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广义自回归条件异方差AI 解读

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.

ARCH 模型的渐近理论：估计与检验AI 解读

In the context of a linear dynamic model with moving average errors, we consider a heteroscedastic model which represents an extension of the ARCH model introduced by Engle [4]. We discuss the properties of maximum likelihood and least squares estimates of the parameters of both the regression and ARCH equations, and also the properties of various tests of the model that are available. We do not assume that the errors are normally distributed.

联立方程系统中单方程估计量的比较AI 解读

Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k -class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as…

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.

部分似然理论AI 解读

A general asymptotic theory is developed for the maximum likelihood estimator based on a partial likelihood. Conditions are given for consistency and asymptotic normality, and a method is provided for the calculation of the asymptotic efficiency of the estimator. The implications of the general theory are examined in special cases such as inference in stochastic processes, Cox regression models, and AR processes with missing segments.

基于时间删失第 r 阶次序统计量的指数分布尺度估计AI 解读

The problem of estimating the mean of an exponential distribution is studied, when the data available are a random sample of time-censored rth-order statistics. Examples for such empirical situations are cited. Maximum likelihood estimators (MLE's) and moment-equation estimators (MEE's) are studied. Theoretical derivations are provided for the large sample variances and distributions of these estimators. The efficiency of the MEE compared to the MLE is studied.

存在非应答时利用面板数据估计总流量：加拿大劳动力调查实例AI 解读

This article considers the problem of using categorical data from a panel survey in which there is nonrandom nonresponse to estimate gross flows. The methods are illustrated for the case of estimating gross flows in labor force participation using data from the Canadian Labour Force Survey. Three models are proposed that allow nonresponse to be related to employment classification, time, or both employment classification and time. Maximum likelihood estimation is used to fit…

二项分布试验次数参数估计的稳定化AI 解读

The maximum likelihood estimator of the binomial parameter n can be highly unstable, resulting in huge fluctuations in the estimate when the data are only slightly perturbed. A method of assessing this sensitivity, based on perturbing the log-likelihood function, is proposed and examined.

NEAR(2) 模型的最大似然估计AI 解读

SUMMARY The NEAR(2) model is a model for nonlinear time series with exponential marginals. It formed the subject of a recent discussion paper by Lawrance and Lewis. We explore the possibility of maximum likelihood estimation with particular reference to the difficulties created by discontinuities in the likelihood function. Two exploratory techniques are proposed for resolving those difficulties. This note is an expanded version of a contribution presented orrally at the…

不依赖参数分布假设的取向统计AI 解读

SUMMARY Maximum likelihood estimation using the matrix von Mises-Fisher distribution in orientation statistics leads to unacceptably complicated likelihood equations, essentially because of the inconvenient form of the normalizing constant in the probability distribution. For the case of 3 × 2 or 3 × 3 orientations, the main cases of practical importance, an alternative approach is developed here by transforming the data into unsigned four-dimensional directions and using…

病例—对照或选择依赖抽样下的 Logistic 模型拟合AI 解读

SUMMARY There has been a great deal of interest in recent years in fitting logistic and log-linear models to tables of population counts estimated from survey data. Since maximum likelihood methods are not available in general for complex survey designs, most work has concentrated on adapting standard methods developed for multinomial sampling. Maximum likelihood methods have been developed for some special designs, however, and we might expect ad hoc methods to be less…

ARCH 与双线性时间序列模型：比较与结合AI 解读

Two extensions to the ARMA model, bilinearity and ARCH errors are compared, and their combination is considered. Starting with the ARMA model, tests for each extension are discussed, along with various least squares and maximum likelihood estimates of the parameters and tests of the estimated models based on these. The effects each may have on the identification, estimation, and testing of the other are given, and it is seen that to distinguish between the two properly, it…

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删失观测、重复测量与混合效应模型：正态误差下的 EM 方法AI 解读

Maximum likelihood estimation of a vector regression parameter and variance com ponents is considered for the mixed effects model when observations are right censored. A general scheme of estimation is given using the EM algorithm and detailed results found for the model with between and within block variation. This model is applied to the logarithms of survival times from a repeated measures design.

