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协方差矩阵与参数向量存在函数关系时的最小二乘估计AI 解读

Estimation for the linear model y = Xβ + e with unknown diagonal covariance matrix G is considered. The diagonal elements of G are assumed to be known functions of the explanatory variables X and an unknown parameter vector Θ, where Θ is permitted to contain elements of β. A weighted joint least squares estimator is developed that is asymptotically equivalent to the maximum likelihood estimator. Asymptotic properties of the simple least squares estimator and of the weighted…

分类程序错误率的一般分布及其在逻辑回归判别中的应用AI 解读

The large-sample distribution of the error rate of an arbitrary estimator of the optimal classification rule is given. The asymptotic distribution of the logistic regression estimator is found. These results are used to show that the efficiency of logistic regression classification in some nonnormal cases is low. This suggests that maximum likelihood discrimination should be used whenever possible.

硬限幅后平稳自回归过程的参数估计AI 解读

Estimates of the parameters in normal autoregressive (AR(p)) processes may be obtained as functions of certain runs and subsequences in the associated clipped 0 − 1 processes. For example, the parameter in AR (1) is a function of the number of 1 runs only. Equivalently, this parameter can be estimated by counting only the number of axis crossings by the process. The estimates are obtained by a modification of the likelihood function of the clipped data. The loss of…

不同参数序列下线性函数关系最大似然估计的改进AI 解读

We propose an improvement of the maximum likelihood (ML) estimate in linear functional relationships. The improved estimate is a linear combination of the ML and the least squares estimate so as to remove the bias of the former. Approximations to the distribution of the estimate are derived for two alternative parameter sequences: a sequence in which the noncentrality parameter (the spread of the true values) increases while the number of observations stays fixed, and that…

非线性回归中参数函数的显式估计量AI 解读

When repetitive estimations are to be made under field conditions using data that follow a nonlinear regression law, a simple polynomial function of the observations has considerable appeal as an estimator. The polynomial estimator of finite degree with smallest average mean squared error is found. Conditions are given such that as degree increases it converges in probability to the Bayes estimator and its average mean squared error converges to the lower bound of all square…

离散噪声中二项分布信号的最大似然估计AI 解读

Let X be the sum of independent variables Y and Z, where Y is binomially distributed and Z is a nonnegative integer-valued variable whose distribution does not depend on the binomial parameter p. Convoluted binomial distributions describing variables like X are characterized by regularity conditions and equations of the form ∂/∂p P(X = x)=c[P(X = x − 1) − P(X = x)]. The characterization, together with a monotonicity property for probability ratios, is shown to facilitate…

Summary A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation.…

Prais–Houthakker 家庭等价尺度模型的估计AI 解读

Given a preference basis for the model, a household's general equivalence scale is seen to be a cost of living index relative to the reference household type defined at constant prices. A maximum likelihood estimation procedure which can be applied both to cross-section data and pooled time-series/cross-sections is derived. The lack of identification of the model is established theoretically and checked empirically on British family expenditure survey data. With prior…

广义极值分布参数的极大似然估计AI 解读

Explicit expressions are provided for the information matrix of the three-parameter generalized extreme-value distribution. A condition for regular estimation is established.

逆相关函数的自回归与窗估计AI 解读

The concept of the inverse correlation function of a stationary process xt was first introduced by Cleveland (1972), who also introduced the autoregressive and the window methods for estimating this function. The asymptotic distribution of the estimates provided by these two methods is derived and their asymptotic covariance structure is shown to be in accordance with a remark of Parzen (1974). The results are extended to show that the two procedures suggested by Durbin…

有效得分检验统计量的局部功效AI 解读

SUMMARY The test statistic based on the efficient scores is shown to be locally biased in general. Comparisons of the local powers of this statistic, the likelihood ratio and maximum likelihood statistics reveal no uniform superiority properties. The performance of all three criteria in testing the sphericity hypothesis is examined and conditions which result in equivalence are discussed. A second example on testing for serial correlation suggests that computational…

出生—扩散过程扩散系数的最大似然估计AI 解读

The individuals of a population reproduce according to the linear birth process and simultaneously diffuse on the real line according to a Brownian motion process. The maximum likelihood estimator of the coefficient of diffusion is shown to be unbiased, strongly consistent and asymptotically normal under three different sampling schemes.

