Estimation of Multivariate Smooth Functions via Convex Programs

Eunji Lim, Fanny Gonzalez


A new method for estimating an unknown, multivariate function from noisy data is proposed in the case where the unknown function is assumed to be smooth. The proposed method finds the minimizer of the smoothness of a function while imposing an upper bound on the sum of squared errors between the function and the data set. The proposed estimator is designed to be numerically sound by eliminating the dependency on any artificially plugged-in parameters that traditional methods use and by tackling the ill-conditioned numerical settings that traditional methods suffer from. Hence, it is expected to perform better than existing estimators numerically. We prove the existence of the proposed estimator and show that we can compute the proposed estimator through a convex program. Empirical studies illustrate that the proposed method is effectively applied to the problem of estimating the average payoff of a stock option that is contingent on two different stocks.

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International Journal of Statistics and Probability   ISSN 1927-7032(Print)   ISSN 1927-7040(Online)

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