Approximation of functional spatial regression models using bivariate splines
Seminar Room 1, Newton Institute
We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, with bounded or normal noise. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function with or without a penalization term. Under the assumptions that the regressors in the sample are bounded and span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an aplication to ozone forecasting over the US that illustrates the predictive skills of the method.
This is joint work with Ming-Jun Lai.
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