functional regression

‎The high-dimensional data analysis using classical regression approaches is not applicable, and the consequences may need to be more accurate. This study tried to analyze such data by introducing new and powerful approaches such as support vector regression, functional regression, LASSO and ridge regression. On this subject, by investigating two high-dimensional data sets  (riboflavin and simulated data sets) using the suggested approaches, it is progressed to derive the most efficient model based on three criteria (correlation squared, mean squared error and mean absolute error percentage deviation) according to the type of data.

Functional data analysis is used to develop statistical approaches to the data sets that are functional and continuous essentially‎, ‎and because these functions belong to the spaces with infinite dimensional‎, using conventional methods in classical statistics for analyzing such data sets is challenging‎.
The most popular technique for statistical data analysis is the functional principal components approach‎, ‎which is an important tool for dimensional reduction‎. In this research, using the method of‎ functional principal component regression based on the second derivative penalty‎, ‎ridge and lasso, ‎the ‎analysis of ‎Canadian climate and spectrometric data sets ‎is proceed‎. ‎To ‎do ‎this, ‎to ‎obtain ‎the ‎optimum ‎values ‎of ‎the ‎penalized ‎parameter ‎in ‎proposed ‎methods, ‎the generalized cross validation, which is a ‎valid ‎and ‎efficient ‎criterion, ‎is ‎applied.‎

‎The most popular technique for functional data analysis is the functional principal component approach‎, ‎which is also an important tool for dimension reduction‎. ‎Support vector regression is branch of machine learning and strong tool for data analysis‎. ‎In this paper by using the method of functional principal component regression based on the second derivative penalty‎, ‎ridge and lasso and support vector regression with four kernels (linear‎, ‎polynomial‎, ‎sigmoid and radial) in spectroscopic data‎, ‎the dependent variable on the predictor variables was modeled‎. ‎According to the obtained results‎, ‎based on the proposed criteria for evaluating the goodness of fit‎, ‎support vector regression with linear kernel and error equal to $0.2$ has had the most appropriate fit to the data set‎.

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Sometimes, in practice, data are a function of another variable, which is called functional data. If the scalar response variable is categorical or discrete, and the covariates are functional, then a generalized functional linear model is used to analyze this type of data. In this paper, a truncated generalized functional linear model is studied and a maximum likelihood approach is used to estimate the model parameters. Finally, in a simulation study and two practical examples, the model and methods presented are implemented.