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利用拟 Newton 方法加速 EM 算法AI 解读

Summary The EM algorithm is a popular method for maximum likelihood estimation. Its simplicity in many applications and desirable convergence properties make it very attractive. Its sometimes slow convergence, however, has prompted researchers to propose methods to accelerate it. We review these methods, classifying them into three groups: pure, hybrid and EM-type accelerators. We propose a new pure and a new hybrid accelerator both based on quasi-Newton methods and…

极大似然分析中的带符号根偏差剖面与置信区间AI 解读

We investigate a natural extension of the profile t plot of Bates and Watts to a general parametric function g(θ) of the parameters θ in a general maximum likelihood analysis. Although the basic purpose of the extension, called the signed root deviance profile (SRDP), is to construct likelihood ratio (LR) confidence intervals for g(θ), it has various other applications that significantly extend its usefulness. The tangent to the plot of the SRDP at the maximum likelihood…

最大似然分析中的带符号根离差剖面与置信区间AI 解读

We investigate a natural extension of the profile t plot of Bates and Watts to a general parametric function g(θ) of the parameters θ in a general maximum likelihood analysis. Although the basic purpose of the extension, called the signed root deviance profile (SRDP), is to construct likelihood ratio (LR) confidence intervals for g(θ), it has various other applications that significantly extend its usefulness. The tangent to the plot of the SRDP at the maximum likelihood…

改善非线性回归线性化置信区间的变换方法AI 解读

We investigate linear approximation (LA) confidence intervals for functions g(θ) of the parameters θ in a nonlinear regression model. These intervals are almost universally used and generally perform well, but at times have poor coverage probabilities. Using gradient direction plots, we identify transformations of g(θ) that lead to more accurate LA intervals. These include power transformations, whose effectiveness is demonstrated in a variety of nonlinear regression…

通过变换改善非线性回归的线性化置信区间AI 解读

We investigate linear approximation (LA) confidence intervals for functions g(θ) of the parameters θ in a nonlinear regression model. These intervals are almost universally used and generally perform well, but at times have poor coverage probabilities. Using gradient direction plots, we identify transformations of g(θ) that lead to more accurate LA intervals. These include power transformations, whose effectiveness is demonstrated in a variety of nonlinear regression…

非线性回归中线性化置信区间的诊断AI 解读

We investigate linear approximation (LA) confidence intervals for functions g(θ) of the parameters θ in a nonlinear regression model. These intervals are almost universally used and generally perform well, but at times they have poor coverage probabilities. A diagnostic plot and index are developed to detect these failures. We show how these diagnostics may be used to estimate coverage probabilities and these are used to calibrate the diagnostics. The performance of the…

We investigate linear approximation (LA) confidence intervals for functions g(θ) of the parameters θ in a nonlinear regression model. These intervals are almost universally used and generally perform well, but at times they have poor coverage probabilities. A diagnostic plot and index are developed to detect these failures. We show how these diagnostics may be used to estimate coverage probabilities and these are used to calibrate the diagnostics. The performance of the…

利用共轭梯度加速 EM 算法AI 解读

The EM algorithm is a very popular and widely applicable algorithm for the computation of maximum likelihood estimates. Although its implementation is generally simple, the EM algorithm often exhibits slow convergence and is costly in some areas of application. Past attempts to accelerate the EM algorithm have most commonly been based on some form of Aitken acceleration. Here we propose an alternative method based on conjugate gradients. The key, as we show, is that the EM…

线性参数模型中扩展最大似然估计的计算AI 解读

SUMMARY Methods are given for computing extended maximum likelihood estimates in which one or more parameter estimates are infinite at the supremum of the likelihood. The results are given for a broad class of regression-like models based on independent observations with linearly related parameters including, in particular, the generalized linear models. The estimation consists of two steps: A linear programming step to identify the infinite components and a more…

不等右删失下比较生存曲线的精确检验AI 解读

It is shown that through the use of conditional tests after artificial censoring one may produce analogues of standard nonparametric tests, such as the log rank and generalized Wilcoxon, that are exact even in the presence of unequal right censoring where standard permutation tests fail. The artificial censoring leads to a loss in power, but in important special cases, as for example in the study of rare diseases, this can be minor. The power loss is investigated through a…

不等右删失下比较生存曲线的若干精确检验AI 解读

It is shown that through the use of conditional tests after artificial censoring one may produce analogues of standard nonparametric tests, such as the log rank and generalized Wilcoxon, that are exact even in the presence of unequal right censoring where standard permutation tests fail. The artificial censoring leads to a loss in power, but in important special cases, as for example in the study of rare diseases, this can be minor. The power loss is investigated through a…

不等删失下对数秩置换检验的表现AI 解读

This note studies the extent to which the type I error of the permutation test based on the log rank score departs from its nominal value in the presence of unequal right censoring. For the asymptotic case, situations are identified that lead to conservative and to nonconservative behaviour, and the amount of conservatism is computed for some specific constant hazard situations. A small Monte Carlo study is used to support the relevance of the asymptotic results in a finite…

不等删失下对数秩置换检验的表现AI 解读

This note studies the extent to which the type I error of the permutation test based on the log rank score departs from its nominal value in the presence of unequal right censoring. For the asymptotic case, situations are identified that lead to conservative and to nonconservative behaviour, and the amount of conservatism is computed for some specific constant hazard situations. A small Monte Carlo study is used to support the relevance of the asymptotic results in a finite…

检验两个相关矩阵相等的渐近卡方检验AI 解读

An asymptotic χ2 test for the equality of two correlation matrices is derived. The key result is a simple representation for the inverse of the asymptotic covariance matrix of a sample correlation matrix. The test statistic has the form of a standard normal theory statistic for testing the equality of two covariance matrices with a correction term added. The applicability of asymptotic theory is demonstrated by two simulation studies and the statistic is used to test the…

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