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纵向研究中变化速率函数的半参数随机建模AI 解读

In longitudinal biomedical studies, there is often interest in the rate functions, which describe the functional rates of change of biomarker profiles. This paper proposes a semiparametric approach to model these functions as the realizations of stochastic processes defined by stochastic differential equations. These processes are dependent on the covariates of interest and vary around a specified parametric function. An efficient Markov chain Monte Carlo algorithm is…

含 Box–Cox 变换的 Logistic 模型中的处理效应AI 解读

We consider a logistic model for binary response data that allows the possibility of power transformation of x; that is, log[p/(1 - p)] = α + βx (λ) + γI, where x is a continuous variable, x (λ) is the Box–Cox transformation, and I is a binary variable indicating treatment or group. This model is applicable to observational studies or randomized trials when a treatment effect is investigated after controlling for a confounding variable x. Our focus is on inference concerning…

模型增加参数的代价AI 解读

SUMMARY For a general regression model with n independent observations we consider the variance of the estimate of a quantity of interest under two scenarios. One scenario is where all the parameters are estimated from the data; the other scenario is where a subset of the parameters is assumed known at their true values and the remaining parameters are estimated. We focus on quantities of interest which are defined on the scale of the response variable. We show that, under…

参数线性约束下最大似然估计的受限 EM 算法AI 解读

The EM algorithm is one of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete-data problems. But when the parameters must satisfy a set of linear restrictions, the EM algorithm may be too complicated to apply directly. In this article we propose maximum likelihood estimation procedures under a set of linear restrictions for situations in which the EM algorithm could be used if there were no such restrictions on the parameters. We…

试验次数未观测时过度离散二项数据的两侧变换方法AI 解读

A common complication in analyzing binomial data is overdispersion, where the observed variation exceeds that predicted from the binomial distribution with parameters N and P. We consider the situation where N is not observed and variable. To estimate the regression parameters associated with covariates, we apply the transform-both-sides method. Based on the first-order asymptotic variance stabilizing transformation, we develop the arcsine transformation family indexed by a…

摘要暂缺

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…

摘要暂缺

推广 Logistic 回归的代价AI 解读

Binary-response regression models in which the link function is a family defined by one or more unknown shape parameters are considered. Detailed attention is given to the two single-parameter families proposed by Aranda-Ordaz (1981) that incorporate the logistic, linear, and complementary log-log link functions as special cases. One model is a symmetric family of alternatives to the logistic shape and the second model is an asymmetric family. The increase in variance of…

拟合幂变换后的原尺度均值估计AI 解读

An approximate method is given to estimate the mean of a dependent variable after a linear model is fitted to the Box—Cox power transformation of this variable. The estimate is accurate except when the transformation power parameter is near zero. The properties of the estimate in the one-sample and regression cases are considered, by both asymptotic calculations and Monte Carlo simulations, and comparisons are made with the smearing estimate (Duan 1983). It is shown that…

通过 Box–Cox 变换获得偏态分布的位置度量AI 解读

Box—Cox power transformations are used to transform a set of observations to symmetry. A measure of location of the original data is obtained by applying the inverse transformation to the center of the transformed data. Its properties are discussed, and it is compared with other measures of location.

实现分布对称性的幂变换AI 解读

Power transformations for achieving distributional symmetry are discussed. Estimates of the transformation power are based on general measures of symmetry. They are shown to be consistent and asymptotically normal. Use of the skewness coefficient as a measure of symmetry is shown to be optimal in an important special case. The methods are compared to the likelihood methods of Box & Cox (1964) and alternative methods of Hinkley (1975, 1977). The Box-Cox method or a robust…

使分布对称的幂变换AI 解读

Power transformations for achieving distributional symmetry are discussed. Estimates of the transformation power are based on general measures of symmetry. They are shown to be consistent and asymptotically normal. Use of the skewness coefficient as a measure of symmetry is shown to be optimal in an important special case. The methods are compared to the likelihood methods of Box & Cox (1964) and alternative methods of Hinkley (1975, 1977). The Box-Cox method or a robust…