of information about the treatment effect when going from a…
两个伯努利总体的渐近有效分配规则
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.
利用次序统计量伴随变量估计分布：自助法 Monte Carlo 模拟应用
SUMMARY We show that a simulation method suggested by Efron for approximating bootstrap distributions is closely related to techniques based on concomitants of order statistics and develop its asymptotic properties from that viewpoint. We prove that the method produces Monte Carlo approximations with variance and mean-squared error decreasing like B− 1 n− 1/2, where B denotes the number of simulations and n equals the sample size. Therefore Efron's method can be a competitor…
合并二乘二列联表：估计量的渐近矩
SUMMARY Consider J independent pairs of mutually independent binomial variates which can be considered as 72 times 2 tables. We assume a common measure of association, such as the odds ratio, between the tables. This paper studies the asymptotic moments of the ‘pooled' estimators, i.e. those constructed from the data summed over all the tables. For balanced designs, or proportional subclass numbers, it is shown that the pooled estimator of the common odds ratio is…
经验泛函与高效平滑参数选择
SUMMARY A striking feature of curve estimation is that the smoothing parameter ĥ 0, which minimizes the squared error of a kernel or smoothing spline estimator, is very difficult to estimate. This is manifest both in slow rates of convergence and in high variability of standard methods such as cross-validation. We quantify this difficulty by describing nonparametric information bounds and exhibit asymptotically efficient estimators of ĥ 0 that attain the bounds. The…
一致的非参数阶数确定与混沌
SUMMARY We give a brief introduction to deterministic chaos and a link between chaotic deterministic models and stochastic time series models. We argue that it is often natural to determine the embedding dimension in a noisy environment first in any systematic study of chaos. Setting the stochastic models within the framework of non-linear autoregression, we introduce the notion of a generalized partial autocorrelation and an order. We approach the estimation of the…
线性滤波器与非线性系统
SUMMARY It has been asserted in the literature that the low pass filtering of time series data may lead to erroneous results when calculating attractor dimensions. Here we prove that finite order, non-recursive filters do not have this effect. In fact, a generic, finite order, non-recursive filter leaves invariant all the quantities that can be estimated by using embedding techniques such as the method of delays.
拉丁超立方抽样的中心极限定理
SUMMARY Latin hypercube sampling (LHS) is a technique for Monte Carlo integration, due to McKay, Conover and Beckman. M. Stein proved that LHS integrals have smaller variance than independent and identically distributed Monte Carlo integration, the extent of the variance reduction depending on the extent to which the integrand is additive. We extend Stein's work to prove a central limit theorem. Variance estimation methods for nonparametric regression can be adapted to…
SUMMARY This paper is concerned with estimating the dimension of an attractor. The Grassberger–Procaccia procedure for estimating the correlation dimension is reviewed, and some alternative estimators considered. A particularly important problem is to estimate dimension in the presence of noise in the data. In pursuit of this, a modification of the Grassberger–Procaccia procedure is proposed, and illustrated on both artificial and real data sets.
一般随机流行病模型中感染率估计量的渐近性质
SUMMARY Some estimators for the infection rate in the general stochastic epidemic model are presented. The first estimator follows the approach of maximum likelihood. However, this approach requires us to observe most if not all of the epidemic process. As an alternative, an estimator which uses less detailed data is derived from a suitable martingale. Both estimators are shown to be consistent only when a major outbreak of disease is observed. Minor out-breaks do not…
线性估计方程的刀切法：渐近理论与随机过程应用
SUMMARY Let (X 1, X 2, ..., Xn) be a vector of (possibly dependent) random variables having distribution F(X, θ). Let θn be an estimating equation for θ, e.g. the score function or the maximum pseudolikelihood estimating equation in spatial processes. Let θn be the estimator obtained from G such that θn → θ0 in probability and n1/2(θn−θ0)→N(0,V) in distribution. In many situations, it is difficult to derive an analytical expression for V, e.g. for maximum pseudolikelihood…
交叉验证函数中的局部极小值
SUMMARY The method of least squares cross-validation for choosing the bandwidth of a kernel density estimator has been the object of considerable research, through both theoretical analysis and simulation studies. The method involves the minimization of a certain function of the bandwidth. One of the less attractive features of this method, which has been observed in simulation studies but has not previously been understood theoretically, is that rather often the…
比较拟合优度检验的图形方法
SUMMARY A method for comparing tests of normality using their ‘isotones‘, i.e. contours on the surfaces representing p-values, is proposed. Select a family of distributions labelled by two parameters λ1 and λ2 to represent the null and alternative hypotheses. For each (λ1, λ2) take an ‘ideal sample’ from that distribution, calculate the value of the goodness-of-fit statistic and determine the corresponding P-value under the normality assumption. This generates a surface of…