Partial Hypothesis Testing of Parameter in Spline Truncated Nonparametric Regression for Longitudinal Data Widya Amalia Rahma (a*), I Nyoman Budiantara (a), Ismaini Zain(a)
a) Statistika Insititut Teknologi Sepuluh Nopember
Abstract
One of the very popular methods used in statistics is regression analysis which can show patterns of relationships between the response variables and the predictor variables through the regression curve. The regression curve formed can be approached by several approaches, such as parametric, nonparametric, and semiparametric regression. In fact, the formed regression curve does not always obtain a curve with a known pattern or there is not enough past information regarding data patterns so it can be approached with nonparametric regression. The nonparametric regression model that is widely used by researchers is Spline because it has very good statistical and visual interpretations. One of the spline estimator developments in nonparametric regression is to use the basis of truncated spline functions. The truncated spline function is a spline function that is cut at a knot point. Selection of the optimal knot point on the spline estimator can use the Generalized Cross Validation (GCV) method. The application of nonparametric spline truncated regression is not only for cross-sectional data but also be applied to longitudinal data because it reduces the collinearity between predictor variables so the estimates obtained are more efficient. The truncated spline nonparametric regression method which discusses hypothesis testing is limited to simultaneous testing and cross-section data. Therefore the purpose of this study is to examine partial hypothesis testing which includes the form of the hypothesis, test statistics using the Likelihood Ratio Test (LRT) and data distribution, critical area (H0 rejection area) and decision-making on partial hypothesis testing results from splice truncated nonparametric regression on longitudinal data.
