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  • Statistics In Transition

 

Research paper

CLASSIFICATION PROBLEMS BASED ON REGRESSION MODELS FOR MULTI-DIMENSIONAL FUNCTIONAL DATA

Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. We use multivariate functional regression techniques for the classification of multivariate functional data. The approaches discussed are illustrated with an application to two real data sets.

Tomasz Górecki, Mirosław Krzyśko, Waldemar Wołyński

Statistics in Transition New Series , ISSUE 1, 97–110

Article

AN EXTENSION OF THE CLASSICAL DISTANCE CORRELATION COEFFICIENT FOR MULTIVARIATE FUNCTIONAL DATA WITH APPLICATIONS

The relationship between two sets of real variables defined for the same individuals can be evaluated by a few different correlation coefficients. For the functional data we have one important tool: canonical correlations. It is not immediately straightforward to extend other similar measures to the context of functional data analysis. In this work we show how to use the distance correlation coefficient for a multivariate functional case. The approaches discussed are illustrated with an

Tomasz Górecki, Mirosław Krzy´sko, Waldemar Ratajczak, Waldemar Woły´nski

Statistics in Transition New Series , ISSUE 3, 449–466

Article

VARIABLE SELECTION IN MULTIVARIATE FUNCTIONAL DATA CLASSIFICATION

A new variable selection method is considered in the setting of classification with multivariate functional data (Ramsay and Silverman (2005)). The variable selection is a dimensionality reduction method which leads to replace the whole vector process, with a low-dimensional vector still giving a comparable classification error. Various classifiers appropriate for functional data are used. The proposed variable selection method is based on functional distance covariance (dCov) given by Sz

Tomasz Górecki, Mirosław Krzyśko, Waldemar Wołyński

Statistics in Transition New Series , ISSUE 2, 123–138

Article

AN APPLICATION OF FUNCTIONAL DATA ANALYSIS TO LOCAL DAMAGE DETECTION

identify the frequency bands where the impulsivity is most marked (the so-called informative frequency bands or IFB). We propose the functional approach known in modern time series analysis to overcome these difficulties. We will process data sets as collections of random functions to apply techniques of the functional data analysis. As a result, we will be able to represent massive data sets through few real-valued functions and corresponding parameters, which are the eigenfunctions and eigen-values

Jacek Leśkow, Maria Skupień

Statistics in Transition New Series , ISSUE 1, 131–151

Article

Measuring and Testing Mutual Dependence of Multivariate Functional Data

This paper considers new measures of mutual dependence between multiple multivariate random processes representing multidimensional functional data. In the case of two processes, the extension of functional distance correlation is used by selecting appropriate weight function in the weighted distance between characteristic functions of joint and marginal distributions. For multiple random processes, two measures are sums of squared measures for pairwise dependence. The dependence measures are

Mirosław Krzyśko, Łukasz Smaga

Statistics in Transition New Series , ISSUE 3, 21–37

Research Article

AN APPLICATION OF FUNCTIONAL MULTIVARIATE REGRESSION MODEL TO MULTICLASS CLASSIFICATION

In this paper, the scale response functional multivariate regression model is considered. By using the basis functions representation of functional predictors and regression coefficients, this model is rewritten as a multivariate regression model. This representation of the functional multivariate regression model is used for multiclass classification for multivariate functional data. Computational experiments performed on real labelled data sets demonstrate the effectiveness of the proposed

Mirosław Krzyśko, Łukasz Smaga

Statistics in Transition New Series , ISSUE 3, 433–442

Article

The Achievements of Students at the Stages of Education from the Second to Fourth Using Functional Principal Component Analysis

research covers the average exam results received on graduation from the second, third and fourth stage of education. Functional principal component analysis, which is based on functional data, will be applied in the study. This method allows an analysis of dynamic data.

Mirosława Sztemberg-Lewandowska

Statistics in Transition New Series , ISSUE 1, 139–150

Article

GENERALIZED EXPONENTIAL SMOOTHING IN PREDICTION OF HIERARCHICAL TIME SERIES

Daniel Kosiorowski, Dominik Mielczarek, Jerzy P. Rydlewski, Małgorzata Snarska

Statistics in Transition New Series , ISSUE 2, 331–350

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