摘要暂缺

右删失观测下递增失效率分布函数的最大似然估计AI 解读

The maximum likelihood estimator of a distribution function with increasing failure rate is derived based on a set of observations subject to arbitrary right censorship. This estimator is defined everywhere on the positive real line while the Kaplan-Meier estimator may not be. The small sample properties of this estimator are indicated by results of a Monte Carlo study for the Weibull distribution.

偏似然近似：侧重病例对照研究AI 解读

For many case-control applications, previously suggested approximations to Cox's (1972, 1975) partial likelihood in prospective applications are shown to be seriously inadequate. Alternative approximations based on unconditional maximum likelihood estimation and Taylor series expansion are developed and shown to yield an improvement over the previous methods. In particular, an approximation to the maximum partial likelihood estimator is proposed using the log partial…

零一观测变点问题的简单累积和型统计量AI 解读

A simple cumulative sum type statistic for the change-point with zero-one observations is introduced. A conditional test of no change against change is introduced and compared with a likelihood ratio test. The estimation of the change-point is also considered, using the simple statistic, and the method is shown to be asymptotically equivalent to the maximum likelihood estimator in certain circumstances and almost equivalent in others. To investigate the small sample…

关于伽马过程与稳定过程估计的一个注记AI 解读

Maximum likelihood estimators of the parameters of nondecreasing pure-jump gamma and stable processes based on the jumps of size greater than or equal to ε were studied in a previous paper (Basawa & Brockwell, 1978). In particular, for a single realization {X( u ), 0 ≤ u ≤ t }, the estimators for the stable process are consistent as ε ↓ 0, but this is not so for the gamma process. In the present note we derive asymptotic distributions as ε ↓ 0 for these estimators, centred…

基于似然比准则的稳健方差分析AI 解读

Robust tests of general linear hypotheses in linear models are developed. These are likelihood ratio type tests in the same sense that M -estimates are maximum likelihood type estimates. Construction of the tests suggests a decomposition of the data into terms analogous to classical sums of squares, providing a robust analysis of variance. Asymptotic efficiency and robustness properties of the tests are the same as those of the M -estimates upon which they are based.

基于伽马分布的不同收入不平等指标性质分析AI 解读

The Gini, Theil entropy, and Pietra measures of inequality associated with the gamma distribution function are expressed in terms of the parameters defining the gamma distribution. Method of moments (MME) and maximum likelihood estimators (MLE) of these measures are obtained along with expressions for the asymptotic standard errors of the MLE measures. A table is presented that facilitates the calculation of MLE of inequality measures and the associated asymptotic standard…

恰好识别情形下 LIML 与 2SLS 结构系数分布函数的说明AI 解读

Many alternative techniques of estimating coefficients appearing in the structural representation of econometric models have been developed. The techniques of two-stage least squares (2SLS) and limited information maximum likelihood (LIML) yield identical estimates in the exactly identified case. The derivations of the density functions of these estimators for overidentified structural equations do not formally include the exactly identified case. In this note we demonstrate…

含潜变量的结构 Probit 模型AI 解读

A model with dichotomous indicators of latent variables is developed. The latent variables are related to each other and to a set of exogenous variables in a system of structural relations. Identification and maximum likelihood estimation of the model are treated. A sociological application is presented in which a theoretical construct (an attitude) is related to a set of background variables. The construct is not measured directly, but is indicated by the answers to a pair…

恰好识别情形下 LIML 与 2SLS 结构系数分布函数札记AI 解读

Many alternative techniques of estimating coefficients appearing in the structural representation of econometric models have been developed. The techniques of two-stage least squares (2SLS) and limited information maximum likelihood (LIML) yield identical estimates in the exactly identified case. The derivations of the density functions of these estimators for overidentified structural equations do not formally include the exactly identified case. In this note we demonstrate…

天气干预试验的若干分析方法AI 解读

Using generalized densities, maximum likelihood and ancillarity, methods are developed for the analysis of randomized weather modification experiments that incorporate predictor variables. The linear logistic form is used to model the distributional singularity at the origin, while a gamma model with predictors is developed for the component conditional on the presence of precipitation. Connexions between the component submodels are explored and illustrated using an…

协方差结构分析中的约束估计AI 解读

In covarianoe structure analysis, the method of weighted least squares for estimating parameters that are subject to functional constraints is developed. Statistical properties of the estimator are studied and a goodness-of-fit statistic is presented. Based on the penalty function technique, an algorithm is developed. This algorithm is able to produce not only the constrained weighted least squares estimator but also the constrained maximum likelihood estimator, if we choose…