Search results

1

Classification problems based on regression models for multi-dimensional functional data

100%

Górecki T., Krzyśko M., Wołyński W.

Statistics in Transition new series

|

2015

|

vol. 16

|

issue 1

97–110

EN

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.

2

An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications

100%

Górecki T., Krzyśko M., Ratajczak W., Wołyński W.

Statistics in Transition new series

|

2016

|

vol. 17

|

issue 3

449-466

EN

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 application to some socio-economic data.

3

Variable selection in multivariate functional data classification

88%

Górecki T., Krzyśko M., Wołyński W.

Statistics in Transition new series

|

2019

|

vol. 20

|

issue 2

123-138

EN

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 Székely and Rizzo (2009, 2012) and the Hilbert-Schmidt Independent Criterion (HSIC) given by Gretton et al. (2005). This method is a modification of the procedure given by Kong et al. (2015). The proposed methodology is illustrated with a real data example.

4

Ocena zróżnicowania poziomu życia mieszkańców województw w latach 2003–2013 za pomocą składowych głównych dla wielowymiarowych danych funkcjonalnych oraz analizy skupień

75%

Krzyśko M., Majka A., Wołyński W.

Przegląd Statystyczny

|

2016

|

vol. 63

|

issue 1

81-98

EN

The paper presents an estimation of life standard diversity for residents of Polish voivodships in 2003–2013. The principal component analysis was applied for multidimensional functional data and the dendrite method was used for cluster analysis. These methods made it possible to isolate relatively homogeneous groups of voivodships that had similar values of characteristics under consideration, for the whole period at issue.

PL

W artykule przedstawiono ocenę zróżnicowania poziomu życia mieszkańców województw w latach 2003–2013. Do oceny zastosowano analizę składowych głównych dla wielowymiarowych danych funkcjonalnych oraz dendrytową analizę skupień. Metody te pozwoliły na wyodrębnienie względnie jednorodnych grup województw o zbliżonym poziomie rozpatrywanych cech dla całego rozpatrywanego okresu łącznie.

5

Measuring and Testing Mutual Dependence of Multivariate Functional Data

75%

Krzyśko M., Smaga Ł.

Statistics in Transition new series

|

2020

|

vol. 21

|

issue 3

21-37

EN

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 zero if and only if the random processes are mutually independent. This property is used to construct permutation tests for mutual independence of random processes. The finite sample properties of these tests are investigated in simulation studies. The use of the tests and the results of simulation studies are illustrated with an example based on real data.

Refine search results

4 Statistics in Transition new series

1 Przegląd Statystyczny

5 Krzyśko M.

4 Wołyński W.

3 Górecki T.

1 Majka A.

1 Ratajczak W.

1 Smaga Ł.

1 2020

1 2019

2 2016

1 2015

Classification problems based on regression models for multi-dimensional functional data

An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications

Variable selection in multivariate functional data classification

Ocena zróżnicowania poziomu życia mieszkańców województw w latach 2003–2013 za pomocą składowych głównych dla wielowymiarowych danych funkcjonalnych oraz analizy skupień

Measuring and Testing Mutual Dependence of Multivariate Functional Data