# Estimating parameters in autoregressive models in non-normal situations: Asymmetric innovations

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
Communications in Statistics - Theory and Methods

# Suggestions

 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...
 Robust estimation in multiple linear regression model with non-Gaussian noise Akkaya, Ayşen (2008-02-01) 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.
 Non-normal bivariate distributions: estimation and hypothesis testing Qunsiyeh, Sahar Botros; Tiku, Moti Lal; Department of Statistics (2007) When using data for estimating the parameters in a bivariate distribution, the tradition is to assume that data comes from a bivariate normal distribution. If the distribution is not bivariate normal, which often is the case, the maximum likelihood (ML) estimators are intractable and the least square (LS) estimators are inefficient. Here, we consider two independent sets of bivariate data which come from non-normal populations. We consider two distinctive distributions: the marginal and the conditional dist...
 Applications of estimation techniques on genetic and other types of data Aslan, Murat; Akkaya, Ayşen; Department of Statistics (2003) The parameters of genetic and other types of data, particularly with small samples, are estimated by using method of moments, least squares, minimum chi- square, maximum likelihood and modified maximum likelihood estimation methods. These methods are also compared in terms of their efficiencies and robustness property.
 Analysis of variance in experimental design with nonnormal error distributions Senoglu, B; Tiku, ML (2001-01-01) We consider a two-way classification model with interaction and assume that the errors have a location-scale nonnormal distribution. From an application of the modified likelihood estimation, we obtain efficient and robust estimators of the parameters. We define F statistics for testing main effects and interaction. We analyze the Box-Cox data and show that the method developed in this paper gives accurate results besides being easy theoretically and computationally.
Citation Formats
A. Akkaya, “Estimating parameters in autoregressive models in non-normal situations: Asymmetric innovations,” Communications in Statistics - Theory and Methods, pp. 517–536, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52274.