P-spline estimation of functional classification methods for improving the quality in the food industry Articles uri icon

publication date

  • November 2015

start page

  • 2513

end page

  • 2534

issue

  • 10

volume

  • 44

international standard serial number (ISSN)

  • 0361-0918

electronic international standard serial number (EISSN)

  • 1532-4141

abstract

  • The aim of this article is to improve the quality of cookies production by classifying them as good or bad from the curves of resistance of dough observed during the kneading process. As the predictor variable is functional, functional classification methodologies such as functional logit regression and functional discriminant analysis are considered. A P-spline approximation of the sample curves is proposed to improve the classification ability of these models and to suitably estimate the relationship between the quality of cookies and the resistance of dough. Inference results on the functional parameters and related odds ratios are obtained using the asymptotic normality of the maximum likelihood estimators under the classical regularity conditions. Finally, the classification results are compared with alternative functional data analysis approaches such as componentwise classification on the logit regression model.

keywords

  • functional linear discriminant analysis; functional logit regression; functional partial least squares; functional principal components analysis; p-splines