Shrinkage Estimators of Intercept Parameters of Two Simple Regression Models with Suspected Equal Slopes

Estimators of the intercept parameter of a simple linear regression model involves the slope estimator. In this article, we consider the estimation of the intercept parameters of two linear regression models with normal errors, when it is a priori suspected that the two regression lines are parallel, but in doubt. We also introduce a coefficient of distrust as a measure of degree of lack of trust on the uncertain prior information regarding the equality of two slopes. Three different estimators of the intercept parameters are defined by using the sample data, the non sample uncertain prior information, an appropriate test statistic, and the coefficient of distrust. The relative performances of the unrestricted, shrinkage restricted and shrinkage preliminary test estimators are investigated based on the analyses of the bias and risk functions under quadratic loss. If the prior information is precise and the coefficient of distrust is small, the shrinkage preliminary test estimator overperforms the other estimators. An example based on a medical study is used to illustrate the method.     

Estimation of Slope for Linear Regression Model with Uncertain Prior Information and Student-t Error

This article considers estimation of the slope parameter of the linear regression model with Student-t errors in the presence of uncertain prior information on the value of the unknown slope. Incorporating uncertain non sample prior information with the sample data the unrestricted, restricted, preliminary test, and shrinkage estimators are defined. The performances of the estimators are compared based on the criteria of unbiasedness and mean squared errors. Both analytical and graphical methods are explored. Although none of the estimators is uniformly superior to the others, if the non sample information is close to its true value, the shrinkage estimator over performs the rest of the estimators.     

On Estimating the Finite Population Mean Using Two Auxiliary Variables in Two Phase Sampling in the Presence of Non Response

This article considers the problem of estimating the population mean using information on two auxiliary variables in the presence of non response under two-phase sampling. Some improved ratio-in-regression type estimators have been proposed in four different situations of non response along with their properties under large sample approximation. Efficiency comparisons of the proposed estimators with the usual unbiased estimator by Hansen and Hurwitz (1946 Hansen , M. H. , Hurwitz , W. N. ( 1946 ). The problem of non response in sample surveys . J. Amer. Statist. Assoc. 41 : 517 – 529 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), conventional ratio and regression estimators using single auxiliary variable and Singh and Kumar (2010b Singh , H. P. , Kumar , S. ( 2010b ). Improved estimation of population mean under double sampling with sub-sampling the non-respondents . J. Statist. Plann. Infer. 140 ( 9 ): 2536 – 2550 .[Crossref], [Web of Science ®] , [Google Scholar]) estimators using two auxiliary variables have been made. Finally, these theoretical findings are illustrated by a numerical example.     

Shrinkage Estimation Under Multivariate Elliptic Models

The estimation of the location vector of a p-variate elliptically contoured distribution (ECD) is considered using independent random samples from two multivariate elliptically contoured populations when it is apriori suspected that the location vectors of the two populations are equal. For the setting where the covariance structure of the populations is the same, we define the maximum likelihood, Stein-type shrinkage and positive-rule shrinkage estimators. The exact expressions for the bias and quadratic risk functions of the estimators are derived. The comparison of the quadratic risk functions reveals the dominance of the Stein-type estimators if p ≥ 3. A graphical illustration of the risk functions under a “typical” member of the elliptically contoured family of distributions is provided to confirm the analytical results.     

Building Financial Knowledge Is Not Enough: Financial Self-Efficacy as a Mediator in the Financial Capability of Low-Income Families

ABSTRACT

Policymakers in many countries have taken an interest in population-level financial capability. Limited empirical work has examined how constructs that makeup financial capability relate and how they function for individuals with low incomes. Using a national sample of low-income Canadians, we investigate relationships between financial knowledge, financial self-efficacy, and savings outcomes. Overall, we find that financial self-efficacy fully mediated the relationship between objective financial knowledge and postsecondary-education saving. The association between objective financial knowledge and retirement saving and emergency saving passed through financial self-efficacy. Efforts to promote financial capability need to focus on more than objective financial knowledge.     

New Styles of Community Building and Philanthropy by Arab-American Muslims

Among Arab-American Muslims, secular ethnic and humanitarian giving, focused on ‘results’ and ‘measurable impact,’ is displacing religiously inspired giving, that is driven by ‘charity’ and ‘love of mankind.’ This trend is supported by evidence of the way donors position themselves and philanthropic organizations appeal to their donor base. The case is supported by qualitative data drawn from interviews with key informants and from trend data on giving. I propose a new model of giving based on identity and giving, using Grounded Theory methods. This model challenges our understanding about the connection between community and philanthropy and proposes that philanthropy can create ‘community.’     

Wald's approximations to the average run length in cusum procedures

Wald's approximation to the ARL(average run length in cusum) (cumulative sum) procedures are given for an exponential family of densities. From these approximations it is shown that Page's (1954) cusum procedure is (in a sense) identical with a cusum procedure defined in terms of likelihood ratios. Moreover, these approximations are improved by estimating the excess over the boundary and their closeness is examined by numerical comparisons with some exact results. Some examples are also given.     

Sri Lanka: current status of family planning

In Sri Lanka the family planning program is closely related to socioeconomic and cultural variables. The expectation is that in the near future family planning will be included as a component of a network of social services. The official program is a response to the economic necessities and welfare demands of individuals and families. The method of family planning most frequently requested is female sterilization, and no attempts are being made to direct people to other methods. 12 United Nations Fund for Population Activities assisted projects have provided the framework and basis for the institutional coverage of family planning activities in Sri Lanka. However, the experience of these projects revealed a lack of facilities, shortage of personnel and management inadequacies, all related to the delivery of family planning services. The following steps are suggested as a means of overcoming the current problems and expanding the program: 1) establish a pattern of interacting relationship between the mass media, community health education and the available services; 2) provide an operational approach to program management, monitoring and periodic reviews of the program; 3) involve the private sector health facilities; and 4) incur additional capital cost to increase the capacity for delivery of better health facilities and personnel.