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Optimal design problems for random coefficient regression model with heteroscedastic errors are considered.

The maximum likelihood estimation in a regression model with heteroscedastic errors is considered.

'A × E-A × E-A × C het' is the ACE A × E-A × C model with heteroscedastic residual variances.

According to a likelihood ratio test, this model fitted better than a model with heteroscedastic residuals [χ(4) = 6.158], this was confirmed by the AIC and BIC (see Table  7).

For a fixed-effects analysis, this network can be written in matrix notation as the following general linear model with heteroscedastic sampling variances: (1) Y = X θ net + ∈; Y is a vector of observed treatment effects of all S studies, e.g. log odds ratios for a binary outcome and the design matrix X with T columns contains the structure of the network at the study level.

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In "Building a prediction model for BUX stock time series and results" section, the resulting statistical models with heteroscedastic noise, the neural networks, and SVMs are applied on 1-day prediction of the BUX stocks index.

We conclude that for most applications of introgression populations, where few genes are assumed to control the trait, a BLUP analysis is expected to be inferior to models with heteroscedastic marker variances, such as an RMLV analysis.

To model Gaussian process with heteroscedastic noise, this paper introduces a weighting strategy into the standard GPR algorithm, and proposes three weighted GPR algorithms: the clustered GPR (C-GPR) algorithm, the partial weighted GPR (PW-GPR) algorithm and the weighted GPR (W-GPR) algorithm.

We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data.

However, GWP approaches with heteroscedastic marker variances model better the genetic basis of traits when the number of markers is substantially greater than number of genes underlying the trait.

Moreover, a residual error model with one homoscedastic (additive) and one heteroscedastic (proportional) component would enable different types of errors for different parameters.

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