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历史身高的估计AI 解读

Historical samples of military, naval, and merchant marine heights suffer from undercounts of short people, undercounts highly irregular compared to the truncated distributions for which standard methods are available. Our knowledge is too imprecise for parametric models of the undercount process but it suffices for intuitive description of the deviations from normality with which estimators should cope. Two new estimators are developed. The first adapts maximum likelihood…

含缺失数据列联表的最大似然估计与模型选择AI 解读

In many studies the values of one or more variables are missing for subsets of the original sample. This article focuses on the problem of obtaining maximum likelihood estimates (MLE) for the parameters of log-linear models under this type of incomplete data. The appropriate systems of equations are presented and the expectation-maximization (EM) algorithm (Dempster, Laird, and Rubin 1977) is suggested as one of the possible methods for solving them. The algorithm has…

两个指数分布联合Ⅱ型删失样本的置信区间AI 解读

Strong consistency and asymptotic normality of the maximum likelihood estimators are established in the context of jointly type-II censored samples from two exponential populations. Large-sample confidence intervals are derived for the individual scale parameters as well as their ratio, and some applications to series and parallel systems are discussed. For the ratio of the scale parameters, an exact confidence procedure is developed on the basis of the failure counts in the…

移动平均过程估计中的准则函数AI 解读

It is well known that unconditional and conditional least squares estimators are asymptotically maximum likelihood for invertible moving average (MA) processes. By writing the criteria functions for these three estimators in comparable form, we establish simple inequalities between them and also between the corresponding disturbance variance estimates. Further analysis is carried out by examining the expected values of the criteria functions for given (true) coefficients in…

摘要暂缺

Maximum likelihood estimation of the parameters of the binary logistic regression model for pr(H|x) is discussed with separate discussion of sampling from (i) the conditional distribution of H given x, (ii) the joint distribution of H and x, and (iii) the conditional distribution of x given H. Difficulties associated with continuous x in the latter sampling scheme are discussed. To avoid these, penalized maximum likelihood estimates are introduced, which give estimates of…

四阶累积量谱密度积分的估计AI 解读

It is known that the asymptotic variance of a quasimaximum likelihood estimate for a non-Gaussian process contains certain integrals of the fourth order cumulant spectral density. If we apply the asymptotic theory we are required to estimate these integrals. Here we shall propose some operational consistent estimates for them.

位置参数 M 估计量的小样本渐近分布AI 解读

Asymptotic formulae for the distribution of M-estimators, i.e. maximum likelihood type estimators, of location, including the arithmetic mean, are derived which numerical studies show to give relative errors for densities and tail areas of the order of magnitude of 1% down to sample sizes 3 and 4 even in the extreme tails. The paper is the continuation of earlier work by the second author and is also closely related to Daniels's work on the saddlepoint approximation. The…

分组观测的单调回归估计AI 解读

The maximum likelihood estimator of a nondecreasing regression function with normally distributed errors has been considered in the literature. Its asymptotic distribution at a point is related to a solution of the heat equation, and its rate of convergence to the underlying regression function is of order $n^{-1/3}$. This estimator can be modified by grouping adjacent observations and then "isotonizing" the corresponding means. It is shown that the resulting estimator has…

线性与仿射函数模型中的最大似然及最小二乘估计AI 解读

In a linear (or affine) functional model the principal parameter is a subspace (respectively an affine subspace) in a finite dimensional inner product space, which contains the means of $n$ multivariate normal populations, all having the same covariance matrix. A relatively simple, essentially algebraic derivation of the maximum likelihood estimates is given, when these estimates are based on single observed vectors from each of the $n$ populations and an independent…

含协变量生存数据的分段指数模型AI 解读

A general class of models for analysis of censored survival data with covariates is considered. If $n$ individuals are observed over a time period divided into $I(n)$ intervals, it is assumed that $\lambda_j(t)$, the hazard rate function of the time to failure of the individual $j$, is constant and equal to $\lambda_{ij} > 0$ on the $i$th interval, and that the vector $\ell = \{\log \lambda_{ij}: j = 1, \ldots, n; i = 1, \ldots, I(n)\}$ lies in a linear subspace. The maximum…

