Bootstrap estimation of the variance of the error term in monotonic regression models

The variance of the error term in ordinary regression models and linear smoothers is usually estimated by adjusting the average squared residual for the trace of the smoothing matrix (the degrees of freedom of the predicted response). However, other types of variance estimators are needed when using monotonic regression (MR) models, which are particularly suitable for estimating response functions with pronounced thresholds. Here, we propose a simple bootstrap estimator to compensate for the over-fitting that occurs when MR models are estimated from empirical data. Furthermore, we show that, in the case of one or two predictors, the performance of this estimator can be enhanced by introducing adjustment factors that take into account the slope of the response function and characteristics of the distribution of the explanatory variables. Extensive simulations show that our estimators perform satisfactorily for a great variety of monotonic functions and error distributions.     

On a sampling scheme with inclusion probability proportional to size

A sampling scheme for selection of a sample of two units with inclusion probability proportionalto size is suggested which provides a non–negative variance estimator of the variance of Horvitz–Thompson estimator. The suggested sampling scheme is shown to perform better than many of the existing unequal probability and inclusion probability proportional to size sampling Achemes for a number of natural populations.     

The spokane heart study: weibull regression and coronary artery disease

Coronary artery calcium is a marker of coronary artery disease and measures the progression of atherosclerosis. It is measured by electron beam computed tomography, and the measured amount of coronary artery calcium is highly skewed to the right and left censored. The distribution of coronary artery calcium appears to be Weibull. We propose a Weibull regression model and we analyze the data using these techniques. Our analysis is based on data from the Spokane Heart Study, which is a cohort of about a thousand subjects that are assessed every two years for coronary artery calcium and risk factors of coronary artery disease. The major focus of the heart study is to determine the natural history of atherosclerosis in its early phase, and we analyze the data as a cross-sectional study with 859 subjects. We would also like to highlight the use of Weibull regression techniques in situations like this, where we have extreme right skewed data. Our main emphasis will be on examining the effect of the traditional risk factors of age, gender, lipid profile (cholesterol and HDL), patient history of lipid abnormality, hypertension, and smoking, and other family history risks on coronary artery calcium. We found that the most important factors influencing the disease were age, sex, and patient history of smoking and lipid abnormality.     

Estimation and Simulation for the M-Wright Function

In this article, a structural form of an M-Wright distributed random variable is derived. The mixture representation then led to a random number generation algorithm. A formal parameter estimation procedure is also proposed. This procedure is needed to make the M-Wright function usable in practice. The asymptotic normality of the estimator is established as well. The estimator and the random number generation algorithm are then tested using synthetic data.     

Maximum likelihood estimation of the parameters of the bivariate binomial distribution

We consider the problem of maximum likelihood estimation of the parameters of the bxvariate binomial distribution, In the statistical literature, this problem is solved when the observed sample is available in the form of a 2x2 contingency table, that is, with all four cell fre quencies given,, The present paper provides a solution for this problem when only the marginal totals of the 2x2 table are observed, which is the natural set-up in a bivariate sampling situation.. Thus, based on a sample [(X_i,Y_i:), i = 1, …, k] from a bivariate binomial population, we derive maximum likelihood (ML) estimators for the two marginal parameters p₁,p₂: and the covariance parameter p₁₁: It. turns out that the ML estimators for P₁: and P₂: are expressed explicitly in terms of the sample values, whereas the ML estimator for p₁₁: can only be obtained numerically by iterative methods Two nu merical illustrations are also presented     

On the estimation of the mean vector of a multivariate normal distribution under symmetry

The problem of estimation of the mean vector of a multivariate normal distribution with unknown covariance matrix, under uncertain prior information (UPI) that the component mean vectors are equal, is considered. The shrinkage preliminary test maximum likelihood estimator (SPTMLE) for the parameter vector is proposed. The risk and covariance matrix of the proposed estimato are derived and parameter range in which SPTMLE dominates the usual preliminary test maximum likelihood estimator (PTMLE) is investigated. It is shown that the proposed estimator provides a wider range than the usual premilinary test estimator in which it dominates the classical estimator. Further, the SPTMLE has more appropriate size for the preliminary test than the PTMLE.     

Which Factor has More Impact? An Examination of the Effects of Income Level, Perceived Neighborhood Disorder, and Crime on Community Care and Vigilance Among Low-Income African American Residents

This study investigated predictors of community care and vigilance among 70 African American residents living in high-crime, low-income neighborhoods. A stratified random sampling procedure was employed to select residents who completed a 20-item questionnaire assessing their sense of community care and vigilance and perceptions of perceived neighborhood physical and social disorder. We used police crime reports to assess the levels of property and violent offenses in the targeted neighborhoods. Our goal was to determine which of these variables best predicted community care and vigilance. The results of this study showed that social disorder and violent offenses negatively predicted community care and vigilance. Interestingly, the results also indicated that residents who reported the lowest income expressed the highest levels of community care and vigilance. Implications for community practice are discussed.