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Consider a probit regression problem in which Y1, . . . ,Yn are independent Bernoulli random variables such that Pr.Yi D1/DΦ.xT i β/ where xi is a p-dimensional vector of known covariates that are associated with Yi ,β is a p-dimensional vector of unknown regression coefficients and Φ. / denotes the standard normal distribution function. We study Markov… (More)

- Vivekananda Roy
- 2007

Consider a probit regression problem in which Y1, . . . , Yn are independent Bernoulli random variables such that Pr(Yi = 1) = Φ(xi β) where xi is a p-dimensional vector of known covariates associated with Yi, β is a p-dimensional vector of unknown regression coefficients and Φ(·) denotes the standard normal distribution function. We study Markov chain… (More)

This paper introduces a flexible skewed link function for modeling binary as well as ordinal data with covariates based on the generalized extreme value (GEV) distribution. Extreme value techniques have been widely used in many disciplines relating to risk analysis. However, its application in the binary and ordinal data from a Bayesian context is sparse… (More)

- Vivekananda Roy
- Computational Statistics & Data Analysis
- 2014

It is known that the robit regression model for binary data is a robust alternative to the more popular probit and logistic models. The robit model is obtained by replacing the normal distribution in the probit regression model with the Student’s t distribution. Unlike the probit and logistic models, the robit link has an extra degrees of freedom (df)… (More)

- Vivekananda Roy, James P. Hobert
- J. Multivariate Analysis
- 2010

We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavy-tailed. Let π denote the intractable posterior density that results when this regression model is combined with the… (More)

- Vivekananda Roy
- 2011

The sandwich algorithm (SA) is an alternative to the data augmentation (DA) algorithm that uses an extra simulation step at each iteration. In this paper, we show that the sandwich algorithm always converges at least as fast as the DA algorithm, in the Markov operator norm sense. We also establish conditions under which the spectrum of SA dominates that of… (More)

Abstract: Most common regression models for analyzing binary random variables are logistic and probit regression models. However it is well known that the estimates of regression coefficients for these models are not robust to outliers [26]. The robit regression model [1, 16] is a robust alternative to the probit and logistic models. The robit model is… (More)

- Vivekananda Roy, Evangelos Evangelou, Zhengyuan Zhu
- Biometrics
- 2016

Spatial generalized linear mixed models (SGLMMs) are popular models for spatial data with a non-Gaussian response. Binomial SGLMMs with logit or probit link functions are often used to model spatially dependent binomial random variables. It is known that for independent binomial data, the robit regression model provides a more robust (against extreme… (More)

The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable support, as is nearly always the case in practice, it is generally quite difficult to get a handle on these spectra. We show… (More)

- Krishna B. Athreya, Vivekananda Roy
- J. Applied Probability
- 2015

Let f be an integrable function on an infinite measure space (S,S , π). We show that if a regenerative sequence {Xn}n≥0 with canonical measure π could be generated then a consistent estimator of λ ≡ ∫ S fdπ can be produced. We further show that under appropriate second moment conditions, a confidence interval for λ can also be derived. This is illustrated… (More)