Estimation of the parameters of a regression model with a multivariate t error variable

Sutradhar, Brajendra C.; Ali, M. Masoom

doi:10.1080/03610928608829130

Cited by 87 publications

(52 citation statements)

References 3 publications

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“…The robustness obtained using the t distribution in linear models have been studied by Sutradhar and Ali (1986), Lange, Little, and Taylor (1989), and Taylor, Yu, and Sandler (2005). In our joint model we may replace the normal distribution assumption for measurement errors with a t distribution to take into account longer-thannormal tails.…”

Section: Discussionmentioning

confidence: 99%

A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types

2007

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SummaryIn this article we study a joint model for longitudinal measurements and competing risks survival data. Our joint model provides a flexible approach to handle possible nonignorable missing data in the longitudinal measurements due to dropout. It is also an extension of previous joint models with a single failure type, offering a possible way to model informatively censored events as a competing risk. Our model consists of a linear mixed effects submodel for the longitudinal outcome and a proportional cause-specific hazards frailty submodel (Prentice et al., 1978, Biometrics 34, 541-554) for the competing risks survival data, linked together by some latent random effects. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their standard errors using a profile likelihood method. The developed method works well in our simulation studies and is applied to a clinical trial for the scleroderma lung disease.

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Section: Discussionmentioning

confidence: 99%

A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types

2007

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“…Bayesian and classical analysis for the SUR models with normal errors have been considered by Zellner [10], Srivastava and Giles [8] and Percy [7], among others. Where heavy-tailed error distribution is assumed, the multivariate t-distributed errors have been used as in Kowalski et al [5] for the SUR model, and in Zellner [11] and Sutradhar and Ali [9] for the traditional regression models which are special cases of the SUR model. Inferential and predictive methods include likelihood estimation (e.g., Kowalski et al [5]), Bayes posterior distribution of the parameters (e.g., Zellner [10], Kowalski et al [5]) and prediction distribution for future observations (e.g., Kowalski et al [5], Percy [7]).…”

Section: Introductionmentioning

confidence: 99%

Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

2002

Journal of Multivariate Analysis

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Bayesian inference is considered for the seemingly unrelated regressions with an elliptically contoured error distribution. We show that the posterior distribution of the regression parameters and the predictive distribution of future observations under elliptical errors assumption are identical to those obtained under independently distributed normal errors when an improper prior is used. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution. © 2002 Elsevier Science (USA) AMS 2000 subject classifications: 62F15, 62H05. Key words and phrases: seemingly unrelated regression models; elliptical contoured distributions; posterior and predictive distributions.

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“…Moment estimators for s 2 j and ν j (based on sample variance and kurtosis) are given e.g. in [48,49].…”

Section: Defining the Prior Distribution's Parametersmentioning

confidence: 99%

Modelling coloured residual noise in gravitational-wave signal processing

Röver

Meyer

Christensen

2010

Class. Quantum Grav.

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Abstract. We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal (Gaussian) model. This way, it allows for uncertainty in the noise spectrum, or more generally is also able to accommodate outliers (heavy-tailed noise) in the data. Examples are given pertaining to data from gravitational wave detectors.

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Estimation of the parameters of a regression model with a multivariate t error variable

Cited by 87 publications

References 3 publications

A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types

A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types

Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

Modelling coloured residual noise in gravitational-wave signal processing

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