Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established in the iid Gaussian case. Our work uses the approach that generalizes the one used in [A. Munk, Bissantz, T. Wagner, G. Freitag, On difference based variance estimation in nonparametric regression when the covariate is high dimensional, J. R. Stat. Soc. B 67 (Pa...

Hypothesis error (HE) plots, introduced in Friendly (2007), provide graphical methods to visualize hypothesis tests in multivariate linear models, by displaying hypothesis and error covariation as ellipsoids and providing visual representations of effect size and significance. These methods are implemented in the heplots for R (Fox, Friendly, and Monette 2009a) and SAS (Friendly 2006), and appl...

Western blot data are widely used in quantitative applications such as statistical testing and mathematical modelling. To ensure accurate quantitation and comparability between experiments, Western blot replicates must be normalised, but it is unclear how the available methods affect statistical properties of the data. Here we evaluate three commonly used normalisation strategies: (i) by fixed ...

As with ordinary least squares regression or logistic regression, we can consider significance tests for individual estimates, such as intercepts, slopes, and their variances, as well as whether the full model accounts for a significant amount of variance in the dependent variable. In between, there is also the possibility of determining whether of subset of predictors contribute significantly....

analysis of variance (ANOVA): one-way nested, hierarchical two-way linear model fixed, random, and mixed models factorial arrangement of treatments variance components sum of squares, mean square, expected mean square sampling fraction, fixed effects, random effects simple effects, main effects, interaction effects, additive effects analysis of covariance, covariate, concomitant variable data t...

The results on optimal designs for diallel crosses are based on standard linear model assumptions where the general combining ability effects are taken as fixed. Recently Ghosh and Das (2003) proposed a random effects model that allows one to first estimate the variance components and then obtain the variances of these estimates. In this paper we first propose an unbiased estimate of the ratio ...

the aim of the present study was the estimation of (co) variance components and genetic parameters for body weight of moghani sheep, using random regression models based on b-splines functions. the data set included 9165 body weight records from 60 to 360 days of age from 2811 moghani sheep, collected between 1994 to 2013 from jafar-abad animal research and breeding institute, ardabil province,...

This paper designs two kinds of recursive least-squares Wiener fixed-point smoothers based on an innovation approach in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white noise. The proposed fixed-point smoothers require the information of the observation matrix, the system matrix for the state variable, related with the signal, the variance o...