Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation coefficient is effective for capturing linear dependence, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their rela...

The term “empirical predictor” refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML ...

In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is a striking observation that the ensemble mean often out-performs at least half of the ensemble members in mean squared error (measured with respect to observations). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often out-performs all...

The usual definition of R (variance of the predicted values divided by the variance of the data) has a problem for Bayesian fits, as the numerator can be larger than the denominator. We propose an alternative definition similar to one that has appeared in the survival analysis literature: the variance of the predicted values divided by the variance of predicted values plus the variance of the e...

In order to obtain better coverage of the population of interest and cost less, a number of surveys employ dual frame structure, in which independent samples are taken from two overlapping sampling frames. This research considers chi-squared tests in dual frame surveys when categorical data is encountered. We extend generalized Wald’s (1943) test, Rao-Scott first-order and second-order correcte...

This paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three applications of minimum MSE shaping are considered, specifically matched filter detection, multiuser ...

We recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in many algorithmic frameworks routinely used in nonlinear programming. Numerical examples performed with the sequential quadratic programming method illustrate those reasons.

A common derivation of principal component analysis (PCA) is based on the minimization of the squared-error between centered data and linear model, corresponding to the reconstruction error. In fact, minimizing the squared-error leads to principal subspace analysis where scaled and rotated principal axes of a set of observed data, are estimated. In this paper, we introduce and investigate an al...