VIF-based adaptive matrix perturbation method for heteroskedasticity-robust covariance estimators in the presence of multicollinearity

In this study, we investigate linear regression having both heteroskedasticity and collinearity problems. We discuss the properties related to the perturbation method. Important observations are summarized as theorems. We then prove the main result that states the heteroskedasticity-robust variances can be improved and that the resulting bias is minimized by using the matrix perturbation method. We analyze a practical example for validation of the method.     

Difference-based matrix perturbation method for semi-parametric regression with multicollinearity

This paper addresses the collinearity problems in semi-parametric linear models. Under the difference-based settings, we introduce a new diagnostic, the difference-based variance inflation factor (DVIF), for detecting the presence of multicollinearity in semi-parametric models. The DVIF is then used to device a difference-based matrix perturbation method for solving the problem. The electricities distribution data set is analyzed, and numerical evidences validate the effectiveness of the proposed method.     

An Enhanced Double MEWMA Controller for Drifted MIMO Systems

For a drifted multiple-input and multiple-output (MIMO) system, the double multivariate exponentially weighted moving average (dMEWMA) controller is a popular run-to-run (RTR) controller for adjusting the process mean to a desired target. The stability and performance of dMEWMA controller had been widely studied in literature. Although the dMEWMA controller (with suitable discount matrices) can guarantee long-term stability, it usually requires a moderately large number of runs to bring the process output to approach its desired target if the initial recipe is not chosen appropriately. Due to the initial recipe possibly having an infinite number of feasible solutions for MIMO systems, “how to determine an optimal setting for the initial recipe” turns out to be an interesting research topic. In this article, by solving a constrained optimization problem, we first obtain an optimal initial setting for the input recipe. Then, motivated by this setting, we propose an enhanced dMEWMA controller. The long-term stability conditions and short-term performance of the proposed controller are also addressed. Given a fixed and finite production run, it reveals that the proposed controller has the ability of reducing total mean squared error (TMSE) better than the conventional dMEWMA controller.     

Industrial Pollution and the Regional Variations of Life Expectancy at Birth in Taiwan

This paper examines variables influencing the regional variations of life expectancy at birth in Taiwan. It is argued that rapid industrialization has been accompanied by negative factors which produced unexpected environmental pollution in Taiwan. We present an analysis focusing on the relationship between industrial pollution and regional variations of life expectancy at birth. The total nmber of factories is adopted as an indirect measure of industrial pollution. The 361 local areal units under study include precincts and urban and rural townships across the island. Findings support the hypothesis that there is a negative and significant relationship between total number of factories and the level of life expectancy at birth, after controlling other independent variables.     

A new multicollinearity diagnostic for generalized linear models

We propose a new collinearity diagnostic tool for generalized linear models. The new diagnostic tool is termed the weighted variance inflation factor (WVIF) behaving exactly the same as the traditional variance inflation factor in the context of regression diagnostic, given data matrix normalized. Compared to the use of condition number (CN), WVIF shows more reliable information on how severe the situation is, when data collinearity does exist. An alternative estimator, a by-product of the new diagnostic, outperforms the ridge estimator in the presence of data collinearity in both aspects of WVIF and CN. Evidences are given through analyzing various real-world numerical examples.     

Mindfulness-based programme on the psychological health of pregnant women

Problem

Preparation of psychological well-being is an important component of antenatal education for childbirth, but few courses focus on this component.

Sleep quality at 3 months postpartum considering maternal age: A comparative study

Background

Poor sleep quality is related to old age among the general population, but few studies have focused on postpartum women of advanced maternal age. The present study aimed to describe and compare sleep quality between women younger or older than 35 years of age at 3 months postpartum, and to examine the related factors.

The second largest number of maximal independent sets in connected graphs with at most one cycle

A maximal independent set is an independent set that is not a proper subset of any other independent set. In this paper, we determine the second largest number of maximal independent sets among all graphs (respectively, connected graphs) of order n??4 with at most one cycle. We also characterize those extremal graphs achieving these values.