Using the Delta method, we also derived formulas for estimating the sampling variances of the genetic parameters.
However, the complexities of these surveys render prohibitive the analytical determination of the properties of the resulting estimators and of the estimators of their sampling variances.
The covariance matrix is obtained by adding the matrix with design-based estimates of the sampling variances and covariances and the covariance matrix of the model errors.
Brese and Tatto (2012) explain in detail the correct use of the weight variables and the steps needed to correctly estimate sampling variances when analyzing TEDS-M data.
Statistical software packages that feature BRR (e.g., the IDB Analyzerm or WesVarn) have to be used to obtain correct estimates for sampling variances.
Five space time designs were compared under a first order autoregressive time series model for the spatial means, through the average and generalized sampling variances of the estimated spatial means, and through the sampling variance of the estimated linear trend.
Computer simulations indicated that the proposed method for estimating genetic parameters and their sampling variances was feasible and the reliability of the estimates was positively associated with the level of heritability of the trait.
Females from both populations preferred songs with a high proportion of the long-chirp element, and preferences appeared to have high genetic and residual variability, although the sampling variances on these parameters were high.
Similarly, Maravall (2003) derived expressions for the asymptotic variance of the sampling variances and autocorrelations of the smoothed components using classic results for linear stationary Gaussian processes (see e.g. Lomnicki and Zaremba 1959 or Anderson and Walker 1964).
In the case study the data of the first campaign of the French Soil Monitoring Network are used to estimate the spatial means of six soil variables (C, Tl, Cd, Ni, K, Mn) for aggregated soil map units of France, and to approximate their sampling variances.
With regard to the estimation accuracy of the context-level fixed-effect parameters, however, simulation studies conducted by Maas and Hox (2005) as well as Bryan and Jenkins (2016) indicate that with 63 contextual observations one can expect fairly stable estimates with negligible bias at the most, but with a marginal underestimation of their sampling variances.
