Abstract
Classical techniques for modeling numerical data associated to a regular grid have been widely developed in the literature. When a trigonometric model for the data is considered, it is possible to use the corresponding least squares (classical) estimators, but when the data are not observed on a regular grid, these estimators do not show appropriate properties. In this article we propose a novel way to model data that is not observed on a regular grid, and we establish a practical criterion, based on the mean squared error (MSE), to objectively decide which estimator should be used in each case: the inappropriate classical or the new unbiased estimator, which has greater variance. Jackknife and cross-validation techniques are used to follow a similar criterion in practice, when the MSE is not known. Finally, we present an application of the methodology to univariate and bivariate data.
Acknowledgments
The refereee and editor are acknowledged with thanks as their comments have improved an earlier version of the article.
Work partially funded by grant MTM2004-06231 from the Spanish Ministry of Science and Culture, and CTBPRB/2002/201 from the Generalitat Valenciana.