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Simple Penalties on Maximum-Likelihood Estimates of Genetic Parameters to Reduce Sampling Variation

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Figure 1 Probability densities (left) and correspondingfor effective prior sample sizes of(penalties (including a factor of 1/2; right) for a variablewith Beta distribution on ½0; 1� with mode of m ¼ 0:3 n ¼ 4 (–––), n ¼ 8– –), and n ¼ 16 (– - –).
Figure 2 Distribution of percent-of a value estimated from thesizes whilephenotypic values [aregenetic, partial autocorrelations,shrinking toward zero [tered circles give mean values.Numerical values on theage reduction in average loss forestimates of gene
Table 1 Selected mean and minimum values for percentage reduction in average loss for estimates of genetic (Sphenotypic (G), residual (SE), andSP) covariance matrices together with mean change in unpenalized log-likelihood from the maximum (DL) for penalties oncanonical eigenvalues (Pl) and genetic correlations, shrinking partial autocorrelations toward zero [Ppð0Þ] or phenotypic values [PpðPÞ]
Table 2 Selected mean and minimum values for percentage reduction in average loss for estimates of genetic (Sphenotypic (G), residual (SE), andSP) covariance matrices together with mean change in unpenalized log-likelihood from the maximum (DL) for penalties onboth genetic and residual partial autocorrelations, shrinking toward zero [Ppð0Þ] or phenotypic values [PpðPÞ]
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