Robust estimation in multiple linear regression model with non-Gaussian noise

The traditional least squares estimators used in multiple linear regression model are very sensitive to design anomalies. To rectify the situation we propose a reparametrization of the model. We derive modified maximum likelihood estimators and show that they are robust and considerably more efficient than the least squares estimators besides being insensitive to moderate design anomalies.


Nonnormal regression. I. Skew distributions
İslam, Muhammed Qamarul; Yildirim, F (2001-01-01)
In a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we deriv...
Multiple linear regression model with stochastic design variables
İslam, Muhammed Qamarul (Informa UK Limited, 2010-01-01)
In a simple multiple linear regression model, the design variables have traditionally been assumed to be non-stochastic. In numerous real-life situations, however, they are stochastic and non-normal. Estimators of parameters applicable to such situations are developed. It is shown that these estimators are efficient and robust. A real-life example is given.
Fuzzy versus statistical linear regression
Kim, KJ; Moskowitz, H; Köksalan, Mustafa Murat (1996-07-19)
Statistical linear regression and fuzzy linear regression have been developed from different perspectives, and thus there exist several conceptual and methodological differences between the two approaches. The characteristics of both methods, in terms of basic assumptions, parameter estimation, and application are described and contrasted. Their descriptive and predictive capabilities are also compared via a simulation experiment to identify the conditions under which one outperforms the other. It turns out...
Estimating parameters in autoregressive models in non-normal situations: Asymmetric innovations
Akkaya, Ayşen (2001-01-01)
The estimation of coefficients in a simple autoregressive model is considered in a supposedly difficult situation where the innovations have an asymmetric distribution. Two distributions, gamma and generalized logistic, are considered for illustration. Closed form estimators are obtained and shown to be efficient and robust. Efficiencies of least squares estimators are evaluated and shown to be very low. This work is an extension of that of Tiku, Wong and Bian [1] who give solutions for a simple AR(I) model
Regression analysis with a dtochastic design variable
Sazak, HS; Tiku, ML; İslam, Muhammed Qamarul (Wiley, 2006-04-01)
In regression models, the design variable has primarily been treated as a nonstochastic variable. In numerous situations, however, the design variable is stochastic. The estimation and hypothesis testing problems in such situations are considered. Real life examples are given.
Citation Formats
A. Akkaya, “Robust estimation in multiple linear regression model with non-Gaussian noise,” AUTOMATICA, pp. 407–417, 2008, Accessed: 00, 2020. [Online]. Available: