Simple and efficient improvements of multivariate local linear regression

Envelope Models for Parsimonious and Efficient Multivariate Linear Regression

We propose a new parsimonious version of the classical multivariate normal linear model, yielding a maximum likelihood estimator (MLE) that is asymptotically less variable than the MLE based on the usual model. Our approach is based on the construction of a link between the mean function and the covariance matrix, using the minimal reducing subspace of the latter that accommodates the former. T...

Challenging the curse of dimensionality in multivariate local linear regression

Local polynomial fitting for univariate data has been widely studied and discussed, but up until now the multivariate equivalent has often been deemed impractical, due to the so-called curse of dimensionality. Here, rather than discounting it completely, we use density as a threshold to determine where over a data range reliable multivariate smoothing is possible, whilst accepting that in large...

Efficient Bayesian Multivariate Surface Regression

Efficient Multivariate Quantile Regression Estimation

We propose an efficient semiparametric estimator for the multivariate linear quantile regression model in which the conditional joint distribution of errors given regressors is unknown. The procedure can be used to estimate multiple conditional quantiles of the same regression relationship. The proposed estimator is asymptotically as efficient as if the conditional distribution were known. Simu...

Correlation and simple linear regression.

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, s...