### Journals Information

Mathematics and Statistics Vol. 8(4), pp. 472 - 479
DOI: 10.13189/ms.2020.080415
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## Penalized Maximum Likelihood Estimation of Semiparametric Generalized Linear Models with Application to Climate Temperature Data

Azumah Karim 1,*, Ananda Omutokoh Kube 2, Bashiru Imoro Ibn Saeed 3
1 Pan African University Institute for Basic Sciences, Technology and Innovation, Kenya
2 Department of Mathematics, Kenyatta University, Kenya
3 Department of Mathematics and Statistics, Kumasi Technical University, Ghana

ABSTRACT

Global temperature change is an important indicator of climate change. Climate time series data are characterized by trend, seasonal/cyclical as well as irregular components. Adequately modeling these components cannot be overemphasized. In this paper, we have proposed an approach of modeling temperature data using semiparametric additive generalized linear model. We have derived a penalized maximum likelihood estimation of the additive component of the semiparametric generalized linear models, that is, of regression coefficients and smooth functions. A statistical modeling with real time series data set was conducted on temperature data. The study has provided indications on the gain of using semiparametric modeling in situations where a signal component can be additively decomposed in to trend, cyclical and irregular components. Thus, we recommend semiparametric additive penalized models as an option to fit time series data sets in modelling the different component with different functions to adequately explain the relation inherent in data.

KEYWORDS
Cubic Spline, Fourier Function, Trend, Cyclical/Periodic, Maximum Likelihood, Semiparametric, Generalized Linear Models

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Azumah Karim , Ananda Omutokoh Kube , Bashiru Imoro Ibn Saeed , "Penalized Maximum Likelihood Estimation of Semiparametric Generalized Linear Models with Application to Climate Temperature Data," Mathematics and Statistics, Vol. 8, No. 4, pp. 472 - 479, 2020. DOI: 10.13189/ms.2020.080415.

(b). APA Format:
Azumah Karim , Ananda Omutokoh Kube , Bashiru Imoro Ibn Saeed (2020). Penalized Maximum Likelihood Estimation of Semiparametric Generalized Linear Models with Application to Climate Temperature Data. Mathematics and Statistics, 8(4), 472 - 479. DOI: 10.13189/ms.2020.080415.