Abstract
Suppose that two estimators, and
, are available for estimating an unknown parameter θ, and are known to have convergence rates n1/2 and rn = o(n1/2), respectively, based on a sample of size n. Typically, the more efficient estimator
is less robust than
, and a definitive choice cannot be easily made between them under practical circumstances. We propose a simple mixture estimator, in the form of a linear combination of
and
, which successfully reaps the benefits of both estimators. We prove that the mixture estimator possesses a kind of oracle property so that it captures the fast n1/2 convergence rate of
when conditions are favorable, and is at least rn-consistent otherwise. Applications of the mixture estimator are illustrated with examples drawn from different problem settings including orthogonal function regression, local polynomial regression, density derivative estimation, and bootstrap inferences for possibly dependent data.
Additional information
Notes on contributors
Stephen S. M. Lee
Stephen M. S. Lee is Professor (E-mail: [email protected]) and Mehdi Soleymani is Research Associate (E-mail: [email protected]), Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong.
Mehdi Soleymani
Stephen M. S. Lee is Professor (E-mail: [email protected]) and Mehdi Soleymani is Research Associate (E-mail: [email protected]), Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong.