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单调性、凸性及其他形状约束下的非参数函数估计AI 解读

This paper uses free-knot and fixed-knot regression splines in a Bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log-concave likelihood functions. The shape constraints we consider include monotonicity, convexity and functions with a single minimum. A computationally efficient MCMC sampling algorithm is developed that converges faster than previous methods for non-Gaussian models. Simulation…

非参数单调函数估计的贝叶斯方法AI 解读

Summary The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of…

利用数据驱动先验进行加性非参数回归的变量选择与函数估计AI 解读

A hierarchical Bayesian approach is proposed for variable selection and function estimation in additive nonparametric Gaussian regression models and additive nonparametric binary regression models. The prior for each component function is an integrated Wiener process resulting in a posterior mean estimate that is a cubic smoothing spline. Each of the explanatory variables is allowed to be in or out of the model, and the regression functions are estimated by model averaging.…

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时间序列回归中 Durbin–Watson 等不变检验统计量分布的快速计算AI 解读

A method is given for evaluating p values in O(n) operations for a general class of invariant test statistics that can be expressed as the ratio of quadratic forms in time series regression residuals. The best known of these is the Durbin-Watson statistic, although several others have been discussed in the literature. The method is numerically exact in the sense that the user specifies the error tolerance at the outset. As with existing exact methods, the problem is…

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