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摘要暂缺

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…

Papadakis估计量在一维和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.

It is demonstrated that maximum likelihood estimators exist for the intercept, slope and unknown error variance in Dolby's (1976) unreplicated ultrastructural model with known error variance ratio even when the ratio of the variability of the measured variables to the variability of the measurement errors is unknown. This corrects an assertion in Dolby's paper. Patefield's (1978) adjusted maximum likelihood estimators for this model are shown to be strongly consistent and…

混合泊松模型中极大似然估计的渐近性质AI 解读

This paper considers the asymptotic behavior of the maximum likelihood estimators (mle's) of the probabilities of a mixed Poisson distribution with a nonparametric mixing distribution. The vector of estimated probabilities is shown to converge in probability to the vector of mixed probabilities at rate $n^{1/2-\varepsilon}$ for any $\varepsilon > 0$ under a generalized $\chi^2$ distance function. It is then shown that any finite set of the mle's has the same joint limiting…

混合分布泛函估计量的渐近效率AI 解读

Suppose $F$ is a mixture of a known parametric family of distributions with an unknown nonparametric mixing distribution. Consider the problem of estimating the value $T(dF)$ of a smooth functional $T$ at the mixed distribution $F$. One nonparametric estimator of $T(dF)$ is $T(dF_n)$ where $F_n$ denotes the empirical distribution. Under a differentiability condition on $T$ given in this note, $T(dF_n)$ is shown to be fully efficient asymptotically in the sense that the…

非随机缺失分类数据的推断：特纳综合征遗传研究示例AI 解读

The process leading to partial classification with categorical data is sometimes nonrandom. A particular model accounting for incomplete data, which allows the probability of uncertain classification to depend on category identity, is utilized for an analysis of data obtained from a genetic study on Turner's syndrome. Estimates of population proportions are obtained from maximum likelihood. A method for handling nonrandomly missing data arrayed in contingency tables is…

线性结构关系的参数估计：对误差方差比选择的敏感性AI 解读

Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. This paper investigates the use of asymptotic formulae for variances and mean squared errors as a function of sample size and the…

关于 Daniels 最大似然估计渐近有效性证明的注记AI 解读

A corrected proof of an important preliminary result of Daniels (1961) is presented. Daniels's work, showing that a well-behaved second dericative of the expected log likelihood function, rather than of the log likelihood function, is the key to asymptotic efficiency, is thus complete.

This paper develops a finite-horizon dynamic stochastic model of discrete choice with respect to life-cycle fertility within an environment where infant survival is uncertain. The model yields implications for the number, timing, and spacing of children. A tractable estimation method is developed for the linear constraint-quadratic utility case that is intimately tied to the dynamic optimization problem, and the method is applied to Malaysian household data. Estimation is…

ARMA 模型极大似然估计量的渐近展开AI 解读

SUMMARY A technique is given for the Edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving-average (ARMA) models. Our methodology is illustrated and results on the expansions for some simple ARMA models are presented.

回归模型与有序分类变量AI 解读

SUMMARY A general approach to regression modelling for ordered categorical response variables, y, is given, which is equally applicable to ordered and unordered y. The regressor variables xT = (x 1 ,…,xp) may be continuous or categorical. The method is based on the logistic family which contains a hierarchy of regression models, ranging from ordered to unordered models. Ordered properties of the former, the stereotype model, are established. The choice between models is made…

最小判别信息调整AI 解读

Minimum discriminant information adjustment has primarily been used in the analysis of multinomial data; however, no such restriction is necessary. Let $P$ be a distribution on $R^a$, and let $\mathscr{C}$ be a convex set of distributions on $R^a$. Let $\mathbf{X}_i, 1 \leq i \leq n$, be independent and identically distributed observations with common distribution $P$. The minimum discriminant information adjustment (MDIA) of $P$ relative to $\mathscr{C}$ is the element $Q$ o…

