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删失下 Kaplan–Meier 及其他最大似然估计量的可容许性AI 解读

For the nonparametric estimation of a survival function when censoring is present, the Kaplan-Meier estimator is often used. The admissibility of this estimator and other related maximum likelihood estimators is demonstrated. This is done by reducing the problem to one involving just the multinomial distribution and then using the stepwise Bayes technique to prove admissibility.

自相似过程的有效参数估计AI 解读

Asymptotic normality of the maximum likelihood estimator for the parameters of a long range dependent Gaussian process is proved. Furthermore, the limit of the Fisher information matrix is derived for such processes which implies efficiency of the estimator and of an approximate maximum likelihood estimator studied by Fox and Taqqu. The results are derived by using asymptotic properties of Toeplitz matrices and an equicontinuity property of quadratic forms.

不规则纵向数据中发生率与诊断误差率的联合估计AI 解读

Longitudinal studies often involve the repeated diagnosis across time of each patient's status with respect to a progressive categorical process. When the occurrence of a change in status is not readily apparent, two factors can make modeling and assessing the incidence rates of progression difficult. First, because diagnoses may be difficult, they may not be performed with the frequency necessary to pinpoint exact times of incidence. Second, uncertainty in the diagnostic…

致畸效应的定量风险评估AI 解读

This article presents a quantitative procedure for using a “benchmark dose” to obtain low-dose risk estimates for reproductive and developmental toxic effects. This procedure combines the best features of the previously proposed methods for handling litter effects for teratology data and the currently used methods for quantitative risk assessment. The beta-binomial distribution is used to account for litter effects, and the Weibull dose—response model is used for modeling…

使用 t 分布进行稳健统计建模AI 解读

The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling…

不规则纵向数据中发生率与诊断错误率的联合估计AI 解读

Longitudinal studies often involve the repeated diagnosis across time of each patient's status with respect to a progressive categorical process. When the occurrence of a change in status is not readily apparent, two factors can make modeling and assessing the incidence rates of progression difficult. First, because diagnoses may be difficult, they may not be performed with the frequency necessary to pinpoint exact times of incidence. Second, uncertainty in the diagnostic…

不可逆移动平均模型中极大似然与非线性最小二乘估计的渐近性质AI 解读

Dealing with noninvertible, infinite-order moving average (MA) models, we study the asymptotic properties of an estimator of the noninvertible coefficient. The estimator is constructed acting as if the data were generated from a Gaussian MA process. Allowing for two cases on the initial values of the error process, we first discuss the condition for the existence of a consistent estimator. We then compute the probability of the estimator occurring at the boundary of the…

摘要暂缺

辅助性与联立方程中单个结构方程的有限信息最大似然估计AI 解读

The concepts of the curved exponential family of distributions and ancillarity are applied to estimation problems of a single structural equation in a simultaneous equation model, and the effect of conditioning on ancillary statistics on the limited information maximum-likelihood (LIML) estimator is investigated. The asymptotic conditional covariance matrix of the LIML estimator conditioned on the second-order asymptotic maximal ancillary statistic is shown to be efficiently…

半参数 Tobit 估计量的蒙特卡洛比较AI 解读

Abstract This paper focuses on a performance comparison of semiparametric Tobit estimators. Firstly, a conditional expectation version of Horowitz's distribution‐free least‐squares estimator is proposed, together with a short description of the other estimators considered in the later Monte Carlo experiment. Then, a performance comparison of the following selected estimators is made through a Monte Carlo experiment: the standard Tobit maximum‐likelihood estimator, the…

利用 EM 自身计算步骤实现快速改进AI 解读

SUMMARY The EM algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models. It is easy to apply in many problems and is stable but slow. The algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the Louis method is performed. Newton-type or other gradient methods are faster and provide error estimates but…

分类与多假设检验中的最优划分不等式AI 解读

Optimal-partitioning and minimax risk inequalities are obtained for the classification and multi-hypotheses testing problems. Best possible bounds are derived for the minimax risk for location parameter families, based on the tail concentrations and Levy concentrations of the distributions. Special attention is given to continuous distributions with the maximum likelihood ratio property and to symmetric unimodal continuous distributions. Bounds for general (including…

高维对数线性模型最大似然估计量的 BootstrapAI 解读

The notion of a bootstrap estimator of the distribution of the maximum likelihood estimator in log-linear models is defined for common sampling models. It is shown that the bootstrap estimator is consistent under assumptions which allow the dimension of the model to increase to infinity. Such an approach allows treatment of large, sparse contingency tables.

