Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm

2022-09-01
GÜNEY, YEŞİM
ARSLAN, OLÇAY
Gökalp Yavuz, Fulya
© 2022 Elsevier Inc.In the analysis of repeated or clustered measurements, it is crucial to determine the dynamics that affect the mean, variance, and correlations of the data, which will be possible using appropriate models. One of these models is the joint mean–covariance model, which is a multivariate heteroscedastic regression model with autoregressive covariance structures. In these models, parameter estimation is usually carried on under normality assumption, but the resulting estimators will be very sensitive to the outliers or non-normality of data. In this study, we propose a robust alternative method and an EM algorithm for estimating the parameters of joint mean–covariance models. Robustification is achieved using a multivariate heavy-tailed distribution with the same number of parameters as the multivariate normal distribution. To simplify the estimation procedure, a modified Cholesky decomposition is adopted to factorize the dependence structure in terms of unconstrained autoregressive and scale innovation parameters. Also, the technique for the prediction of future responses is given. An intensive simulation study and a real data example are provided to demonstrate the performance of the proposed method.
Journal of Multivariate Analysis

Suggestions

Linear mixed model with Laplace distribution (LLMM)
Gökalp Yavuz, Fulya (2018-03-01)
Linear mixed modeling (LMM) is a comprehensive technique used for clustered, panel and longitudinal data. The main assumption of classical LMM is having normally distributed random effects and error terms. However, there are several situations for that we need to use heavier tails distributions than the (multivariate) normal to handle outliers and/or heavy tailness in data. In this study, we focus on LMM using the multivariate Laplace distribution which is known as the heavy tailed alternative to the normal...
Algorithm Overview and Design for Mixed Effects Models
Koca, Burcu; Gökalp Yavuz, Fulya (2021-06-06)
Linear Mixed Model (LMM) is an extended regression method that is used for longitudinal data which has repeated measures within the individual. It is natural to expect high correlation between these repeats over a period of time for the same individual. Since classical approaches may fail to cover these correlations, LMM handles this significant concern by introducing random effect terms in the model. Besides its flexible structure in terms of modeling, LMM has several application areas such as clinical tri...
Robust Attitude Estimation Using IMU-Only Measurements
Candan, Batu; Söken, Halil Ersin (2021-01-01)
© 1963-2012 IEEE.This article proposes two novel covariance-tuning methods to form a robust Kalman filter (RKF) algorithm for attitude (i.e., roll and pitch) estimation using the measurements of only an inertial measurement unit (IMU). KF-based and complementary filtering (CF)-based approaches are the two common methods for solving the attitude estimation problem. Efficiency and optimality of the KF-based attitude filters are correlated with appropriate tuning of the covariance matrices. Manual tuning proce...
Estimation methods for the three-parameter gamma distribution
İçli, Tülay; Yıldırım, Fetih; Department of Statistics (1991)
As a positively skewed distribution, gamma distribution plays an important role in the analysis of sample data originating from life-span, reaction time, reliability, | survival and related studies. Therefore, it is worth-while to deal with the estimation of its parameters. Since gamma distribution does not satisfy some of the regularity conditions, it is a member of non-regular distributions. Inclusion of the threshold parameter creates complications. This parameter can be estimated by the first order stat...
Analysis Window Length Selection For Linear Signal Models
Yazar, Alper; Candan, Çağatay (2015-05-19)
A method is presented for the selection of analysis window length, or the number of input samples, for linear signal modeling without compromising the model assumptions. It is assumed that the signal of interest lies in a known linear space and noisy samples of the signal is provided. The goal is to use as many signal samples as possible to mitigate the effect of noise without violating the assumptions on the model. An application example is provided to illustrate the suggested method.
Citation Formats
Y. GÜNEY, O. ARSLAN, and F. Gökalp Yavuz, “Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm,” Journal of Multivariate Analysis, vol. 191, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85131070529&origin=inward.