Resample With-Replacement from a given data.frame and recompute MSE risk-optimal estimates of Beta-Coefficients and their Relative MSE risks using MLcalcs() to compute ML point-estimates.
MLboot(form, data, reps=100, seed, rscale=1)Regression formula [y~x1+x2+...] suitable for use with lm().
data.frame containing observations on all variables in the formula.
Number of Bootstrap replications: Minimum reps = 10, Default is reps = 100. While reps = 10000 is reasonable for bivariate (p=2) linear models, even that many reps could be excessive for models with p >> 2.
Either an Integer between 1 and 999 or else missing to generate a random seed.
One of three possible choices (0, 1 or 2) for "rescaling" of variables (after being "centered") to remove all "non-essential" ill-conditioning: 0 implies no rescaling; 1 implies divide each variable by its standard error; 2 implies rescale as in option 1 but re-express answers as in option 0.
An output list object of class MLboot:
Name of the data.frame object specified as the second argument.
The regression formula specified as the first argument.
Number of Bootstrap replications performed.
Seed used to start random number generator.
Number of complete observations after removal of all missing values.
Number of beta, rmse or dmse estimates resampled.
OLS matrix (reps x p) of unbiased beta-coefficient estimates.
OLS matrix (reps x p) of beta-coefficient relative variances.
OPT matrix (reps x p) of delta shrinkage-factors with minimum MSE risk.
OPT matrix (reps x p) of biased beta-coefficient estimates.
OPT matrix (reps x p) of beta-coefficient relative MSE risks.
Ill-conditioned and/or nearly multi-collinear linear regression models are unlikely to yield reasonable ML unbiased (OLS) point-estimates. But more reasonable ML "optimally-biased" point-estimates from generalized ridge regression (GRR) typically have questionable MSE risk characteristics because they are complicated non-linear functions of the observed y-outcome vector. Thus the distribution of bootstrap resamples is of considerable interest in both theory and practice.
Thompson JR. (1968) Some shrinkage techniques for estimating the mean. Journal of the American Statistical Association 63, 113-122. (The "cubic" estimator.)
Obenchain RL. (2021) RXshrink_in_R.PDF RXshrink package vignette-like document, Version 2.0. http://localcontrolstatistics.org