Approximations for Prediction Error Variances

Prediction error variances for interbreed genetic evaluations.

A table for adjusting expected progeny differences (EPD) to a base year and breed basis depends on analyses of records of progeny of bulls of different breeds in a common environment and requires that those reference bulls also have other progeny to provide within-breed EPD. Currently, the germ plasm evaluation project at the Meat Animal Research Center (MARC) provides such a common environment...

Prediction Error of Small Area Predictors Shrinking Both Means and Variances

The article considers a new approach for small area estimation based on a joint modelling of mean and variances. Model parameters are estimated via expectation–maximization algorithm. The conditional mean squared error is used to evaluate the prediction error. Analytical expressions are obtained for the conditional mean squared error and its estimator. Our approximations are second-order correc...

Exponential Models: Approximations for Probabilities

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...

Error estimates for approximations from control nets

Lp error estimates for projection approximations

We provide an error estimate for the local mean projection approximation in L p([0, τ∗]) for p ∈ [1,+∞[, in terms of the regularity of the underlying grid, and we apply it to the corresponding projection approximation of weakly singular Fredholm integral equations of the second kind. © 2004 Elsevier Ltd. All rights reserved.