Regressão polinomial local bivariada: estimação e aplicações. - Isabel Cristina Gomes (2010)
The local polynomial regression is a nonparametric approach toregression analysis, relevant when the relation among the responseand the predictors cannot be well established by a parametricmodel. The surface estimation is done at each point by applicationof linear regression function to determined amount of observationsin neighborhood of the point. Therefore, it is necessary to determinethe size of the neighborhood around the point in which theregression function will be estimated (bandwidth), and the functionthat sets weights to the neighbors observations (kernel). The purposeof this dissertation is to estimate a nonparametric regressionmodel for cases which we have one response and two predictors,all continuous, to points at interior of support of the joint densityfunction of predictors. In the text will be discussed ways to obtainthe global bandwidth (the same to all points) and local (is dierentto each point), and will be presented purposes of estimationto conditional variance, Hessian matrix and determination coe-cient. The simulation results shows that the t by global diagonalbandwidth produces better results, with lower errors and betterapproximation to theoretical surface, when compared to constantsbandwidths global and local. The determination coecient obtainedin applications to real data in nonparametric t is upperthan the parametric model, making better the explanation of thevariability of response and allowing indentify the points where theadjust was reasonable.