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半参数 ARCH 模型AI 解读

A semiparametric ARCH model is introduced with conditional first and second moments given by ARMA and ARCH formulations, and a conditional density that is approximated by a nonparametric density estimator. For several densities, the relative efficiency of the quasi-maximum likelihood estimator is compared with maximum likelihood under correct specification. These potential efficiency gains for a fully adaptive procedure are compared in a Monte Carlo experiment with the…

一般随机流行病模型中感染率估计量的渐近性质AI 解读

SUMMARY Some estimators for the infection rate in the general stochastic epidemic model are presented. The first estimator follows the approach of maximum likelihood. However, this approach requires us to observe most if not all of the epidemic process. As an alternative, an estimator which uses less detailed data is derived from a suitable martingale. Both estimators are shown to be consistent only when a major outbreak of disease is observed. Minor out-breaks do not…

平移原点三参数模型中区间删失数据的最大似然估计存在性AI 解读

SUMMARY Given data in the form of interval-censored observations from a three-parameter distribution, practical criteria are established for the existence of maximum likelihood estimates for three kinds of parameter space. These criteria can be derived by analysing the behaviour of the log-likelihood near a type of boundary of the parameter space, called the probability contents inner boundary. The effectiveness of the criteria is discussed. In the case where the underlying…

利用指数族序列逼近概率密度函数AI 解读

Probability density functions are estimated by the method of maximum likelihood in sequences of regular exponential families. This method is also familiar as entropy maximization subject to empirical constraints. The approximating families of log-densities that we consider are polynomials, splines and trigonometric series. Bounds on the relative entropy (Kullback-Leibler distance) between the true density and the estimator are obtained and rates of convergence are…

近非平稳 AR(1) 过程的高斯似然估计AI 解读

An asymptotic analysis is presented for estimation in the three-parameter first-order autoregressive model, where the parameters are the mean, autoregressive coefficient and variance of the shocks. The nearly nonstationary asymptotic model is considered wherein the autoregressive coefficient tends to 1 as sample size tends to $\infty$. Three different estimators are considered: the exact Gaussian maximum likelihood estimator, the conditional maximum likelihood or least…

近非平稳自回归时间序列的最大似然型估计AI 解读

The nearly nonstationary first-order autoregression is a sequence of autoregressive processes $y_n(k + 1) = \phi_ny_n(k) + \varepsilon(k + 1), 0 \leq k \leq n$, where the $\varepsilon(k)$'s are iid mean zero shocks and the autoregressive coefficient $\phi_n = 1 - \beta/n$ for some $\beta > 0$, so that $\phi_n \rightarrow 1$ as $n \rightarrow \infty$. We consider a class of maximum likelihood type estimators called $M$ estimators, which are not necessarily robust. The…

约束极大似然：以单调凸逻辑回归为例AI 解读

Maximum likelihood estimates in problems in which the likelihood is smooth and the parameter space is defined by linear or smooth nonlinear inequality constraints can be obtained using available nonlinear optimization packages, such as NPSOL. This class of models includes generalized linear models with order restrictions, convexity, or smoothness constraints on the parameters (smoothness constraints being in the form of bounds on finite differences of the regression…

暂定死亡率序列的调整：含结构化测量误差的动态线性模型AI 解读

The authors "consider the problem of adjusting provisional time series using a bivariate structural model with correlated measurement errors. Maximum likelihood estimators and a minimum mean squared error adjustment procedure are derived for a provisional and final series containing common trend and seasonal components. The model also includes measurement errors common to both series and errors that are specific to the provisional series. [The authors] illustrate the…

带切换的动态线性模型AI 解读

The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and…

带切换机制的动态线性模型AI 解读

The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and…

长度偏倚数据的核密度估计AI 解读

A new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated. It has various advantages over an alternative method suggested by Bhattacharyya, Franklin & Richardson (1988): it is necessarily a probability density, it is particularly better behaved near zero, it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems…

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随机空间模式分形维数的极大似然估计AI 解读

Two approximate maximum likelihood estimates of the fractal dimension are suggested for random point patterns and planar curves, based on the distributions of the Palm probability and the spectrum.

