TY - JOUR
AU - Shiller,Robert J.
TI - Smoothness Priors and Nonlinear Regression
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 25
PY - 1982
Y2 - August 1982
DO - 10.3386/t0025
UR - http://www.nber.org/papers/t0025
L1 - http://www.nber.org/papers/t0025.pdf
N1 - Author contact info:
Robert J. Shiller
Yale University, Cowles Foundation
Box 208281
30 Hillhouse Avenue
New Haven, CT 06520-8281
Tel: 203/432-3708
Fax: 203/432-6167
E-Mail: robert.shiller@yale.edu
AB - In applications, the linear multiple regression model is often modified to allow for nonlinearity in an independent variable. It is argued here that in practice it may often be desirable to specify a Bayesian prior that the unknown functional form is "simple" or "uncomplicated" rather than to parametize the nonlinearity. "Discrete smoothness priors" and "continuous smoothness priors" are defined and it is shown how posterior mean estimates can easily be derived using ordinary multiple linear regression modified with dummy variables and dummy observations. Relationships with spline and polynomial interpolation are pointed out. Illustrative examples of cost function estimation are provided.
ER -