International Journal of Multivariate Data Analysis (4 papers in press)
Discriminating between first and second order linear and non linear models for optimality
by Ijomah Maxwell Azubuike, Oyinebifun Emmanuel Biu, Toru Temitayo Olaide
Abstract: In this paper, an examination of the relationship between a response variable and several explanatory variables was considered for first and second order regression models (with and without interaction). To achieve this, the behaviour of the controllable variables (i.e. reaction time, reaction temperature and moisture content) against response variable (Drying rate of bush mango seeds) was examined using ordinary least square method with the aid of Microsoft Excel and Minitab 16. Furthermore, the comparison of the fitted models, using model adequacy criteria procedure and optimality criterion technique was also done. This was to determine the most suitable model that best predicts optimal response variable for given settings of the controllable variables. The result showed that the second order regression model with interaction was the most suitable model, and a new operating region in which a process or product may be improved was identified using optimizing multivariable function. This research recommends the extreme points and the identified optimal value for production process.
Keywords: Data transformation; optimality criterion; model adequacy criteria and optimizing multivariable function.
On the adequacy of the polynomial approximation to the exponential growth curve model
by Oyinebifun Emmanuel Biu, Iheanyi Sylvester Iwueze
Abstract: Exponential growth curves are usually approximated with a finite order polynomial curve in the study of trending curves in many areas of Statistics. This is done because the most popular way of removing the trend component is by differencing. Exponential growth curves are usually approximated with a finite order polynomial curve in the study of trending curves in many areas of Statistics. This is done because the most popular way of removing the trend component is by differencing. This paper first, shows that the trend curve cannot be removed by differencing when the trend curve is the exponential growth curve. Exponential curves are transcendental functions which can be reduced to a finite order polynomial by Taylor series expansion or its equivalence evaluated at the origin: the Maclaurin series expansion. The main objective of this paper is to examine the adequacy of the polynomial approximation of the exponential growth curve with respect to its growth rate and sample size. The coefficients of the associated polynomial curve were obtained theoretically by the use of Maclaurin series expansion method. Next, exponential growth curves with varying growth rates and sample sizes were simulated. Adequate polynomials were fitted to the simulated exponential growth curves and the coefficients obtained were compared with the theoretical coefficients using absolute error and paired tests. Results obtained show that adequacy depend on both growth rate and sample size. For the purpose of statistical analysis, the highest sample size of 28 is not useful, especially in times series analysis where the demand of samples of 60 or more is made.
Keywords: Trending curves; exponential growth curve; polynomial growth curve; absolute error; paired observation test.
The Method Sub-D for variance components estimation in random one-way designs
by Adilson Silva, Miguel Fonseca
Abstract: This paper approachs the new estimator for variance components in mixed linear models with an arbitrary number of variance components, called Sub-D. This estimator was deduced and tested in random one-way and twoway nested and crossed designs with balanced or unbalanced data, by Silva (2017); specifically, this paper aims to give the Sub-D explicit formula for both the two variance components in random one-way designs, ensuring their existence through consistent theoretical results. In order to derive the explicit above announced formula, we propose and prove some robust algebraic results. A numerical example where both the two variance components are estimated is given.
Keywords: Orthogonal Matrix; Sub-D; “One-way” designs; Variance components.
NEW ENHANCED CLASS OF ESTIMATORS OF POPULATION MEAN USING KNOWN MEDIAN OF STUDY VARIABLES
by S.K. Yadav, Dinesh Sharma, S.S. Mishra
Abstract: The present paper estimates the population mean of the variable under study by improving the class of estimator utilizing known information of population median of the study variable. In view of a comparison of this class with the competing estimators, the sampling properties have been derived up to the first order of approximation. In sampling properties, bias and mean squared errors (MSE) have been obtained. This is because a characterizing scalar is involved in the estimator and it takes different values. Thus, the optimum value of this characterizing constant which minimizes the MSE of proposed class has also been obtained. The least value of the MSE of the proposed estimator is obtained for the optimal value of characterizing constant. The proposed estimator has been compared with the mean per unit estimator, ratio estimator, linear regression estimator, Bahl and Tuteja (1981) estimator, Subramani (2016) estimator and Kadilar (2016) estimator for various natural populations under simple random sampling scheme. The conditions under which, a proposed estimator performs better than above estimators have been given. The numerical study shows that the proposed estimator performs better than the mean per unit estimator, ratio estimator, linear regression estimator, Bahl and Tuteja (1981) estimator, Subramani (2016) estimator and Kadilar (2016) estimator as it has the least mean squared error among above estimators.
Keywords: Study variable; Auxiliary variable; Median; Bias; MSE; Percentage relative efficiency.