title: Oracle estimation of parametric models under boundary constraints.
abstract: In many classical estimation problems, the parameter space has a boundary. In most cases, the standard asymptotic properties of the estimator do not hold when some of the underlying true parameters lie on the boundary. However, without knowledge of the true parameter values, confidence intervals constructed assuming that the parameters lie in the interior are generally over-conservative. A penalized estimation method is proposed in this article to address this issue. An adaptive lasso procedure is employed to shrink the parameters to the boundary, yielding oracle inference which adapt to whether or not the true parameters are on the boundary. When the true parameters are on the boundary, the inference is equivalent to that which would be achieved with a priori knowledge of the boundary, while if the converse is true, the inference is equivalent to that which is obtained in the interior of the parameter space. The method is demonstrated under two practical scenarios, namely the frailty survival model and linear regression with order-restricted parameters. Simulation studies and real data analyses show that the method performs well with realistic sample sizes and exhibits certain advantages over standard methods.
authors.affiliation: Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
authors.forename: Kin Yau
authors.initials: KY
authors.lastname: Wong
authors.affiliation: Department of Statistics, University of Haifa, Haifa 31905, Israel.
authors.forename: Yair
authors.initials: Y
authors.lastname: Goldberg
authors.affiliation: Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
authors.forename: Jason P
authors.initials: JP
authors.lastname: Fine
mesh_terms: D003198:Computer Simulation; D016208:Databases, Factual; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008175:Lung Neoplasms / Q000401:mortality; D015233:Models, Statistical; D012044:Regression Analysis; D018401:Sample Size; D016019:Survival Analysis; D014481:United States; D014493:United States Department of Veterans Affairs
keywords: Constrained parameter space; Maximum likelihood; Order restrictions; Penalization; Selection consistency