1 research outputs found
A Block Minorization--Maximization Algorithm for Heteroscedastic Regression
The computation of the maximum likelihood (ML) estimator for heteroscedastic
regression models is considered. The traditional Newton algorithms for the
problem require matrix multiplications and inversions, which are bottlenecks in
modern Big Data contexts. A new Big Data-appropriate minorization--maximization
(MM) algorithm is considered for the computation of the ML estimator. The MM
algorithm is proved to generate monotonically increasing sequences of
likelihood values and to be convergent to a stationary point of the
log-likelihood function. A distributed and parallel implementation of the MM
algorithm is presented and the MM algorithm is shown to have differing time
complexity to the Newton algorithm. Simulation studies demonstrate that the MM
algorithm improves upon the computation time of the Newton algorithm in some
practical scenarios where the number of observations is large