ESTIMASI MODEL LINEAR PARSIAL DENGAN PENDEKATAN KUADRAT TERKECIL DAN SIMULASINYA MENGGUNAKAN PROGRAM S-PLUS - Nur Salam; Dewi Sri Susanti; Dewi Anggraini (EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN, 2012)
Partial linear model (model semiparametric) is a new approach in the regressionmodels between the two regression models are already popular parametric regression andnonparametric regression. Partial linear model is a model that includes both thecombination of parametric components and nonparametric components. This study usesliterature by studying semiparametric regression analysis, finding and determining theestimated parameters. Partial linear model has the form: : ???????? = ???????????????? + g(????????)+ ???????? with???????? and ???????? are explanatory variables, g (.) is an unknown function (smooth function), β isthe parameter of unknown function, ???????? response variable and ???????? is an error with the mean(????????) = 0 and variance ????????2 = ????(????????2).The results showed that the partial linear model parameter estimation canbe performed using the least squares method in which part of the linear model usingnonparametric kernel approach and subsequent estimation results are substituted into thepartial linear model to estimate the parametric part of the model by using the linear leastsquares method. Results obtained partial linear estimation is ???? ???? (t) = ????????????????????=1 (Yi - ???????????? +???????? ) dengan ???????? = (???? ???? ???? )−???? ???? ???? ???? .Based on the simulation results obtained output values and graphs are for theparametric, graphical display and qqline qqnorm estimator beta (β) is (????) yaitu ????0, ????1and ????2 can be seen clearly, where if n is greater (n → ∞) and the greater replicationiteration r , then the points are spread around the more straight line and a straight line.This indicates the greater n and r, the beta (β) closer to the normal distribution.Nonparametric estimator simulation results in this section are taken as an example of anormal kernel function values approaching g (T). So it can be concluded briefly that if thelarger n (n → ∞), the estimator of the nonparametric part closer to the partial linearmodel g (T).