Kernel Estimation Of β In Nonparametric Regression Models

In nonparametric statistical theory, the nonparametric regression model that isy_i=m(x_i)+ε_i, i=1,…n with the given sample of observations are X_i, i=1,…nindependent and identically distributed and the response Y, whereε_i(i=1,…, n) is therandom errors. In the view of this, our interest is to find kernel estimators of m(x) in orderto have a better simulation model. In this paper, we provide the nonparametric models suchthat Y=F(β^τX)+ε, and F is an unfixed Borel function with onlyβisunknown. Weapply the kernel methods of regression functions and conditional density functions to obtain aseries ofβas the estimators ofβ. In the method of regression function, we show twomodels with selectedχare discrete and continuous and discuss these reasonedly . InChapter 3, we simulate the two nonparametric regression models of (2.6) and (2.7) withχare continuous. Then using Monte Carlo Analysis method, we can get the optimal choiceof the unknown parametricβthat isβ_opt and the standard error t. Examples illustrate themodels and will show these estimations are effective. Finally, we simply show the effect ofthe window-width choosing on estimations of unknown parameterβ.