Sparse alternatives to ridge regression: a random effects approach

In a calibration of near-infrared (NIR) instrument, we regress some chemical compositions of interest as a function of their NIR spectra. In this process, we have two immediate challenges: first, the number of variables exceeds the number of observations and, second, the multicollinearity between variables are extremely high. To deal with the challenges, prediction models that produce sparse solutions have recently been proposed. The term ‘sparse’ means that some model parameters are zero estimated and the other parameters are estimated naturally away from zero. In effect, a variable selection is embedded in the model to potentially achieve a better prediction. Many studies have investigated sparse solutions for latent variable models, such as partial least squares and principal component regression, and for direct regression models such as ridge regression (RR). However, in the latter, it mainly involves an L₁ norm penalty to the objective function such as lasso regression. In this study, we investigate new sparse alternative models for RR within a random effects model framework, where we consider Cauchy and mixture-of-normals distributions on the random effects. The results indicate that the mixture-of-normals model produces a sparse solution with good prediction and better interpretation. We illustrate the methods using NIR spectra datasets from milk and corn specimens.     

论苏格拉底式教学法及在法理学教学中的应用

苏格拉底式教学法从师生的平等关系出发,通过教师的“助产”技艺而达到除蔽的效果。在法理学教学中,适当引入这一教学法不仅有助于引导学生独立思考,培养其法律思维能力及提升法科学生的人文素养,而且也有助于对学生的成绩测评并反馈教师的教学效果。运用这一教学法时,要改革法理学的课程设置,有适当的教学班与教学课时,适时引导学生阅读经典并不断提高教师自身“为”与“不为”的技艺。     

利益·权利·法律——从四大机制看妇女法

结合妇女法的相关规定及其运行状况,从利益切入,可对四大机制作出新的解读利益协调机制切中了妇女从立法层面维权的法律之源,诉求表达机制侧重于妇女从法律层面主张利益要求,矛盾调处机制和权益保障机制则从法律运作层面分别把调和涉及妇女利益的冲突和救济妇女利益缺损视为判定标准.     

Resolving Zeckhauser’s paradox

Theory and Decision - Zeckhauser’s paradox has puzzled and entertained many rationality enthusiasts for almost half a century. You are forced to play a Russian Roulette with a 6-chamber...     

Quasi-likelihood Estimation of Non-invertible Moving Average Processes

Classical methods based on Gaussian likelihood or least-squares cannot identify non-invertible moving average processes, while recent non-Gaussian results are based on full likelihood consideration. Since the error distribution is rarely known a quasi-likelihood approach is desirable, but its consistency properties are yet unknown. In this paper we study the quasi-likelihood associated with the Laplacian model, a convenient non-Gaussian model that yields a modified L ₁ procedure. We show that consistency holds for all standard heavy tailed errors, but not for light tailed errors, showing that a quasi-likelihood procedure cannot be applied blindly to estimate non-invertible models. This is an interesting contrast to the standard results of the quasi-likelihood in regression models, where consistency usually holds much more generally. Similar results hold for estimation of non-causal non-invertible ARMA processes. Various simulation studies are presented to validate the theory and to show the effect of the error distribution, and an analysis of the US unemployment series is given as an illustration.     

Wallet Game: Probability,Likelihood, and Extended Likelihood

We propose a likelihood explanation to the two-person wallet game, a probability-related paradox, where an obviously fair game may appear favorable to both players. Yet a small variation of the game, without changing its fairness, turns it to seem unfavorable. The extended likelihood concept seems logically necessary if we want to allow the sense of uncertainty associated with a realized but still unobserved random outcome, while at the same time avoid potential probability-related paradoxes.     

妇女权益保障法与妇女利益实现机制的构建

本文以法律的视角，从利益切入，对妇女权益保障法与妇女利益实现机制的构建问题进行了探讨。文章认为，妇女权利的核心是妇女利益，妇女权益保障法不仅以法律的形式确认了妇女利益。而且为构建有助于妇女利益实现的利益协调机制、诉求表达机制、矛盾调处机制和权益保障机制奠定了法律基础。