Comparing two mean humidity curves using functiona t-tests: Turkey Case


Abstract


Abstract: The goal of thisstudy is to show the usefulness of functional t tests and rainbow plots as aguideline. Meteorological data like humidity is used for this aim. In thisstudy, functional t-tests are used in order to observe if humidity meanfunctions of coastal area and hinterland of Turkey are statistically different.Turkey is selected because of its variable geographical landform and locationand their effects on humidity. On the other hand, analysis for ten years ismade in order to observe if these expectations changes in years. Rainbow plots,which are one of the graphical presentations, are used to interpret changes inyears. Additionally, functional t-test results for 10 years are presentedgraphically and interpreted.

DOI Code: 10.1285/i20705948v7n2p254

Keywords: Keywords: Functional data analysis, functional t-tests, Fourier series, meteorological data, rainbow plots.

References


References

Ainsworth, L. M., Routledge, R. and Cao, J.(2011). Functional data analysis in ecosystem research: the decline of Oweekeno Lake Sockeye Salmon and Wannock River Flow. Journal of Agricultural, Biological, and Environmental Statistics , 16(2), 282-300.

Andersson,J., Lillestøl,J.(2010). Modeling and forecasting electricity consumption by functional data analysis. The Journal of Energy Markets, 3(1), 3-15.

Barra, V. (2004) Analysis of gene expression data using functional principal components. Computer methods and programs in biomedicine, 75(1), 1-9.

Benko, M. (2004). Functional Principal Components analysis, Implementation and Applications. A Master Thesis. Humboldt University Center of Applied Statistics and Economics, Berlin.

Besse P.,Ramsay, J.O. (1986). Principal components analysis of sampled functions. Psychometrica, 51(2), 285-311.

Bugli, C., Lambert, P. (2006). Functional ANOVA with random functional effects: an application to event-related potentials modelling for electroencephalograms analysis. Statıstıcs In Medıcıne, 25(21), 3718–3739.

Cerioli, A., Laurini, F. and Corbellini, A. (2005). Functional cluster analysis of financial time series. In New Developments in Classification and Data Analysis, eds. Vichi, M., Monari, P., Mignani, S., Montanari, A. Springer-Verlag, Berlin, 333-341.

Cheng,C. Xu,Y. and Gubian, M.(2010). Exploring the mechanism of tonal contraction in taiwan Mandarin. INTERSPEECH 2010: 2010-2013.

Chiou, J.M., Müller, H.G. (2007). Diagnostics for functional regression via residual processes. Computational Statistics & Data Analysis, 51(10), 4849 – 4863.

Coffey, N., Hinde, J.(2011). Analyzing time-course microarray data using functional data analysis-a review. Statistical Applications in Genetics and Molecular Biology, 10(1),1-32.

Coğrafya Dünyası.(2013). URL: http://www.cografya.gen.tr/

Hall, P. , Nasab, H. M. (2006). On properties of functional principal components analysis. Journal of the Royal Statistical Society: Series B, 68(1), 109-126.

He, G., Müller, H.G. and Wang, J.L. (2000). Extending correlation and regression from multivariate to functional data. In Asymptotics in Statistics and Probability, eds. Puri, M.L. , VSP, Zeist, 197-210.

He, G., Müller, H.G. and Wang, J.L. (2003). Functional canonical analysis for square ıntegrable stochastic processes. Journal of Multivariate Analysis, 85, 54-77.

He, G., Müller, H.G. and Wang, J.L. (2004). Methods of canonical analysis of functional data. Journal of Statistical Planning and Inference, 122, 141-159.

Hyndman, R., Shang, H.L.(2010). Rainbow plots, bagplots and boxplots for functional data. Journal of Computational and Graphical Statistics. 19(1), 29-45.

Ingrassia, S., Costanzo, G.D.(2005). Functional principal component analysis of financial time series. In New Developments in Classification and Data Analysis, eds. Vichi, M., Monari, P., Mignani, S., Montanari, A. Springer-Verlag, Berlin, 351-358.

James, G.M. (2002). Generalized linear models with functional predictors. Journal of the Royal Statistical Society Series B, 64(3),411-432.

Kaziska, D.M.(2011). Functional analysis of variance, discriminant analysis, and clustering in a manifold of elastic curves. Communications in Statistics—Theory and Methods, 40, 2487–2499.

Kupresanin, A.M.(2008). Topıcs In Functional Canonical Correlation And Regression, Ph.D. diss , Arızona State Unıversıty.

Lee, J. S. (2005). Aspects of Functional Data Inference and Its Applications. Doctor of Philosophy, Houston, Texas.

Leurgans, S.E., Moyeed, R.A. and Silverman, B.W. (1993). Canonical correlation analysis when data are curves. Journal of the Royal Statistical Society Series B, 55 (3), 725-740.

Lober, E.M., Villa, C. (2004). Functional Principal Component Analysis of the Yield Curve. URL: http://www.u-cergy.fr/AFFI_2004/IMG/pdf/MATZNER.pdf

Meteoroloji Genel Müdürlüğü.(2013).URL: http://www.mgm.gov.tr/

Ramsay, J.O., Dalzell, C.J.(1991). Some tools for functional data analysis. Journal of the Royal Statistical Society, Series B (Methodological),53(3),539–572.

Ramsay J.O., Hooker, G., Graves, S. (2009). Functional Data Analysis with R and MATLAB, Springer, New-York.

Ramsay, J.O. (2013), FDAPackage, URL:http://www.psych.mcgill.ca/faculty/ramsay/ramsay.html

Ratcliffe, S. J., Leader, L. R. and Heller, G. Z. (2002). Functional data analysis with application to periodically stimulated foetal heart rate data. I: Functional regression. Statıstıcs In Medıcıne, 21(8), 1103–1114.

Shang, H.L.,Hyndman, R. (2008). Bagplots, Boxplots and Outlier Detection for Functional Data. In Functional and Operational Statistics, eds. Dabo-Niang S., Ferraty F., . Springer-Verlag, Heidelberg, 201-207.

Türkiye İstatistik Kurumu.(2013).URL. www.tuik.gov.tr

Ullah, S., Finch,C.F. (2013).Applications of functional data analysis: A systematic review, Medical Research Methodology, URL: http://www.biomedcentral.com/1471-2288/13/43.

Yaree, K. (2011). Functional data analysis with application to ms and cervical vertebrae data. Master of Science in Statistics, Edmonton, Alberta.

Zhang,C. , Peng, H. and Zhang,J.T. (2010). Two samples tests for functional data. Communications in Statistics - Theory and Methods, 39(4), 559-578.


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