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Showing 4 results for Functional Data
, , ,
Volume 24, Issue 2 (3-2020)
Abstract
A sequence of functions (curves) collected over time is called a functional time series. Functional time series analysis is one of the popular research areas in which statistics from such data are frequently observed. The main purpose of the functional time series is to predict and describe random mechanisms that resulted in generating the data. To do so, it is needed to decompose functional time series into trend, periodic, and error components. However, we need to identify and recognize these components beforehand. Hence, in this study, a non-parametric method is presented for detecting and testing the existence of a process in a functional time series using record functions. Then, we implement and use this method for investigating the application of this method in a real functional time series. The effectiveness of this method for determining the trend in a set of real data on fertility rates in Australia has been investigated.
Mohammadreza Faridrohani, Behdad Mostafaiy, Seyyed Mohammad Ebrahim Hosseininasab,
Volume 25, Issue 2 (3-2021)
Abstract
Recently with science and technology development, data with functional nature are easy to collect. Hence, statistical analysis of such data is of great importance. Similar to multivariate analysis, linear combinations of random variables have a key role in functional analysis. The role of Theory of Reproducing Kernel Hilbert Spaces is very important in this content. In this paper we study a general concept of Fisher’s linear discriminant analysis that extends the classical multivariate method to the case functional data. A bijective map is used to link a second order process to the reproducing kernel Hilbert space, generated by its within class covariance kernel. Finally a real data set related to Iranian weather data collected in 2008 is also treated.
Mr Arta Roohi, Ms Fatemeh Jahadi, Dr Mahdi Roozbeh,
Volume 27, Issue 1 (3-2023)
Abstract
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.
Dr Mahdi Roozbeh, , ,
Volume 27, Issue 2 (3-2023)
Abstract
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.
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