From Artificial Intelligence: A modern approach: Most nonparametric models have the advantage that it is easy to do leave-one-out crossvalidation without having to recompute everything. With a k-nearest-neighbors model, for instance, when given a test example (x, y) we retrieve the k nearest neighbors once, compute the per-example loss L(y, h(x)) from them, and record … Read more
How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)? This question has been asked before but the answer just states it follows easliy. More precisely, we consider $y_{i}=f(x_{i})+epsilon_{i}$ with $epsilon_{i}$ being independent with standard deviation $sigma.$ … Read more
How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)? This question has been asked before but the answer just states it follows easliy. More precisely, we consider $y_{i}=f(x_{i})+epsilon_{i}$ with $epsilon_{i}$ being independent with standard deviation $sigma.$ … Read more
I use the library method loess of the R programming language for non parametric data fitting. The dataset is two-dimensional. I have not found any proper documentation of the method parameter weights. My data points are normally distributed random variables, and I also have an estimate of their respective standard deviations. I am wondering whether … Read more