Confidence Intervals for Curve of Biresponse Truncated Spline Nonparametric Regression Mardiyah Muhgni*, I Nyoman Budiantara, Vita Ratnasari
Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya.
Abstract
One of the objectives of statistical analysis is to obtain point estimates and interval estimates for parameters or regression curves. Confidence intervals are part of inferential statistics along with point estimates. Confidence intervals have the advantage of a smaller error probability value, where the regression curve confidence interval is able to describe the upper and lower limits of the resulting regression curve. The statistical method used to determine the relationship between response variables and predictor variables whose function form is unknown is the nonparametric regression approach which is only assumed to be smooth in the sense that it is contained in a certain function space. Spline nonparametric regression is one of the most widely used methods in nonparametric regression. The ability of spline regression is that it can estimate data behavior that tends to be different at different intervals and has high flexibility. This ability to estimate data can be done with a function that has been attached to the estimator and a part called the knot point in nonparametric regression. The optimum knot point selection is done by looking at the minimum Generalized Cross Validation (GCV) value. This study will involve two response variables and several predictor variables called biresponse regression which aims to get a better model than single response modeling because the regression model not only considers the effect of predictors on the response, but also the relationship between responses. This study aims to obtain confidence intervals for birespon truncated spline nonparametric regression curves with known population variance and unknown population variance.
