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估计多条平稳时间序列均值函数的经验贝叶斯方法AI 解读

An empirical Bayes procedure is considered for estimating a mean value function imbedded within a collection of N stationary time series. Two cases are considered: a mean value function that is a fixed function of time and one that is a stationary normal process. Estimators for the spectral densities are derived from prior data using an extension to time series of the usual one-way analysis of variance. These estimators are inserted into approximations for the classical…

寿命试验中时间截断指数分布参数的估计AI 解读

This article proves the asymptotic unbiasedness and consistency when the sample size of the maximum likelihood estimate of the mean θ of an exponential distribution in a time-truncated experiment is random. Convergence of to with μ and σ2 independent of x is established. Asymptotic normality is the same under both the conditional and the unconditional distribution, but our procedure and normalizing constants differ from those in Bartholomew (1963).

多维列联表对数线性模型中 û 项的渐近方差AI 解读

Loglinear models are classified as direct or indirect depending on whether the maximum likelihood estimates of cell values are explicit functions of the sufficient statistics or not. For saturated (hence, direct) models, Goodman (1970) and Bishop, Fienberg, and Holland (1975) used the δ method to calculate the asymptotic variances of various û terms in the loglinear models. In the present paper, this approach has been generalized to direct unsaturated hierarchical loglinear…

方差分量估计及相关问题的极大似然方法AI 解读

Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be…

最小方差无偏估计量的渐近效率AI 解读

Consider a regular $p$-dimensional exponential family such that either the distributions are concentrated on a lattice or they have a component whose $k$-fold convolution has a bounded density with respect to Lebesgue measure. Then, if a parametric function has an unbiased estimator, the minimum variance unbiased estimators are asymptotically equivalent to the maximum likelihood estimators; and, hence, are asymptotically efficient. Examples are given to show that a condition…

线性回归中 M 估计与 R 估计的渐近关系AI 解读

Let $\hat{\mathbf{\Delta}}_M$ be an $M$-estimator (maximum-likelihood type estimator) and $\hat{\mathbf{\Delta}}_R$ be an $R$-estimator (rank estimator) of the parameter $\mathbf{\Delta} = (\Delta_1,\cdots, \Delta_p)$ in the linear regression model $X_{Ni} = \sum^p_{j=1} \Delta_jc_{ji} + e_i, i = 1,\cdots, N$. The asymptotic distribution of $\hat\mathbf{\Delta}_M - \hat\mathbf{\Delta}_R$ is derived for $p$ fixed and $N \rightarrow \infty,$ under some assumptions on the…

一般非线性联立方程模型中的极大似然与非线性三阶段最小二乘估计量AI 解读

Takeshi Amemiya, The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model, Econometrica, Vol. 45, No. 4 (May, 1977), pp. 955-968

随机系数模型中的最大似然估计AI 解读

Previous Monte Carlo studies examining properties of estimators in random coefficient models have been hindered in part by computational difficulties. In particular, determination of maximum likelihood estimators appears sensitive to the computational algorithm used. In a small Monte Carlo experiment, several distinctly motivated algorithms are examined with respect to accuracy and cost in searching for global and local maximum likelihood parameter estimates. A noncalculus…

两侧分类均有误差时 2×2 列联表独立性的双样本检验AI 解读

A double sampling scheme is considered for estimation and testing under misclassification in both margins of a 2×2 contingency table; the matrix of misclassification probabilities is assumed to be unknown and nonsingular. Maximum likelihood estimators are given for the error-free and misclassification probabilities. Numerical methods are utilized to obtain maximum likelihood estimates under the independence hypothesis and the regularity conditions are affirmed for the…

随机系数模型中的最大似然估计AI 解读

Previous Monte Carlo studies examining properties of estimators in random coefficient models have been hindered in part by computational difficulties. In particular, determination of maximum likelihood estimators appears sensitive to the computational algorithm used. In a small Monte Carlo experiment, several distinctly motivated algorithms are examined with respect to accuracy and cost in searching for global and local maximum likelihood parameter estimates. A noncalculus…

不同参数序列下联立方程估计量分布的渐近展开AI 解读

The distributions of the LIML and TSLS estimates of the coefficient of an endogenous variable in a single equation can be approximated by asymptotic expansions. This paper relates the expansions in terms of the noncentrality parameter and the sample size going to infinity, the noncentrality parameter going to infinity with the sample size held fixed, and the standard deviation of the disturbance going to zero (small-o). 1. INTRODUCriON RECENTLY, ASYMPTOTIC EXPANSIONS of the…

交通流的排队模型AI 解读

Summary A model for queue formation and disintegration is proposed for traffic on a road where flow is unimpeded. The model assumes that vehicles are travelling in random queues and a distribution for queue length is derived having as a single parameter the ratio of the rate of mergings between pairs of queues and the rate of overtaking from queues of more than one vehicle. The first moment and maximum likelihood estimator associated with the distribution are derived and…

关于ARMA过程参数估计及Akaike、Hannan估计程序的札记AI 解读

Patterson & Thompson (1971) have described a modified maximum likelihood technique for estimating variance components in the additive mixed model. We consider the use of this method in estimating the parameters of the autoregressive-moving average model, and examine its performance relative to some established techniques for 200 simulations of a firstorder moving average process.

