Suppose the random vector (X,Y ) satisfies the regression model Y = m(X) + σ(X)ε, where m(·) = E(Y |·) belongs to some parametric class {mθ(·) : θ ∈ Θ} of regression functions, σ2(·) = Var(Y |·) is unknown, and ε is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new estimation procedure for the true, unknown parameter vector ...

Different predictors and their approximators in nonlinear prediction regression models are studied. The minimal value of the mean squared error (MSE) is derived. Some approximate formulae for the MSE of ordinary and weighted least squares predictors are given.

The task of dimensionality reduction for regression (DRR) is to find a low dimensional representation z ∈ R of the input covariates x ∈ R, with q p, for regressing the output y ∈ R. DRR can be beneficial for visualization of high dimensional data, efficient regressor design with a reduced input dimension, but also when eliminating noise in data x through uncovering the essential information z f...

Diierent predictors and their approximators in nonlinear prediction regression models are studied. The minimal value of the mean squared error (MSE) is derived. Some approximate formulae for the MSE of ordinary and weighted least squares predictors are given.

This document presents a series of examples of the use of multi-layer, non-linear neural networks. An overview of the mathematical derivation of the backpropagation algorithm is presented along with detailed samples of it programming in the R language. Several examples of different input and output dimensionality are presented to address issues of network complexity, training errors and over-fi...