样条平滑：等价变带宽核方法AI 解读

The spline smoothing approach to nonparametric regression and curve estimation is considered. It is shown that, in a certain sense, spline smoothing corresponds approximately to smoothing by a kernel method with bandwidth depending on the local density of design points. Some exact calculations demonstrate that the approximation is extremely close in practice. Consideration of kernel smoothing methods demonstrates that the way in which the effective local bandwidth behaves in…

自回归过程的无穷小稳健性AI 解读

We define the influence function and construct optimal robust estimators for autoregressive processes. We show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination. This function is called the influence function. It is unique only up to an equivalence relation, but there is a natural unique version which describes the limiting influence of an additional observation…

混合比例的最小距离与最大似然估计比较AI 解读

The estimation of mixing proportions in the mixture model is discussed, with emphasis on the mixture of two normal components with all five parameters unknown. Simulations are presented that compare minimum distance (MD) and maximum likelihood (ML) estimation of the parameters of this mixture-of-normals model. Some practical issues of implementation of these results are also discussed. Simulation results indicate that ML techniques are superior to MD when component…

迁移者—留驻者模型的最大似然估计AI 解读

The discrete time mover-stayer model, a special mixture of two independent Markov chains, has been widely used in modeling the dynamics of social processes. The problem of maximum likelihood estimation of its parameters from the data, however, which consist of a sample of independent realizations of this process, has not been considered in the literature. I present a maximum likelihood procedure for the estimation of the parameters of the mover-stayer model and develop a…

非遍历模型的渐近最优推断AI 解读

0. An Over-view.- 1. Introduction.- 2. The Classical Fisher-Rao Model for Asymptotic Inference.- 3. Generalisation of the Fisher-Rao Model to Non-ergodic Type Processes.- 4. Mixture Experiments and Conditional Inference.- 5. Non-local Results.- 1. A General Model and Its Local Approximation.- 1. Introduction.- 2. LAMN Families.- 3. Consequences of the LAMN Condition.- 4. Sufficient Conditions for the LAMN Property.- 5. Asymptotic Sufficiency.- 6. An Example (Galton-Watson…

条件似然方法的渐近效率AI 解读

This paper concerns the efficiency of the conditional likelihood method for inference in models which include nuisance parameters. A new concept of ancillarity, asymptotic weak ancillarity, is introduced. It is shown that the conditional maximum likelihood estimator and the conditional score test of θ, the parameter of interest, are asymptotically equivalent to their unconditional counterparts, and hence are asymptotically efficient, provided that the conditioning statistic…

含变点的风险率模型中的估计AI 解读

This paper discusses the estimation of parameters in hazard rate models with a change-point. Due to the irregularity of the models, the classical maximum likelihood method and the method of moments cannot be used. A consistent estimator of the change-point is obtained by examining the properties of the density represented as a mixture. The performance of the estimator is checked via simulation.

摘要暂缺

The efficiency with which coefficients in probit models are estimated is improved by exploiting data on continuous ancillary variates.In this paper the resulting gains in efficiency are examined and illustrative calculations are provided.Extra precision is achieved at the cost of making an extra assumption but this assumption can be tested.It is shown that fully efficient maximum likelihood estimation of the probit model with a continuous ancillary variate can be achieved by…

似然比统计量的 Bartlett 调整与最大似然估计量的分布AI 解读

SUMMARY For rather general parametric models, a simple connection is established between the Bartlett adjustment factor of the log-likelihood ratio statistic and the normalizing constant c of the formula c | ĵ |½ L̄ for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested. This leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or…

混合比例的有效非参数估计AI 解读

SUMMARY By constructing a sequence of multinomial approximations and related maximum likelihood estimators, we derive a Cramér-Rao lower bound for nonparametric estimators of the mixture proportions and thereby characterize asymptotically optimal estimators. For the case of the sampling model M2 of Hosmer (1973) it is shown that the sequence of maximum likelihood estimators, which can be obtained explicitly, is asymptotically optimal in this sense. The results hold true even…