Age Period Cumulative Environment Model for Analyzing (Age,Period)-Tabulated Data on Breast Cancer Deaths

A model which is an alternative to the age period cohort (APC) model is proposed for analyzing (age, period)-tabulated on breast cancer deaths. The result of fitting the proposed model to the data for females in Japan is shown, where it is seen that the proposed model provides a better fit to the data than APC model in terms of AIC. Besides, the ML estimates of the parameters in the model suggest that the risks of breast cancer death existing in the environment are rapidly increasing since the period of high economic growth in Japan.     

Ridge Regression – A Simulation Study

In this article we assess the suitability of two new ridge estimators by means of a simulation study. We compare these estimators with well-known ridge estimators. We also make direct comparisons between the ordinary least squares (OLS) estimator and the ridge estimators by using ratio of the average total mean square error of the OLS estimator and the ridge estimators. We find that the new estimators perform well under certain conditions.     

Posterior Sampling When the Normalizing Constant is Unknown

This article describes a means by which to undertake Bayesian posterior inference via sampling techniques when the normalizing constant is not computable and hence unavailable. The strategy relies on the introduction of latent variables which removes any integrals associated with the inaccessibility of the normalizing constant.     

A NEW VERSION OF THE LOCAL CONSTANT M-SMOOTHER

ABSTRACT

In the case of the equally spaced fixed design nonparametric regression, the local constant M-smoother (LCM) in Chu, Glad, Godtliebsen, and Marron [1] Chu, C.K., Glad, I., Godtliebsen, F. and Marron, J.S. 1998. Edge-Preserving Smoothers for Image Processing (with discussion). Journal of the American Statistical Association, 93: 526–556. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] has the interesting property of jump-preserving. However, it suffers from the problem of boundary effects. To correct for such adverse effects on the LCM, Rue, Chu, Godtliebsen, and Marron [2] Rue, H., Chu, C.K., Godtliebsen, F. and Marron, J.S. 2001. M-smoother with Local Linear Fit. To appear in Journal of Nonparametric Statistics [Google Scholar] apply the local linear fit to the “inside” of the kernel function, and propose the local linear M-smoother (LLM). Unfortunately, the LLM is more sensitive to random fluctuations, since an extra tuning parameter is included. To avoid such a practical drawback to the LLM, we propose a new version of the LCM by applying the local linear fit to the “outside” of the kernel function. Our proposed estimator employs both the same tuning parameter associated with the ordinary LCM and the same weights assigned to the observations by the local linear smoother in Fan 3-4 Fan, J. 1992. Design-adaptive Nonparametric Regression. Journal of the American Statistical Association, 87: 998–1004. Fan, J. 1993. Local Linear Regression Smoothers and Their Minimax Efficiencies. Annals of Statistics, 21: 196–216.  . It has the same asymptotic mean square error as the LLM. In practice, it can be calculated by using the fast computation algorithm designed for the ordinary LCM by Chu et al. [1] Chu, C.K., Glad, I., Godtliebsen, F. and Marron, J.S. 1998. Edge-Preserving Smoothers for Image Processing (with discussion). Journal of the American Statistical Association, 93: 526–556. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar], and does not suffer from the drawback to the LLM. More importantly, our results obtained for the new version of the LCM in the one-dimensional case can be extended directly to the multidimensional case. Simulation studies demonstrate that the asymptotic effects hold for reasonable sample sizes.     

Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes

This paper develops test procedures for testing the validity of general linear identifying restrictions imposed on cointegrating vectors in the context of a vector autoregressive model. In addition to overidentifying restrictions the considered restrictions may also involve normalizing restrictions. Tests for both types of restrictions are developed and their asymptotic properties are obtained. Under the null hypothesis tests for normalizing restrictions have an asymptotic "multivariate unit root distribution", similar to that obtained for the likelihood ratio test for cointegration, while tests for overidentifying restrictions have a standard chi-square limiting distribution. Since these two types of tests are asymptotically independent they are easy to cotnbine to an overall test for the spccifed identifying restrictions. An overall test of this kind can consistently reveal the failure of the identifying restrictions in a wider class of cases than previous tests which only test for overidentifying restrictions.     

Discrepancy in regression estimates between log-normal and gamma: some case studies

In regression models with multiplicative error, estimation is often based on either the log-normal or the gamma model. It is well known that the gamma model with constant coefficient of variation and the log-normal model with constant variance give almost the same analysis. This article focuses on the discrepancies of the regression estimates between the two models based on real examples. It identifies that even though the variance or the coefficient of variation remains constant, but regression estimates may be different between the two models. It also identifies that for the same positive data set, the variance is constant under the log-normal model but non-constant under the gamma model. For this data set, the regression estimates are completely different between the two models. In the process, it explains the causes of discrepancies between the two models.     

Robust parametric tests of constant conditional correlation in a MGARCH model

This article provides a rigorous asymptotic treatment of new and existing asymptotically valid conditional moment (CM) testing procedures of the constant conditional correlation (CCC) assumption in a multivariate GARCH model. Full and partial quasi maximum likelihood estimation (QMLE) frameworks are considered, as is the robustness of these tests to non-normality. In particular, the asymptotic validity of the LM procedure proposed by Tse (2000 Tse, Y. K. (2000). A test for constant correlations in a multivariate GARCH model. Journal of Econometrics 98 (1):107–127.[Crossref], [Web of Science ®] , [Google Scholar]) is analyzed, and new asymptotically robust versions of this test are proposed for both estimation frameworks. A Monte Carlo study suggests that a robust Tse test procedure exhibits good size and power properties, unlike the original variant which exhibits size distortion under non-normality.     

Measuring diversity in biological populations with logarithmic abundance distributions

Fisher's logarithmic distribution for species abundance is derived under a suitable set of conditions. The derivation explains the explicit meaning of the two parameters of the distribution.     

论孔子之"政"

孔子是儒家创始人,是我国古代史上最有影响的思想家.他周游列国,目的是为了宣传自己的学说,让诸侯国的国君接受他的治国策略,即接受他所谓的"政".孔子有关谈"政"的言论很多,内容也是多方面的,包括政治、经济、伦理道德等,本文主要从某些方面对孔子"政"之内涵进行考察.