Non asymptotic risk bounds for Classification And Regression Trees (CART) classifiers are obtained in the binary supervised classification framework under a margin assumption on the joint distribution of the covariates and the labels. These risk bounds are derived conditionally on the construction of the maximal binary tree and allow to prove that the linear penalty used in the CART pruning alg...

An important class of hybrid Bayesian networks are those that have conditionally deterministic variables (a variable that is a deterministic function of its parents). In this case, if some of the parents are continuous, then the joint density function does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when the deterministic function is linear and continuous va...

The open-loop Threshold Model, proposed by Tong [23], is a piecewise-linear stochastic regression model useful for modeling conditionally normal response time-series data. However, in many applications, the response variable is conditionally non-normal, e.g. Poisson or binomially distributed. We generalize the open-loop Threshold Model by introducing the Generalized Threshold Model (GTM). Speci...

We consider estimation of linear functionals of the error distribution for two regression models: parametric and nonparametric, and for two types of errors: independent of the covariate and centered (type I), and conditionally centered given the covariate (type II). We show that the residual-based empirical estimators for the nonparametric type I model remain efficient in the type II model. For...

The open-loop Threshold Model, proposed by Tong [30], is a piecewise-linear stochastic regression model useful for modeling conditionally normal response time-series data. However, in many applications, the response variable is conditionally non-normal, e.g. Poisson or binomially distributed. We generalize the open-loop Threshold Model by introducing the Generalized Threshold Model (GTM). Speci...

In this paper we consider the following model. We consider n nonnegative random variables T1, T2, . . . , Tn such that they are conditionally independent given some random vector Θ, where Θ takes values on some set χ ⊆ R. If Fi(·|θ) denotes the marginal distribution of Ti(θ) ≡ (Ti|Θ = θ), and G(θ) denotes the joint distribution function of Θ, then the joint distribution of (T1, T2, . . . , Tn) ...

The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (...

This paper studies the stability of nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Conditions under which the model is stable in the sense that its Markov chain repre...

A particular version of a spectral integrator has been designed. It consists of a xenon lamp whose light is dispersed into a color spectrum by dispersing prisms. Using a transmissive LCD panel controlled by a computer, certain fractions of the light in different parts of the spectrum are masked out. The remaining transmitted light is integrated and projected onto a translucent diffusing plate. ...

We present an algorithm to generate samples from probability distributions on the space of curves. Traditional curve evolution methods use gradient descent to find a local minimum of a specified energy functional. Here, we view the energy functional as a negative log probability distribution and sample from it using a Markov chain Monte Carlo (MCMC) algorithm. We define a proposal distribution ...