受限因变量模型：最大似然估计与单侧假设检验AI 解读

The limited dependent variable models with errors having log-concave density functions are studied here. For such models with normal errors, the asymptotic normality of the maximum likelihood estimator was established by Amemiya [1]. We show, when the density of the error distribution is log-concave, that the maximum likelihood estimator exists with arbitrarily large probability for large sample sizes, and is asymptotically normal. The general theory presented here includes…

实现渐近正态性的半非参数估计量自适应规则AI 解读

In econometrics, seminonparametric (SNP) estimators originated in the consumer demand literature. The Fourier flexible form is a well-known example. The idea is to replace the consumer's indirect utility function with a truncated series expansion and then use a parametric procedure, such as nonlinear multivariate regression, to set a confidence interval on an elasticity. More recently, SNP estimators have been used in nonlinear time series analysis. A truncated Hermite…

广义线性模型中的偏误校正AI 解读

SUMMARY In this paper we derive general formulae for first-order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias-corrected maximum likelihood estimates to order n −1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is…

截断计数数据模型AI 解读

Abstract This paper examines a class of maximum‐likelihood regression estimators for count data from truncated samples. Estimators for the truncated Poisson and negative binomial distributions are illustrated. Simulation results are given to illustrate the magnitude of the bias that may result from the failure to account for overdispersion in truncated samples. An empirical application based upon the number of recreational fishing trips taken by a sample of Alaskan fishermen…

多个总体一致随机序的统计推断AI 解读

Stochastic ordering between probability distributions is a widely studied concept. It arises in numerous settings and has useful applications. Since it is often easy to make value judgments when such orderings exist, it is desirable to recognize their occurrence and to model distributional structure under such orderings. Unfortunately, the necessary theory for statistical inference procedures has not been developed for many problems involving stochastic ordering and this…

Löwner 序约束下协方差矩阵的最大似然估计及其方差分量应用AI 解读

The problem of maximum likelihood estimation of Lowner ordered covariance matrices is considered. It is shown that a dual formulation of this problem is tractable and important in its own right. The interplay between the primal and dual problems suggests a general algorithm for computing the solutions to these problems. This algorithm has application to some estimation problems in balanced multivariate variance components models. The speed of convergence is also discussed…

有偏抽样回归模型估计的大样本理论（一）AI 解读

Biased sampling regression models were introduced by Jewell, generalizing the truncated regression model studied by Bhattacharya, Chernoff and Yang. If the independent variable takes on only a finite number of values (as does the stratum variable), we show: 1. That if the slope of the underlying regression model is assumed known, then the nonparametric maximum likelihood estimates of the distribution of the independent and dependent variables (a) can be calculated from…

无限维参数空间中的最大似然估计AI 解读

An approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions. In this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter. We provide conditions under which the rate of convergence can be established. This rate is essentially governed by the size of the space of score functions as measured by an entropy index. We also show that, for a large class of…

Curie–Weiss 模型最大似然估计量的渐近性质AI 解读

We study the asymptotics of the ML estimators for the Curie-Weiss model parametrized by the inverse temperature $\beta$ and the external field $h$. We show that if both $\beta$ and $h$ are unknown, the ML estimator of $(\beta, h)$ does not exist. For $\beta$ known, the ML estimator $\hat{h}_n$ of $h$ exhibits, at a first order phase transition point, superefficiency in the sense that its asymptotic variance is half of that of nearby points. At the critical point $(\beta = 1)$…

统计推断：从似然到显著性AI 解读

The concepts of likelihood and significance were defined and initially developed by R. A. Fisher, but followed almost separate and distinct routes. We suggest that a central function of statistical inference is in fact the conversion of the first, likelihood, into the second, significance: a linking of the Fisher concepts. A first-order asymptotic route for this is incorporated into most statistical packages. It uses the standardized maximum likelihood estimate, the…

无重复观测的超结构模型AI 解读

Dolby's (1976) ultrastructural model is investigated with emphasis on the case with no replications and one of the error variances known. It is shown that, in this situation, the maximum likelihood estimators are not consistent. The method of moments estimators are consistent and asymptotically normal and best in Fisher's sense within a broad class of asymptotically normal estimators discussed by Gleser (1983). Some connections with the errors-in-variables model are examined.