Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non‐stationary Volatility

In this paper, we consider the deterministic trend model where the error process is allowed to be weakly or strongly correlated and subject to non‐stationary volatility. Extant estimators of the trend coefficient are analysed. We find that under heteroskedasticity, the Cochrane–Orcutt‐type estimator (with some initial condition) could be less efficient than Ordinary Least Squares (OLS) when the process is highly persistent, whereas it is asymptotically equivalent to OLS when the process is less persistent. An efficient non‐parametrically weighted Cochrane–Orcutt‐type estimator is then proposed. The efficiency is uniform over weak or strong serial correlation and non‐stationary volatility of unknown form. The feasible estimator relies on non‐parametric estimation of the volatility function, and the asymptotic theory is provided. We use the data‐dependent smoothing bandwidth that can automatically adjust for the strength of non‐stationarity in volatilities. The implementation does not require pretesting persistence of the process or specification of non‐stationary volatility. Finite‐sample evaluation via simulations and an empirical application demonstrates the good performance of proposed estimators.     

Coalition for a Healthier Community: Lessons learned and implications for future work

The Coalition for a Healthier Community (CHC) initiative was implemented to improve the health and well-being of women and girls. Underpinning CHC is a gender-based focus that uses a network of community partners working collaboratively to generate relevant behavior change and improved health outcomes. Ten programs are trying to determine whether gender-focused system approaches are cost-effective ways to address health disparities in women and girls. Programs implemented through coalitions made up of academic institutions, public health departments, community-based organizations, and local, regional, and national organizations, are addressing health issues such as domestic violence, cardiovascular disease prevention, physical activity, and healthy eating. Although these programs are ongoing, they have made significant progress. Key factors contributing to their early success include a comprehensive needs assessment, robust coalitions, the diversity of populations targeted, programs based on findings of the needs assessments, evaluations taking into consideration the effect of gender, and strong academic–community partnerships. A noteworthy impact of these programs has been their ability to shape and impact public, social, and health policies at the state and local levels. However, there have been challenges associated with the implementation of such a complex program. Lessons learned are discussed in this paper.     

An approximation of logarithmic functions in the regression setting

We consider a method of moments approach for dealing with censoring at zero for data expressed in levels when researchers would like to take logarithms. A Box–Cox transformation is employed. We explore this approach in the context of linear regression where both dependent and independent variables are censored. We contrast this method to two others, (1) dropping records of data containing censored values and (2) assuming normality for censored observations and the residuals in the model. Across the methods considered, where researchers are interested primarily in the slope parameter, estimation bias is consistently reduced using the method of moments approach.     

Heteroscedastic Global Tests that the Regression Parameters for Two or More Independent Groups are Identical

Simulation results are reported on methods that allow both within group and between group heteroscedasticity when testing the hypothesis that independent groups have identical regression parameters. The methods are based on a combination of extant techniques, but their finite-sample properties have not been studied. Included are results on the impact of removing all leverage points or just bad leverage points. The method used to identify leverage points can be important and can improve control over the Type I error probability. Results are illustrated using data from the Well Elderly II study.     

Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Hill estimator of projections of functional data on principal components

Functional principal component scores are commonly used to reduce mathematically infinitely dimensional functional data to finite dimensional vectors. In certain applications, most notably in finance, these scores exhibit tail behaviour consistent with the assumption of regular variation. Knowledge of the index of the regular variation, α, is needed to apply methods of extreme value theory. The most commonly used method of the estimation of α is the Hill estimator. We derive conditions under which the Hill estimator computed from the sample scores is consistent for the tail index of the unobservable population scores.     

Using local linear kernel smoothers to test the lack of fit of nonlinear regression models

Herein, we propose a data-driven test that assesses the lack of fit of nonlinear regression models. The comparison of local linear kernel and parametric fits is the basis of this test, and specific boundary-corrected kernels are not needed at the boundary when local linear fitting is used. Under the parametric null model, the asymptotically optimal bandwidth can be used for bandwidth selection. This selection method leads to the data-driven test that has a limiting normal distribution under the null hypothesis and is consistent against any fixed alternative. The finite-sample property of the proposed data-driven test is illustrated, and the power of the test is compared with that of some existing tests via simulation studies. We illustrate the practicality of the proposed test by using two data sets.