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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/4879 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/4879 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/4879 archive 351 disk0/00/00/67/64 2016-01-15 02:14:53 2021-08-27 17:17:59 2016-01-15 02:14:53 monograph show 2 Ermoliev Y.M. 1445 Keyzer M.A. AL1626 Norkin V.I. AL1055 pub iis_ecn iis_luc iis_mod prog_luc prog_rms The paper presents a risk minimization approach to estimate a flexible form that meets a priori restrictions on slope and curvature by means of constraints on both the estimated parameters and the function values. The resulting constrained risk minimization combines parametric and nonparametric estimation and contains integrals and implicit constraints. Within econometrics, simulation has become a common tool to solve problems of this kind. However, it appears that in our case, the simulation approach only applies when the model is linear in parameters, has simple constraints on parameters and a quadratic risk function. To deal with other cases, we use a stochastic optimization technique known as the stochastic quasi-gradient method for stationary and nonstationary problems with Cesaro averaging. This method is also applicable to an expanding series of random observations, and produces asymptotically (weakly) convergent estimates. 2002-03 published IR-02-021 IR-02-021 338 2645 2245 public interim_report IIASA, Laxenburg, Austria 32 FALSE info:eu-repo/semantics/book