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大量干扰参数下的经验贝叶斯与条件推断AI 解读

This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…

基于参数的渐近方法AI 解读

Fisher's theory of maximum likelihood estimation routinely provides approximate confidence intervals for a parameter of interest θ, the standard intervals θ ^ ± zασ ^ where θ ^ is the maximum likelihood estimator, ô is an estimate of standard error based on differentiation of the log likelihood function, and zα is a normal percentile point. Recent work has produced systems of better approximate confidence intervals, which look more like exact intervals when exact intervals…

具有自回归移动平均误差的非参数样条回归AI 解读

We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The…

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带测量误差且受线性约束的数据估计AI 解读

Abstract Variables are often measured subject to error, whether they are collected as part of an experiment or by sample surveys. A consequence of this is that there will be different estimates of the same variable, or, more generally, linear restrictions which the observations should satisfy but fail to. With knowledge of the variances of the various observations, it has been shown elsewhere that maximum‐likelihood estimates of the observations can be produced. This paper…

随机过程的渐近辅助性与条件推断AI 解读

Simple conditions on the observed information ensure asymptotic normality of the conditional distributions of the randomly normed score statistic and maximum likelihood estimator given a suitable asymptotically ancillary statistic. In particular, asymptotic normality holds conditional on any asymptotically ancillary statistic asymptotically equivalent to observed information. The results apply to inference from a general stochastic process and are of particular relevance in…

估计量偏离目标值的最后时点与累计次数AI 解读

Suppose $\hat{\theta}_n$ is a strongly consistent estimator for $\theta_0$ in some i.i.d. situation. Let $N_\varepsilon$ and $Q_\varepsilon$ be, respectively, the last $n$ and the total number of $n$ for which $\hat{\theta}_n$ is at least $\varepsilon$ away from $\theta_0$. The limit distributions for $\varepsilon^2N_\varepsilon$ and $\varepsilon^2Q_\varepsilon$ as $\varepsilon$ goes to zero are obtained under natural and weak conditions. The theory covers both parametric…

格点马尔可夫随机场指数族中一类估计量的一致性AI 解读

We prove strong consistency of a class of maximum objective estimators for exponential parametric families of Markov random fields on $\mathbb{Z}^d$, including both maximum likelihood and pseudolikelihood estimators, using large deviation estimates. We also obtain the optimality property for the maximum likelihood estimator in the sense of Bahadur.

自适应估计中的平滑AI 解读

An adaptive maximum likelihood estimator based on the estimation of the log-density by $B$-splines is introduced. A data-driven method of selecting the smoothing parameter involved in the consequent density estimation is demonstrated. A Monte Carlo study is conducted to evaluate the small sample performance of the estimator in a location and a regression problem. The adaptive estimator is seen to compare favorably to some standard estimates. We show that the estimator is…

This paper discusses robust estimation for structural errors-in-variables (EV) linear regression models. Such models have important applications in many areas. Under certain assumptions, including normality, the maximum likelihood estimates for the EV model are provided by orthogonal regression (OR) which minimizes the orthogonal distance from the regression line to the data points instead of the vertical distance used in ordinary regression. OR is very sensitive to…

人脑电偶极子参数的频域估计AI 解读

Human brain evoked potentials are elicited by a stimulus and can be recorded by scalp electrodes. Many researchers have proposed models in which evoked potentials are generated by equivalent electrical dipoles in the brain. Each dipole is defined by a set of parameters that specify its location, orientation, and magnitude. Existing approaches to estimation of dipole parameters do not realistically account for errors resulting from background brain electrical activity…

含方差分量的非线性回归AI 解读

The nonlinear model with variance components, which combines a nonlinear model for the mean with additive random effects, is applicable to split-plot and nested experiments. We propose two methods of estimation for the parameters of the nonlinear model for the mean: (1) estimated generalized least squares (EGLS), and (2) maximum likelihood (MLE) by the method of scoring. Using a generalization of Klimko and Nelson's theorem on strong consistency of least squares estimators,…

混合分布非参数极大似然估计的计算算法AI 解读

A fast algorithm for calculating the nonparametric maximum likelihood estimate (MLE) of a mixing distribution, G(·). in a mixture model is discussed. The literature contains several methods for computing the nonparametric MLE of G, but these methods are slow. In this article we develop an algorithm for maximizing the log-likelihood l(G) over the family ℊ, of all distribution functions, that yields the nonparametric MLE of G. In some semiparametric problems, a structural or…

基于非对称极大似然的泊松过度离散估计AI 解读

A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…

含方差分量的非线性回归AI 解读

The nonlinear model with variance components, which combines a nonlinear model for the mean with additive random effects, is applicable to split-plot and nested experiments. We propose two methods of estimation for the parameters of the nonlinear model for the mean: (1) estimated generalized least squares (EGLS), and (2) maximum likelihood (MLE) by the method of scoring. Using a generalization of Klimko and Nelson's theorem on strong consistency of least squares estimators,…

基于非对称最大似然的 Poisson 过度离散估计AI 解读

A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…

人脑电偶极子参数的频域估计AI 解读

Human brain evoked potentials are elicited by a stimulus and can be recorded by scalp electrodes. Many researchers have proposed models in which evoked potentials are generated by equivalent electrical dipoles in the brain. Each dipole is defined by a set of parameters that specify its location, orientation, and magnitude. Existing approaches to estimation of dipole parameters do not realistically account for errors resulting from background brain electrical activity…

标志点数据的大小与形状分析AI 解读

The paper deals with statistical analysis of landmark data using the exact joint distribution theory for the size and shape of planar Gaussian configurations. This is an extension of earlier work which considered marginal shape analysis. Special cases of the size and shape distribution are examined and the isotropic Gaussian model is investigated in particular detail. Various properties are studied, including conditional distributions and a curve of regression. Finally we…

二元阈值跨越与二元选择模型的非参数、分布无关估计AI 解读

In this paper, it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term. This identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term. The…

通过自回归近似估计与检验协整系统AI 解读

This paper studies the estimation and testing of general cointegrated systems by using an autoregressive approximation. Simple estimators for both the cointegration vectors and their weight matrix in the autoregressive error correction model representation of the system are developed. Since these estimators assume that the number of cointegration vectors and their normalization are fixed in advance, convenient specification tests for checking the validity of these…

基于相关成分的最大似然回归AI 解读

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…

生存与计划处死实验中约束极大似然估计的显式解AI 解读

Regulatory agencies routinely base conclusions regarding carcinogenicity of compounds tested in long-term animal studies on tests which are known to be biased under conditions of treatment lethality and tumour lethality. The recognition of these biases has led to a variety of proposed approaches which rely on survival and sacrifice data. Williams & Portier (1992) derived analytic expressions for maximum likelihood estimators of the tumour incidence rate and discrete death…

利用替代结局数据与验证样本进行推断AI 解读

In the context of estimating β from the regression model Pβ(Y|X), relating response Y to covariates X, suppose that only a surrogate response S is available for most study subjects. Suppose that for a random subsample of the study cohort, termed the validation sample, the true outcome Y is available in addition to S. We consider maximum likelihood estimation of β from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to…

家庭数据分析的一则说明AI 解读

Because families have varying numbers of offspring, the maximum likelihood estimators of the interclass, or parent-offspring, and intraclass, or offspring-offspring, correlations are difficult to compute (Srivastava, 1984). For this reason, alternative estimators have been proposed, which are not necessarily asymptotically efficient. However, maximum likelihood estimators of the inter- and intraclass correlations in families of constant size can be obtained in closed form,…