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澄清：回归模型选择的残差似然方法AI 解读

In regression models, Shi and Tsai (2002) applied the logarithm of the commonly used residual maximum likelihood function (2.2) to obtain the residual information criterion RIC in equation (2.10). Function (2.2) is the same as the modified profile likelihood function, but it is different from the complete residual maximum likelihood function that contains two additional terms, −12(n−k)log⁡(2π) and 12log⁡|X′X|⁠, on the right-hand side of expression (2.2). Because these two…

将赤池信息准则扩展至混合回归模型AI 解读

We examine the problem of jointly selecting the number of components and variables in finite mixture regression models. We find that the Akaike information criterion is unsatisfactory for this purpose because it overestimates the number of components, which in turn results in incorrect variables being retained in the model. Therefore, we derive a new information criterion, the mixture regression criterion (MRC), that yields marked improvement in model selection due to what…

回归模型选择：残差似然方法AI 解读

Summary We obtain the residual information criterion RIC, a selection criterion based on the residual log-likelihood, for regression models including classical regression models, Box–Cox transformation models, weighted regression models and regression models with autoregressive moving average errors. We show that RIC is a consistent criterion, and that simulation studies for each of the four models indicate that RIC provides better model order choices than the Akaike…

单调 B 样条平滑AI 解读

Estimation of growth curves or item response curves often involves monotone data smoothing. Methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated. Built on the ideas of Koenker, Ng, and Portnoy and Ramsay, we propose monotone B-spline smoothing based on L 1 optimization. This method inherits the desirable properties of spline approximations and the computational…

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