Confidence Interval for Curve of Spline Truncated Nonparametric Regression for Longitudinal Data
Hasri Rahmawati*, I Nyoman Budiantara, Jerry Dwi Trijoyo Purnomo

Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember

Abstract

Regression is one of the analytical methods used to determine the pattern of relationship between response variables and predictor variables. One of the main objectives of regression analysis is to obtain point estimates and confidence intervals for parameters or regression curves. The confidence interval of the regression curve is able to describe the upper limit and lower limit of the resulting regression curve. When the data used is not known the shape of the regression curve pattern, a nonparametric regression approach is used. Truncated splines are able to handle data that have changing behavior at certain sub-intervals and tend to find their own data estimates wherever the data pattern moves, truncated splines provide smoother and more flexible curves that are limited within an interval. Longitudinal data can provide an interpretation of the model over time because it is carried out at a certain period of time, thus the conclusions obtained will be more complete. The purpose of this study is to obtain confidence intervals for nonparametric regression curves on longitudinal data. For parameter estimation using Weighted Least Square (WLS) optimization, in constructing the shortest interval for the spline truncated nonparametric regression curve using pivotal quantity for the case of known population variance and unknown population variance. Confidence intervals provide information about the uncertainty in the estimation of regression curves, so the results of this study can be useful in decision making related to longitudinal data and related regression analysis.

Keywords: Nonparametric Regression- Confidence Interval- Longitudinal Data.

Topic: Mathematics and Statistics