Calculate Bootstrap distribution of Unrestricted Maximum Likelihood (ML) point-estimates for a Linear Model.
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)
form: Regression formula [y~x1+x2+...] suitable for use with lm().data: data.frame containing observations on all variables in the formula.reps: 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.seed: Either an Integer between 1 and 999 or else missing to generate a random seed.rscale: 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.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.
An output list object of class MLboot: - data: Name of the data.frame object specified as the second argument.
form: The regression formula specified as the first argument.
reps: Number of Bootstrap replications performed.
seed: Seed used to start random number generator.
n: Number of complete observations after removal of all missing values.
p: Number of beta, rmse or dmse estimates resampled.
ols.beta: OLS matrix (reps x p) of unbiased beta-coefficient estimates.
ols.rmse: OLS matrix (reps x p) of beta-coefficient relative variances.
opt.dmse: OPT matrix (reps x p) of delta shrinkage-factors with minimum MSE risk.
opt.beta: OPT matrix (reps x p) of biased beta-coefficient estimates.
opt.rmse: OPT matrix (reps x p) of beta-coefficient relative MSE risks.
Thompson JR. (1968) Some shrinkage techniques for estimating the mean. Journal of the American Statistical Association 63 , 113-122. (The "cubic" estimator.)
Obenchain RL. (2022) Efficient Generalized Ridge Regression. Open Statistics
3 : 1-18. tools:::Rd_expr_doi("10.1515/stat-2022-0108")
Obenchain RL. (2022) RXshrink_in_R.PDF RXshrink package vignette-like document, Version 2.1. http://localcontrolstatistics.org
Bob Obenchain wizbob@att.net
eff.ridge, correct.signs