ESTIMASI MODEL LINEAR PARSIAL DENGAN PENDEKATAN KUADRAT TERKECIL DAN SIMULASINYA MENGGUNAKAN PROGRAM S-PLUS

Abstract

Partial linear model (model semiparametric) is a new approach in the regression
models between the two regression models are already popular parametric regression and
nonparametric regression. Partial linear model is a model that includes both the
combination of parametric components and nonparametric components. This study uses
literature by studying semiparametric regression analysis, finding and determining the
estimated parameters. Partial linear model has the form: : 𝑌𝑖 = 𝑿𝑖
𝑇𝜷 + g(𝑻𝑖)+ 𝜖𝑖 with
𝑿𝑖 and 𝑻𝑖 are explanatory variables, g (.) is an unknown function (smooth function), β is
the parameter of unknown function, 𝑌𝑖 response variable and 𝜖𝑖 is an error with the mean
(𝜖𝑖) = 0 and variance 𝜎𝑖
2 = 𝐸(𝜖𝑖
2).
The results showed that the partial linear model parameter estimation can
be performed using the least squares method in which part of the linear model using
nonparametric kernel approach and subsequent estimation results are substituted into the
partial linear model to estimate the parametric part of the model by using the linear least
squares method. Results obtained partial linear estimation is 𝑔 𝑛 (t) = 𝑊𝑛𝑖
𝑛𝑖
=1 (Yi - 𝑿𝑖
𝑇 +
𝜷
𝑛 ) dengan 𝜷
𝑛 = (𝒙 𝑻 𝒚 )−𝟏 𝒙 𝑻 𝒚 .
Based on the simulation results obtained output values and graphs are for the
parametric, graphical display and qqline qqnorm estimator beta (β) is (𝛽) yaitu 𝛽0, 𝛽1
and 𝛽2 can be seen clearly, where if n is greater (n → ∞) and the greater replication
iteration 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 a
normal kernel function values approaching g (T). So it can be concluded briefly that if the
larger n (n → ∞), the estimator of the nonparametric part closer to the partial linear
model g (T).