G Mokeshrayalu

Bio: G Mokeshrayalu is an academic researcher from VIT University. The author has contributed to research in topics: Heteroscedasticity & Matrix calculus. The author has an hindex of 2, co-authored 2 publications receiving 8 citations.

A different approach to estimate nonlinear regression model using numerical methods

Abstract: This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE's (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

New methods of testing nonlinear hypothesis using iterative NLLS estimator

Abstract: This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

A new vision on ordinary least squares estimation of parameters of linear model

Abstract: This paper aims at the method of OLS estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented.An extensive discussion in evaluating BLUE of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and variance-covariance matrix of BLUE are discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, characteristic properties of OLS estimators and problems of linear statistical model by violating the assumptions are extensively discussed.

A Treatise on Ordinary Least Squares Estimation of Parameters of Linear Model

Abstract: This research article primarily focuses on the estimation of parameters of a linear regression model by the method of ordinary least squares and depicts Gauss-Mark off theorem for linear estimation which is useful to find the BLUE of a linear parametric function of the classical linear regression model. A proof of generalized Gauss-Mark off theorem for linear estimation has been presented in this memoir. Ordinary Least Squares (OLS) regression is one of the major techniques applied to analyse data and forms the basics of many other techniques, e.g. ANOVA and generalized linear models [1]. The use of this method can be extended with the use of dummy variable coding to include grouped explanatory variables [2] and data transformation models [3]. OLS regression is particularly powerful as it relatively easy to check the model assumption such as linearity, constant, variance and the effect of outliers using simple graphical methods [4]. J.T. Kilmer et.al [5] applied OLS method to evolutionary and studies of algometry.

On mathematical and statistical aspects of linear models

Abstract: The main goal of this research article is to discuss the mathematical and statistical aspects of linear models and their characteristic properties. Linear model is the most common modeling used in science. Actually linear models have many different meanings depend on the context. Linear model is often preferred than other model such as quadratic model because of its ability to interpret easily. In the other hand most of the real life cases have linear relationship .Modeling the cases using linear model will able us to computethe relative influence of one or more independent variables to the dependent variable. In the present talk an attempt has been made to propose the specific forms of simple and multiple linear regression models. In this conversation mathematical aspects of linear statistical models have been extensively depicted. Different types of mathematical models are depictedhere and the methods of fitting transformed models are proposed.Furthermore specific form of linear statistical model is presented and the crucial assumptions of general linear model are extensively discussed.At the last stage of this article the procedure of OLS estimation of parameters of a linear model has been proposed

A study on mathematical and statistical aspects of linear models

Abstract: The primary objective of this research article is to present the mathematical and statistical aspects of linear models and their characteristic properties. Linear model is the most common modeling used in science. Actually linear models have many different meanings depend on the context. Linear model is often preferred than other model such as quadratic model because of its ability to interpret easily. In the other hand most of the real life cases have linear relationship .Modeling the cases using linear model will able us to determine the relative influence of one or more independent variables to the dependent variable. In the present talk an attempt has been made to propose the specific forms of simple and multiple linear regression models. In this conversation mathematical aspects of linear models have been extensively depicted. Different types of mathematical models are discussed here and the methods of fitting transformed models are proposed.Furthermore specific form of linear statistical model is presented and the crucial assumptions of general linear model are extensively discussed.At the last stage of this article the method of ordinary least squares estimation of parameters of a linear model has been proposed

Assessment of Asymptotic and Logistics Growth Models on A Chemist Data

Abstract: This research considers two growth models; asymptotic growth model and logistic growth model. Both models were compared to establish a better model for modelling and prediction based on a Chemist data on the percentage concentration of isomers versus time for each Isomerization of α-Pinene at 189.50C. Results from the growth curve shows a non-linear relationship between the response (time of isomerization) and the independent variables (percentage of concentration) for all the four isomers considered. Based on the four isomers four different quadratic regressions of second-order were fitted. The problem of the initial parameters was addressed by second-order regression techniques since the models considered have three parameters to be estimated before the iterative approach was used. Estimation of parameters was done using modified version of the Levenberg-Marquardt Algorithm in Gretl statistical software. The results from both models were compared based on Aikaike Information Criteri (AIC), Bayesian Information Criteria (BIC), Mean Squared Error (MSE) and R-square. The Asymptotic Growth Model was identified to be a more adequate model for modelling and predicting growth patterns for three isomers (Dipentene, Pyronene and Dimer) while logistic growth model was seen to be a better model for predicting growth patterns of one isomer (Allo-Ocimene). This study will go a long way in directing Chemists and researchers in that field in choosing the appropriate model for their research.