Data Mining & Statistical Learning ISYE-7406 study guide

ISYE 7404 2 Introduction The objective of this assignment is to study how well three distinct local smoothing techniques (LOESS, Nadaraya-Watson (NW) kernel smoothing, and Spline Smoothing) perform on a simulated additive noise model. �� = �(�) + ��, Consuming the Mexican Hat function �(�) = (1 − �2 ) exp(−0.5�2 ), where � � [-2�, 2�]. In the additive noise model, the error terms follow a normal distribution with mean 0 and standard deviation 0.2, and are both independent and identically distributed. The assignments requires us to need to run Monte Carlo 1000 times to create sets of data. Each set should have 101 observations with added noise. Then, using these sets of data, we have to calculate empirical bias, empirical variances, and empirical mean square error (MSE). We need to generate three datasets using 1000 Monte Carlo simulations with equidistant points in [-2π, 2π] for three smoothing methods. We compare the bias, variance, and mean square error for each dataset to determine the most effective sm