非线性回归中的偏差AI 解读

We investigate the biases of the residuals and maximum likelihood parameter estimates from normal nonlinear regression models. Emphasis is placed on a class of partially nonlinear models, on the role of individual cases in determining bias, on how bias affects standard diagnostic methods, and on the relationship between bias and curvature.

关于逻辑回归最大似然估计存在条件的补充说明AI 解读

This note expands the paper by Albert & Anderson (1984) on the existence and uniqueness of maximum likelihood estimates in logistic regression models. Their three possible mutually exclusive data patterns: (i) overlap, (ii) complete separation, and (iii) quasiseparation are considered. The maximum likelihood estimate exists only in (i). Modifications of the statement and proofs of Albert & Anderson's results are given for (ii) and (iii) The identifiability for a more general…

自回归移动平均模型的普通与似然型位置M估计AI 解读

Proper location M-estimates for a model with non-Gaussian autoregressive-moving average type errors are genuine maximum likelihood type estimates, whereas ordinary location M-estimates are those introduced by P. Huber for independent and identically distributed errors. The relative behaviour of ordinary location M-estimates and proper location M-estimates is studied for situations with dependent errors of purely autoregress ive and purely moving average type. It is shown…

序贯检验后最大似然估计的偏差AI 解读

The bias of maximum likelihood estimates calculated at the end of a sequential procedure is investigated. For the two sequential designs considered in detail, the sequential probability ratio test and the triangular test, this bias is appreciable. A method of calculating an adjusted estimate with reduced bias is described, and an approximation to the standard error of the new estimate is provided. Examples of the implementation of the method are given, and its advantages and…

广义线性模型的最优有界得分函数及其在逻辑回归中的应用AI 解读

We study optimally bounded score functions for estimating regression parameters in a generalized linear model. Our work extends results obtained by Krasker & Welsch (1982) for the linear model and provides a simple proof of Krasker & Welsch's first-order condition for strong optimality. The application of these results to logistic regression is studied in some detail with an example given comparing the bounded-influence estimator with maximum likelihood.

动物致癌实验中肿瘤发生时间分布的估计AI 解读

In most survival-sacrifice experiments for the detection and quantification of risks from chronic exposure to chemical agents, the onset of the condition of interest is not clinically observable. Cancer is typically such an event. In this paper, an approximate maximum likelihood method is proposed for parametric estimation of the distribution of unobservable tumour onset times in the presence of competing risks, when cause-of-death information is unavailable.

部分删失数据的半马尔可夫模型札记AI 解读

A recharacterization of the semi-Markov model described by Lagakos, Sommer & Zelen (1978) permits the nonparametric maximum likelihood estimators to be expressed in terms of familiar and easily computable quantities, such as event-specific hazard estimators and Kaplan & Meier (1958) survival estimators. In addition to simplifying the calculation and clarifying the interpretation of the previously derived estimators, this reformulation also facilitates the estimation of…

近似预测似然AI 解读

A predictive likelihood is given which approximates both Bayes and maximum likelihood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n–2), and from exact predictive likelihood by Op(n–2) but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot…

基于标准化有符号对数似然比的全部或部分参数推断AI 解读

For parametric models it is shown in general that by adjusting the mean and variance of the signed log likelihood ratio for a single parameter of interest ψ one obtains a statistic which is asymptotically standard normally distributed to order O(n–23) , under repeated sampling. This statistic may also be used as an ancillary in the associated problem of drawing inference on the complementary parameter χ for known value of ψ in which case it entails accuracy to the same order…

指数族独立随机变量序列的变点检验与置信区域AI 解读

SUMMARY Maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables, with particular emphasis on the exponential distribution. The exact null and alternative distributions of the test statistics are found, and the power is compared with a test based on a linear trend statistic. Exact and approximate confidence regions for the change-point are based on the values accepted by a level x likelihood ratio test and a…