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Papadakis 估计量在一维与二维田间试验中的作用AI 解读

Field trials when observations are correlated with those in neighbouring or nearby plots in one dimension are examined. The relationships between maximum likelihood solutions and the well-known Papadakis estimator are clarified and it is shown that the Papadakis estimator is appropriate under one covariance assumption but not others.

基于有效得分的异质性检验AI 解读

For cases in which a parameter may be estimated from several independent data sets, Mather (1935) proposed a heterogeneity test based on the efficient scores for the individual data sets evaluated at the overall maximum likelihood estimator. Following Fisher (1946), a modification of the heterogeneity score test is presented wherein a consistent but inefficient estimator of the parameter of interest is substituted for the overall maximum likelihood estimator. The modified…

一类参数问题的 Bootstrap 置信区间AI 解读

We consider the following class of problems: having observed a multivariate normal data vector y with unknown mean vector η, covariance matrix the identity, find an approximate confidence interval for ø = t(η), a real-valued function of η. A simple geometric construction is given which leads to highly accurate solutions. This construction shows that the standard approximation based on maximum likelihood theory, ø7plusmn;σz(α), can be quite misleading when ø is nonlinear in…

高阶连续时间自回归模型的估计AI 解读

A method is presented for computing maximum likelihood, or Gaussian, estimators of the structural parameters in a continuous time system of higherorder stochastic differential equations. It is argued that it is computationally efficient in the standard case of exact observations made at equally spaced intervals. Furthermore it can be applied in situations where the observations are at unequally spaced intervals, some observations are missing and/or the endogenous variables…

平均失效率递增分布的最大似然估计不一致性AI 解读

Marshall and Proschan (1965) showed that the MLE for a life distribution with increasing failure rate is strongly consistent. In this note we show that the MLE for a life distribution with increasing failure rate average is not consistent; in fact, maximum likelihood estimation in the IFRA case yields estimators of the average failure rate and of the distribution function which, in general, converge a.s. to values other than the true values. In the decreasing failure rate…

广义线性模型最大似然估计的一致性与渐近正态性AI 解读

Generalized linear models are used for regression analysis in a number of cases, including categorical responses, where the classical assumptions are violated. The statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator. We present mild general conditions which, respectively, assure weak or strong consistency or asymptotic normality. Most of the previous work has been concerned with natural link functions. In this case…

截断数据下的分布函数估计AI 解读

Let $\mathscr{P}$ be a finite population with $N \geq 1$ elements; for each $e \in \mathscr{P}$, let $X_e$ and $Y_e$ be independent, positive random variables with unknown distribution functions $F$ and $G$; and suppose that the pairs $(X_e, Y_e)$ are i.i.d. We consider the problem of estimating $F, G$, and $N$ when the data consist of those pairs $(X_e, Y_e)$ for which $e \in \mathscr{P}$ and $Y_e \leq X_e$. The nonparametric maximum likelihood estimators (MLEs) of $F$ and $G$…

选择偏差模型中的经验分布AI 解读

The following problem is treated: Given $s$ not-necessarily-random samples from an unknown distribution $F$, and assuming that we know the sampling rule of each sample, is it possible to combine the samples in order to estimate $F$, and if so what is the natural way of doing it? More formally, this translates to the problem of determining whether there exists a nonparametric maximum likelihood estimate (NPMLE) of $F$ on the basis of $s$ samples from weighted versions of $F$,…

Cox回归与一般条件似然的诊断方法AI 解读

Diagnostics for changes in the maximum likelihood estimate of β due to deletion of single observations in linear and logistic regression models are equivalent to diagnostics obtained from fitting augmented regression models. For the Cox proportional hazards model and in conditional models for arbitrarily matched or stratified data, diagnostics derived from augmented regression models are again useful and easy to compute. These diagnostics are applicable to different…