若干多元正态混合分布的渐近展开及误差界AI 解读

This paper deals with the distribution of $\mathbf{X} = \sum^{1/2}\mathbf{Z}$, where $\mathbf{Z}: p \times 1$ is distributed as $N_p(0, I_p), \sum$ is a positive definite random matrix and $\mathbf{Z}$ and $\sum$ are independent. Assuming that $\sum = I_p + BB'$, we obtain an asymptotic expansion of the distribution function of $\mathbf{X}$ and its error bound, which is useful in the situation where $\sum$ tends to $I_p$. A stronger version of the expansion is also given.…

序贯设计线性模型实验的极弱渐近展开AI 解读

In sequentially designed experiments with linear models, each design variable may depend on previous responses. The use of such sequential designs does not affect the likelihood function or the functional form of the maximum likelihood estimator, but it may affect sampling distributions. In this paper, asymptotic expansions for sampling distributions are obtained. The expansions are very weak ones in which a confidence curve (a function of the unknown parameters) is replaced…

极端次序统计量稳定性与极大似然核密度估计收敛的关系AI 解读

Let $f$ be a density on the real line and let $f_n$ be the kernel estimate of $f$ in which the smoothing factor is obtained by maximizing the cross-validated likelihood product according to the method of Duin and Habbema, Hermans and Vandenbroek. Under mild regularity conditions on the kernel and $f$, we show, among other things that $\int|f_n - f| \rightarrow 0$ almost surely if and only if the sample extremes of $f$ are strongly stable.

链接函数设定偏离下的回归分析AI 解读

We study the behavior of regression analysis when there might be some violation of the assumed link function, the functional form of the model which relates the outcome variable $y$ to the regressor variable $\mathbf{x}$ and the random error. We allow the true link function to be completely arbitrary, except that $y$ depends on $\mathbf{x}$ only through a linear combination $\beta\mathbf{x}$. The slope vector $\beta$ is identified only up to a multiplicative scalar. Under…

序贯临床试验结束后的治疗差异估计AI 解读

To reduce the number of patients needed to reach a conclusion in a clinical trial, a sequential trial design may be used. In theory the distribution of responses is biased when a sequential trial is stopped. The usual estimation methods of treatment difference applied in nonsequential situations are, therefore, not necessarily applicable following a sequential test. Whitehead (1983) proposed a method for estimating the treatment effect following some types of two-sample…

随机截断数据的半参数模型AI 解读

For randomly censored data, it is known that the maximum likelihood estimate (MLE) of the survival curve is not affected by parametric assumption on the censoring variable. The Kaplan-Meier (1958) estimate is the MLE for both nonparametric and semiparametric models. For randomly truncated data, the truncation product-limit estimate is the MLE for nonparametric models. This is not the case if the truncation mechanism is parameterized, however. Specifically, let X be a generic…

非线性有界影响估计在美联储银行总借款中的应用AI 解读

Forecasting aggregate discount window borrowing has posed difficulties for the Federal Reserve, due in part to outliers resulting from numerous institutional changes and special borrowing situations. This article applies bounded influence estimation and influence diagnostics to identify and adjust for outliers in the case of discount window borrowing. Since most banks borrow from the Federal Reserve infrequently, the model is nonlinear and of the switching regression class.…

序贯临床试验结束后的治疗差异估计AI 解读

To reduce the number of patients needed to reach a conclusion in a clinical trial, a sequential trial design may be used. In theory the distribution of responses is biased when a sequential trial is stopped. The usual estimation methods of treatment difference applied in nonsequential situations are, therefore, not necessarily applicable following a sequential test. Whitehead (1983) proposed a method for estimating the treatment effect following some types of two-sample…

统计信息与似然：批判性论文集AI 解读

I Information and Likelihood.- I Recovery of Ancillary Information.- 0. Notes.- 1. Introduction.- 2. The Sample Size Analogy.- 3. A Logical Difficulty.- 4. Conceptual Statistical Experiments.- II Statistical Information and Likelihood Part I: Principles.- 0. Notes.- 1. Statistical Information.- 2. Basic Definitions and Relations.- 3. Some Principles of Inference.- 4. Information as a Function.- 5. Fisher Information.- 6. The Likelihood Principle.- III Statistical Information…

受限无偏迭代广义最小二乘估计AI 解读

It is shown that the iterative least-squares procedure for estimating the parameters in a general multilevel random coefficients linear model can be modified to produce unbiased estimates of the random parameters. In the multivariate normal case these are equivalent to restricted maximum likelihood estimates.

混合图交互模型中的极大似然分解AI 解读

We show how decompositions of marked graphs induce corresponding decompositions of maximum likelihood estimates in mixed graphical interaction models. We use this result to obtain explicit formulae for the estimates in decomposable models and to obtain factorizations of likelihood ratio statistics.