Percentile Bootstrap Interval on Univariate Local Polynomial Regression Prediction

This study offers a new technique for constructing percentile bootstrap intervals to predict the regression of univariate local polynomials. Bootstrap uses resampling derived from paired and residual methods. The main objective this is perform comparative analysis between two methods by considering nominal coverage probability. Resampling nonparametric with return method, where each sample point has an equal chance being selected. principle bootstrapping original data as source diversity in contrast parametric bootstrapping, variety comes generating particular distribution. simulation results show that interval probabilities are close coverage. showed no significant difference residual. Increasing size sufficiently large gives scatterplot smoothness confidence interval. Applying smoothing parameter choice second-order polynomial smoother distribution than first-order regression. shows second-degree can capture curvature feature compared first-degree polynomial. bands made polynomials give narrower width In contrast, applying optimal parameters model provides different conclusions using based on choice. addition differences scatterplot, estimates probability also other. Selecting value method 0.93, while 0.96. 0.95, 0.945, 0.93. general, both work well estimating prediction intervals.