自回归移动平均模型分析：估计与预测AI 解读

The exact likelihood function from a set of observations generated by univariate stationary normal autoregressive–moving average models is derived. Convenient methods are developed to evaluate the exact likelihood function, specifically the inverse and determinant of the T × T covariance matrix of the observations, ΣT and the quadratic form, Z′ΣT-1Z, where Z is a T × 1 vector of observations. Computations of the least squares and the maximum likelihood estimates of the…

改进的Box–Jenkins估计量AI 解读

An easily implemented modification of the estimation procedure given by Box & Jenkins (1970) for the autoregressive–moving average time series model is suggested and some new results on covariance determinante are given. The proposed modification provides a closer approximation to the exact maximum likelihood estimators. Simulation experiments which demonstrate the effectiveness of this modification are presented.

删失生存数据中的渐近信息量AI 解读

Various procedures are considered for fitting a regression model to censored survival data in continuous time with time–dependent covariate functions. These include maximum likelihood with the underlying hazard function known completelyand known up to a multiplicative constant, and the maximization of Cox's partial likelihood. Explicit formulae for the asymptotic variances of the estimators are derived informally and compared. It is shown how sample second derivatives may be…

R×C 析因配对比较实验的设计AI 解读

Two designs for R × C factorial paired comparison experimente are compared, assuming the Bradley-Terry model. One design employs comparisons of all paira of the RC treatments, and the other degign restricts comparisons to those pairs which have the same level of one factor. Computation of maximum likelihood estimates under several hypotheses is considered for each design. The restricted design has administrative benefits because it requires comparison of fewer distinct pairs…

已知变异系数时正态分布均值的估计AI 解读

Estimation of the mean θ of a normal distribution N(θ, aθ2) with known coefficient of variation a 1/2 is treated as a decision problem with squared-error loss. It is shown that all estimators linear in the sample mean and sample standard deviation s, as well as the maximum likelihood estimator (MLE), are dominated in risk by the admissible, minimum risk, scale equivariant estimator . A class of Bayes estimators against inverted-gamma priors is constructed, and shown to…

不完整多元数据的均值推断AI 解读

A class of statistics g(v) is proposed for constructing tests and confidence intervals for a linear combination of means v using an incomplete multivariate normal sample. The class includes statistics based on maximum likelihood estimates for all the data, and simpler statistics such as those based on a subset of complete observations. A simple measure of relative efficiency is proposed to decide when a simpler statistic is appropriate. For the case of two variables with…

线性学习模型中的最大似然估计AI 解读

An extension of the Markov model with only a few additional parameters is the linear learning model, as introduced by Bush & Mosteller (1955). To help its application in biological research an iterative procedure for calculating the maximum likelihood estimates of the unknown parameters is presented. Numerical examples, some of which have already been treated by Bush & Mosteller, are included, as well as comparisons between the linear learning model and the Markov model.

复合泊松过程的最大似然估计AI 解读

The problem of estimating the compounding distribution of a compound Poisson process from independent observations of the compound process has been analyzed by Tucker (1963). A maximum likelihood method is proposed. The existence, uniqueness and convergence of the resulting estimator are derived. One obtains practical solutions by means of a very simple algorithm which is briefly described. A numerical example is presented in the risk business framework.

两状态分量复合决策问题的渐近解：贝叶斯方法与比例参数的弥散先验AI 解读

Gilliland and Hannan (1974, Section 3) consider a general finite state compact risk component and reduce the problem of treating the asymptotic excess compound risk of Bayes compound rules to the question of $L_1$ consistency of certain induced estimators. This present paper considers the two state case and for several classes of diffuse symmetric priors on proportions establishes the $L_1$ consistency with rate. The rate $O(n^{-\frac{1}{2}})$ uniform in state sequences is…

A. R. Pagan, D. F. Nicholls; Exact Maximum Likelihood Estimation of Regression Models with Finite Order Moving Average Errors, The Review of Economic Studies, V

依赖观测下的最大似然估计AI 解读

Summary The asymptotic properties of m.l.e. are discussed for generally dependent observations. Conditions are derived for weak consistency and asymptotic Normality of the estimates. We further consider the case where some of the parameters are “transient” in the sense that the accumulated information on them from the sample does not increase indefinitely; then the interest lies in estimating the other parameters consistently. Examples are given, and the work is related to…