Nonparametric function estimation subject to monotonicity, convexity and other shape constraints

作者：Shively Thomas S^*; Walker Stephen G; Damien Paul

来源：Journal of Econometrics, 2011, 161(2): 166-181.

DOI：10.1016/j.jeconom.2010.12.001

• Fixed-knot splines
• Free-knot splines
• Log-concave likelihood functions
• MCMC sampling algorithm
• Small sample properties

This paper uses free-knot and fixed-knot regression splines in a Bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log-concave likelihood functions. The shape constraints we consider include monotonicity, convexity and functions with a single minimum. A computationally efficient MCMC sampling algorithm is developed that converges faster than previous methods for non-Gaussian models. Simulation results indicate the monotonically constrained function estimates have good small sample properties relative to (i) unconstrained function estimates, and (ii) function estimates obtained from other constrained estimation methods when such methods exist. Also, asymptotic results show the methodology provides consistent estimates for a large class of smooth functions. Two detailed illustrations exemplify the ideas.

• 出版日期2011-4