MATRIKS KOVARIANSI DALAM REGRESI NONPARAMETRIK MULTIRESPON PADA KASUS KORELASI SAMA DAN KORELASI TIDAK SAMA - Budi Lestari; I Nyoman Budiantara; Sony Sunaryo; Muhammad Mashuri (Jurnal Ilmiah Matematika dan Pendidikan Matematika, 2012)
In the real cases, we are frequently faced the problem in which two or more dependent variables are observed at several values of the independent variables, such as at multiple time points. Multi-response nonparametric regression model, especially smoothing spline model, provides powerful tools to model the function which represents association of among the variables. The problem is how to estimate nonparametric regression curve of the multi-response nonparametric regression model. The nonparametric regression curve can be estimated using spline estimator approach, that is by carrying out penalized weighted least-squares optimation. Therefore, we need a covariance matrix which will be used as a weight of the optimation. In this paper, we determine the construction of covariance matrix for both equal and unequal of correlations cases. The results show that the covariance matrices have quite similar construction of diagonal elements but the elements outside the diagonal have very different construction that depend on the construction of the Jordan matrix.