Mathematics and Statistics
http://repository.chuka.ac.ke/handle/chuka/753
2022-04-14T00:15:43ZModeling and Forecasting Kenyan GDP Using Autoregressive Integrated Moving Average (ARIMA) Models
http://repository.chuka.ac.ke/handle/chuka/15934
Modeling and Forecasting Kenyan GDP Using Autoregressive Integrated Moving Average (ARIMA) Models
Musundi, Sammy Wabomba; M’mukiira, Peter Mutwiri; Mungai, Fredrick
The Gross Domestic Product (GDP) is the market value of all goods and services produced within the borders of a
nation in a year. In this paper, Kenya’s annual GDP data obtained from the Kenya National Bureau of statistics for the years 1960
to 2012 was studied. Gretl and SPSS 21 statistical softwares were used to build a class of ARIMA (autoregressive integrated
moving average) models following the Box-Jenkins method to model the GDP. ARIMA (2, 2, 2) time series model was
established as the best for modeling the Kenyan GDP according to the recognition rules and stationary test of time series under
the AIC criterion. The results of an in-sample forecast showed that the relative and predicted values were within the range of 5%,
and the forecasting effect of this model was relatively adequate and efficient in modeling the annual returns of the Kenyan GDP.
Finally, we used the fitted ARIMA model to forecast the GDP of Kenya for the next five years.
2016-04-13T00:00:00ZA NOTE ON QUASI-SIMILARITY OF OPERATORS IN HILBERT SPACES
http://repository.chuka.ac.ke/handle/chuka/15733
A NOTE ON QUASI-SIMILARITY OF OPERATORS IN HILBERT SPACES
SAMMY W. MUSUNDI; ISAIAH N.SITATI; BERNARD M. NZIMBI; KIKETE W. DENNIS
In this paper we introduce the notion of Quasi-similarity of bounded linear operators in Hilbert Spaces. We do so by
defining a quasi- affinity from one Hilbert Space H to K. Some results on quasi- affinities are also discussed. It has
already been shown that on a finite dimensional Hilbert Space, quasi similarity is an equivalence relation that is; it is
reflexive, symmetric and also transitive. Using the definition of commutants of two operators, we give an alternative
result to show that quasi similarity is an equivalence relation on an infinite dimensional Hilbert Space. Finally, we
establish the relationship between quasi similarity and almost similarity equivalence relations in Hilbert Spaces using
hermitian and normal operators.
2015-07-23T00:00:00ZThe Banach Numerical Range for Finite Linear Operators
http://repository.chuka.ac.ke/handle/chuka/15708
The Banach Numerical Range for Finite Linear Operators
M. Ohuru, Priscah; W. Musundi, Sammy
The numerical range has been a subject of interest to many researchers and
scholars in the recent past. Based on the research outputs, many results have been obtained.
Besides, several generalizations of the classical numerical range have also been made. The
recent developments have focused on the theory of operators on Hilbert spaces. The
determination of the numerical ranges of linear and nonlinear operators have been given in
both the Hilbert and Banach spaces. In addition, results of these numerical ranges have been
extended to the case of two operators in both spaces. It is important to note that more
generalizations have been made in Hilbert spaces as compared to those that have been made
in the Banach spaces. The Banach space has two major numerical ranges which are: the
spatial and algebraic numerical ranges. This research focuses on determining the numerical
range for a finite number of linear operators in the Banach space based on the classical
definition. Properties which hold for the classical numerical range have been shown to hold
for the Banach space numerical range. The property of convexity has been established using
the Toeplitz-Hausdorff theorem under the condition that the Banach space is smooth.
Furthermore, the numerical radius and the spectrum of these operators have also been
determined.
2020-02-14T00:00:00ZPLS Generalized Linear Regression and Kernel Multilogit Algorithm (KMA) for Microarray Data Classification Problem
http://repository.chuka.ac.ke/handle/chuka/15658
PLS Generalized Linear Regression and Kernel Multilogit Algorithm (KMA) for Microarray Data Classification Problem
Wagala, Adolphus; González-Farías, Graciela; Ramos, Rogelio
This study involves the implentation of the extensions of the partial least
squares generalized linear regression (PLSGLR) by combining it with logistic
regression and linear discriminant analysis, to get a partial least squares
generalized linear regression-logistic regression model (PLSGLR-log), and a
partial least squares generalized linear regression-linear discriminant analysis
model (PLSGLRDA). A comparative study of the obtained classifiers
with the classical methodologies like the k-nearest neighbours (KNN),
linear discriminant analysis (LDA), partial least squares discriminant
analysis (PLSDA), ridge partial least squares (RPLS), and support vector
machines(SVM) is then carried out. Furthermore, a new methodology
known as kernel multilogit algorithm (KMA) is also implemented and its
performance compared with those of the other classifiers. The KMA emerged
as the best classifier based on the lowest classification error rates compared
to the others when applied to the types of data are considered; the unpreprocessed and preprocessed.
2020-01-01T00:00:00Z