多元正态均值最小最大估计量的选择AI 解读

The problem of estimating a $p$-variate normal mean under arbitrary quadratic loss when $p \geq 3$ is considered. Any estimator having uniformly smaller risk than the maximum likelihood estimator $\delta^0$ will have significantly smaller risk only in a fairly small region of the parameter space. A relatively simple minimax estimator is developed which allows the user to select the region in which significant improvement over $\delta^0$ is to be achieved. Since the desired…

多个二乘二列联表共同优势比估计量的有限样本性质AI 解读

A simulation study was used to determine the finite-sample properties of various estimators of a common odds ratio from multiple 2 × 2 tables. The maximum likelihood, Mantel-Haenszel, and Woolf estimators plus four variants of each were considered. The original Woolf estimator and one of its variants are dismissed on the grounds that they often cannot be calculated. In terms of minimum bias, maximum likelihood is the recommended procedure after adding .25 to each cell.

混合样本的参数估计AI 解读

Assume that a sample is a mixture of two samples from two different populations with distributions Fθ1 and Fθ2 . Given the form of Fθ , estimators of θ1 and θ2 are introduced. It is shown that the estimators are consistent and their asymptotic joint distribution is derived. The suggested estimators are compared with the maximum likelihood estimators and the method of moments estimators. For small sample sizes the comparison is done by a Monte Carlo study. For large sample…

Sichel 复合泊松分布的推断AI 解读

In a long-tailed compound Poisson distribution introduced by Sichel, the probabilities can only readily be calculated if one of the parameters λ has half-integer values, that is, λ = m + 1/2, m integer. The maximum likelihood estimation of this parameter is compared with an approximate method derived from a grid of half-integer values. It is found that the approximate method, which avoids excessive special computation, yields inferences indistinguishable from those based on…

混合样本中的参数估计AI 解读

Assume that a sample is a mixture of two samples from two different populations with distributions Fθ1 and Fθ2 . Given the form of Fθ , estimators of θ1 and θ2 are introduced. It is shown that the estimators are consistent and their asymptotic joint distribution is derived. The suggested estimators are compared with the maximum likelihood estimators and the method of moments estimators. For small sample sizes the comparison is done by a Monte Carlo study. For large sample…

独立观测下的工具变量回归AI 解读

INTRODUCTION THE METHOD OF INSTRUMENTAL VARIABLES (IV), proposed independently by Reiersol [15] and Geary [4], is one of the most useful classes of estimation techniques available to econometricians. The method is particularly useful in the context of errors-in-variables and simultaneous equation problems, and it ineludes ordinary least squares (OLS), two-stage least squares (2SLS) (Klein [9]), three-stage least squares (3SLS) (Madansky [12]) and certain full-information…

摘要暂缺

非线性模型的参数化AI 解读

summary in the literature there have been many suggestions on how to parametrize models. some properties you can seek are (1) stability of variance of the mle; (2) normal likelihood; (3) zero asymptotic skewness of the mle; (4) asymptotic unbiasedness of the mle. the parametrizations corresponding to these demands are found in the one-dimensional curved exponential family. they all belong to a general class of transformations, but they are in general not identical. the…

使用 EM 算法时的观测信息矩阵计算AI 解读

Summary A procedure is derived for extracting the observed information matrix when the EM algorithm is used to find maximum likelihood estimates in incomplete data problems. The technique requires computation of a complete-data gradient vector or second derivative matrix, but not those associated with the incomplete data likelihood. In addition, a method useful in speeding up the convergence of the EM algorithm is developed. Two examples are presented.

大型非线性模型的 FIML 与 3SLS 估计算法AI 解读

THIS PAPER PRESENTS a numerical algorithm for computing full information maximum likelihood (FIML) and nonlinear three-stage least squares (3SLS) coefficient estimates for large nonlinear models. (The proposed algorithm will be denoted algorithm A.) Although the theory of FIML estimation has been available for thirty years [20], FIML estimation has long been regarded as impossible on large nonlinear models.2 The more recently proposed nonlinear 3SLS estimator [191 also poses…

This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (QMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to…

利用 EM 算法求结构化协方差矩阵的极大似然估计AI 解读

Some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates. In such cases, the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables. The…

The modified form of the Cramér-von Mises statistic is employed for the problem of testing exponentiality with type I censored samples, in the presence of an unknown scale parameter θ. The asymptotic distribution of the Cramér-von Mises statistic is established when θ is estimated by its maximum likelihood estimator θ^⁠. Percentiles of the asymptotic distribution are obtained for various levels of censoring.