由故障与随访记录非参数估计寿命分布AI 解读

This article deals with the estimation problem of the survival function of an industrial product in which the real operating time is different from its actual calendar time. In an observational study of the product, sometimes only the time until failure is observable from the repair requests made by the owner, but nonfailure times themselves are not. The generalized maximum likelihood estimator of the survival function is presented, and its consistency, asymptotic normality,…

正电子发射断层成像的统计模型AI 解读

Positron emission tomography (PET)—still in its research stages—is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner. Much as in X-ray transmission tomography and other modes of computerized tomography, the quality of the reconstructed image in PET is very sensitive to the mathematical algorithm to be used for reconstruction. In this article, we tailor a mathematical model to the…

基于故障与随访记录的寿命分布非参数估计AI 解读

This article deals with the estimation problem of the survival function of an industrial product in which the real operating time is different from its actual calendar time. In an observational study of the product, sometimes only the time until failure is observable from the repair requests made by the owner, but nonfailure times themselves are not. The generalized maximum likelihood estimator of the survival function is presented, and its consistency, asymptotic normality,…

概率分布下尾的最大似然估计AI 解读

SUMMARY We consider the estimation of the three parameters of the lower tail of a distribution function based on the k smallest out of n observations. The likelihood function has a singularity but it is argued that a local maximum, when it exists, should be taken as the m.l.e. Asymptotic results as k → ∞, n → ∞, k/n → 0 show that such a local maximum does exist, and provides consistent estimators whenever the shape parameter is greater than one; otherwise there is no local…

利用重复观测估计多变量线性结构关系AI 解读

SUMMARY We derive maximum likelihood estimators for parameters of a multivariate linear structural relationship in the replicated case. The asymptotic covariance matrix of the maximum likelihood estimator of the coefficient of the relationship is obtained by using the delta method when the sample size tends to infinity.

二元响应的方差成分模型：访员间变异AI 解读

SUMMARY Interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non-normal family. The maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire. This raises some interesting questions about the use of unbalanced ANOVA methods with these data.

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依赖数据下的优势比推断AI 解读

When data can be presented as a series of k 2×2 tables with cell counts (xi ,ni−xi, yi, mi−yi), it is often assumed that xi and yi are binomially distributed. This paper deals with inference for the common odds ratio Ψ when the binomial assumption is invalid. When k increases, the consistency and asymptotic normality of the Mantel & Haenszel (1959) estimator is derived. The conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is…

相关测量误差下线性结构关系模型的估计AI 解读

Maximum likelihood estimators for model parameters in linear structural relationships having correlated measurement errors are presented. Comparisons between asymptotic mean squared errors of least squares and maximum likelihood estimators of the slope parameter indicate that the least squares estimator is only preferable when the slope parameter is sufficiently small relative to the ratio of error standard deviations; however, unlike structural relationships having…

含缺失值的连续与分类混合数据的最大似然估计AI 解读

Maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented. The general location model of 01kin & Tate (1961) and extensions introduced by Krzanowski (1980, 1982) form the basis for our methods. Maximum likelihood estimation with incomplete data is achieved by an application of the EM algorithm (Dempster, Laird & Rubin, 1977). Special cases of the algorithm include Orchard & Woodbury's (1972) algorithm for incomplete…

临床试验两时期交叉设计中的不完整数据分析AI 解读

A procedure for analysing a simple two-period crossover design is proposed when some observations at the second treatment period are missing. Using all available data, the maximum likelihood estimators of the parameters are obtained and approximate tests proposed under the assumption that the data come from bivariate normal populations. The performances of these tests are compared with those of Grizzle's tests which require complete pairs of observations, using Monte Carlo…

基于有效得分的异质性检验AI 解读

For cases in which a parameter may be estimated from several independent data sets, Mather (1935) proposed a heterogeneity test based on the efficient scores for the individual data sets evaluated at the overall maximum likelihood estimator. Following Fisher (1946), a modification of the heterogeneity score test is presented wherein a consistent but inefficient estimator of the parameter of interest is substituted for the overall maximum likelihood estimator. The modified…

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