The article investigates the relationship between unemployment rate and development indicators: (1) the GDP per capita in Purchasing Power Parities (PPP in current international $); and (2) the Internet penetration rate, defined as the percentage of Internet users per 100 people. For 34 countries in 2013, only two simple linear regression models based on natural logarithms of data and the Ordin...

Abbreviations 3D D three-dimensional; C D molar concentration of a drug; CBG D corticosteroid binding globulin; CoMFA D comparative molecular field analysis; CoMSIA D comparative molecular similarity indices analysis; GOLPE D generating optimal linear PLS estimations; PLS D partial least squares; PRESS D predictive residual sum of squares; RMS D root mean squares; TBG D testosterone binding glo...

This paper proposes a tractable and consistent estimator of the (possibly multi-equation) nonparametric regression model. The estimator is based on least squares over sets of functions bounded in Sobolev norm and is closely related to penalized least squares. We establish consistency and rate of convergence results as well as asymptotic normality of the (suitably standardized) sum of squared re...

Recently, Godfrey (1978), and Breusch and Pagan (1979) have independently proposed testing for heteroscedasticity based on squared least squares residuals. The squared residuals divided by the mean-squared residual are regressed on a set of regressors chosen by the investigator, and the test statistic (GBP hereafter) is one-half the explained sum of squares from this regression. The test statis...

The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

If a real polynomial f can be written as a sum of squares of real polynomials, then clearly f is nonnegative on R, and an explicit expression of f as a sum of squares is a certificate of positivity for f . This idea, and generalizations of it, underlie a large body of theoretical and computational results concerning positive polynomials and sums of squares. In this survey article, we review the...