Notes on likelihood intervals and profiling

In many applications, decisions are made on the basis of function of parameters g(θ). When the value of g(theta;) is calculated using estimated values for te parameters, its is important to have a measure of the uncertainty associated with that value of g(theta;). Likelihood ratio approaches to finding likelihood intervals for functions of parameters have been shown to be more reliable, in terms of coverage probability, than the linearization approach. Two approaches to the generalization of the profiling algorithm have been proposed in the literature to enable construction of likelihood intervals for a function of parameters (Chen and Jennrich, 1996; Bates and Watts, 1988). In this paper we show the equivalence of these two methods. We also provide and analysis of cases in which neither profiling algorithm is appropriate. For one of these cases an alternate approach is suggested Whereas generalized profiling is based on maximizing the likelihood function given a constraint on the value of g(θ), the alternative algorithm is based on optimizing g(θ) given a constraint on the value of the likelihood function.     

Geometric characterization of planar regression

The geometric characterization of linear regression in terms of the ‘concentration ellipse’ by Galton [Galton, F., 1886, Family likeness in stature (with Appendix by Dickson, J.D.H.). Proceedings of the Royal Society of London, 40, 42–73.] and Pearson [Pearson, K., 1901, On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2, 559–572.] was extended to the case of unequal variances of the presumably uncorrelated errors in the experimental data [McCartin, B.J., 2003, A geometric characterization of linear regression. Statistics, 37(2), 101–117.]. In this paper, this geometric characterization is further extended to planar (and also linear) regression in three dimensions where a beautiful interpretation in terms of the concentration ellipsoid is developed.     

Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.     

On approximate likelihood inference in a poisson mixed model

A two-step estimation approach is proposed for the fixed-effect parameters, random effects and their variance σ² of a Poisson mixed model. In the first step, it is proposed to construct a small σ²-based approximate likelihood function of the data and utilize this function to estimate the fixed-effect parameters and σ². In the second step, the random effects are estimated by minimizing their posterior mean squared error. Methods of Waclawiw and Liang (1993) based on so-called Stein-type estimating functions and of Breslow and Clayton (1993) based on penalized quasilikelihood are compared with the proposed likelihood method. The results of a simulation study on the performance of all three approaches are reported.     

中国古代审美观照的拓展与深化——论郭象“独化”哲学中的“俯仰”与“虚静”的整合

郭象独化哲学的崇有把自然山水审美引向独立,相当于掀起一场美学革命。这其中包括对俯仰与虚静两种审美观照的整合,深深影响了此后美学思想发展进程的基本走向。俯仰与虚静各有所长,亦各有所短。俯仰有观物取象之长,亦有思维的类比受限之短;虚静有排斥外通感物之短,亦有拓展心灵自由之长。郭象的无心玄应,唯感是从则构成二者的交融互补。其经无心过滤清洗过的唯感是从,一方面以俯仰的类比之短补入虚静的心灵自由之长,另一方面以隔绝外通之短补入俯仰的接物之长。中古山水审美的寓目辄书蔚然成风、巧言切状的追求及目击道存的观照方式的确认和推行,均得益于这种整合。它既是对庄子虚静排除具体感性的改造,又是对其目击道存理论依据的创造性发展,从而大大拓展和深化了中国古代的审美观照。     

A new lower bound to A2-optimality measure for multi-level and mixed-level column balanced designs and its applications

In this paper, a new lower bound to A₂-optimality measure is derived and is applied to multi-level and mixed-level column balanced designs. A₂-optimal multi-level and mixed-level designs are obtained by the application of the new lower bound.     

Empirical nonparametric control charts for high-quality processes

For attribute data with (very) small failure rates often control charts are used which decide whether to stop or to continue each time r failures have occurred, for some r?1. Because of the small probabilities involved, such charts are very sensitive to estimation effects. This is true in particular if the underlying failure rate varies and hence the distributions involved are not geometric. Such a situation calls for a nonparametric approach, but this may require far more Phase I observations than are typically available in practice. In the present paper it is shown how this obstacle can be effectively overcome by looking not at the sum but rather at the maximum of each group of size r.     

正交多项式逼近下非线性趋势序列单位根检验

 传统单位根检验方法常常假设带有线性的确定性趋势,但如果趋势是非线性的,通常将因为检验功效大幅下降而导致检验失败。本文研究用正交多项式逼近非线性趋势,然后对残差进行单位根检验的方法。研究了用正交多项式进行趋势逼近的性质,推导了这种方法进行单位根检验时统计量的极限分布,提出了正交多项式最高阶数的确定方法,仿真研究了残差相关与不相关时的检验功效。结果表明,检验方法是有效的。     

描写充分与解释充分之张力：原则与参数框架的理论动因

通过总结Chomsky的＂句法理论中的原则与参数＂一文,回顾原则与参数框架产生的历史背景及其理论动因,梳理原则与参数框架的主要思想及内容,分析原则与参数框架提出的意义、它所面临的挑战及其发展前景。描写充分性与解释充分性之间的张力是原则与参数框架形成的理论动因。在生成语法追求＂超越解释的充分性＂这一更高目标的过程中,我们看到的是继续前进中的原则与参数。