The use of curves or functional data in the study analysis is increasingly gaining momentum in the various fields of research. The statistical method to analyze such data is known as functional data analysis (FDA). The first step in FDA is to convert the observed data points which are repeatedly recorded over a period of time or space into either a rough (raw) or smooth curve. In the case of the smooth curve, basis functions expansion is one of the methods used for the data conversion. The data can be converted into a smooth curve either by using the regression smoothing or roughness penalty smoothing approach. By using the regression smoothing approach, the degree of curve’s smoothness is very dependent on k number of basis functions; meanwhile for the roughness penalty approach, the smoothness is dependent on a roughness coefficient given by parameter λ Based on previous studies, researchers often used the rather time-consuming trial and error or cross validation method to estimate the appropriate number of basis functions. Thus, this paper proposes a statistical procedure to construct functional data or curves for the hourly and daily recorded data. The Bayesian Information Criteria is used to determine the number of basis functions while the Generalized Cross Validation criteria is used to identify the parameter λ The proposed procedure is then applied on a ten year (2001–2010) period of PM10 data from 30 air quality monitoring stations that are located in Peninsular Malaysia. It was found that the number of basis functions required for the construction of the PM10 daily curve in Peninsular Malaysia was in the interval of between 14 and 20 with an average value of 17; the first percentile is 15 and the third percentile is 19. Meanwhile the initial value of the roughness coefficient was in the interval of between 10−5 and 10−7 and the mode was 10−6. An example of the functional descriptive analysis is also shown.
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10 July 2014
PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability
6–8 November 2013
Penang, Malaysia
Research Article|
July 10 2014
Data preparation for functional data analysis of PM10 in Peninsular Malaysia
Norshahida Shaadan;
Norshahida Shaadan
Center for Statistical and Decision Science Studies, Faculty of Computer and Mathematical Sciences, 40450 UiTM Shah Alam, Selangor,
Malaysia
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Abdul Aziz Jemain;
Abdul Aziz Jemain
DELTA, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), 43600, Bangi, Selangor,
Malaysia
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Sayang Mohd Deni
Sayang Mohd Deni
Center for Statistical and Decision Science Studies, Faculty of Computer and Mathematical Sciences, 40450 UiTM Shah Alam, Selangor,
Malaysia
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AIP Conf. Proc. 1605, 850–855 (2014)
Citation
Norshahida Shaadan, Abdul Aziz Jemain, Sayang Mohd Deni; Data preparation for functional data analysis of PM10 in Peninsular Malaysia. AIP Conf. Proc. 10 July 2014; 1605 (1): 850–855. https://doi.org/10.1063/1.4887701
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