Parametric empirical Bayes shrinkage (Morris 1983)

Normal-normal shrinkage that estimates the prior mean and shrinks toward it, not toward zero. The prior mean's profile MLE is the precision-weighted mean of the estimates; \(\tau^2\) maximises the marginal likelihood.

Usage

morie_empirical_bayes(estimates, standard_errors)

Arguments

estimates

point estimates \(\hat\theta_k\).

standard_errors

their standard errors.

Value

list with shrunk_estimates, tau2, shrinkage_factors, grand_mean, k.

References

Morris, C. N. (1983). Parametric empirical Bayes inference: theory and applications. Journal of the American Statistical Association, 78(381), 47-55.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_empirical_bayes(V, V)
#> $shrunk_estimates
#> [1] 1.779362 1.779400 1.779403 1.779403 1.779403 1.779402 1.779402 1.779401
#> 
#> $tau2
#> [1] 4.54021e-05
#> 
#> $shrinkage_factors
#> [1] 0.9999546 0.9999886 0.9999950 0.9999972 0.9999982 0.9999987 0.9999991
#> [8] 0.9999993
#> 
#> $grand_mean
#> [1] 1.779397
#> 
#> $k
#> [1] 8
#>