Summary In this article, we propose a positive stable shared frailty Cox model for clustered failure time data where the frailty distribution varies with cluster-level covariates. The proposed model accounts for covariate-dependent intracluster correlation and permits both conditional and marginal inferences. We obtain marginal inference directly from a marginal model, then use a stratified Cox...

Scattering is deened on compact manifolds with boundary which are equipped with an asymptotically hyperbolic metric, g: A model form is established for such metrics close to the boundary. It is shown that the scattering matrix at energy exists and is a pseudo-diierential operator of order 2 + 1 ? dim X: The symbol of the scattering matrix is then used to show that except for a discrete set of e...

We investigate the sample complexity for learning using higher-order neurons. We calculate upper and lower bounds on the Vapnik-Chervonenkis dimension and the pseudo dimension for higher-order neurons that allow unrestricted interactions among the input variables. In particular, we show that the degree of interaction is irrelevant for the VC dimension and that the individual degree of the varia...

We give a one-parameter family of exact solutions to four-dimensional higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3, 1) and parameterized by a zeroform invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS4 regions via a dS3-foliated domainwall and two Robertson-Walker-like H3foliated spacetimes – one in ...

The paper discusses the asymptotic validity of posterior inference of pseudo-Bayesian quantile regression methods with complete or censored data when an asymmetric Laplace likelihood is used. The asymmetric Laplace likelihood has a special place in the Bayesian quantile regression framework because the usual quantile regression estimator can be derived as the maximum likelihood estimator under ...

We consider a version of the knapsack problem in which an item size is random and revealedonly when the decision maker attempts to insert it. After every successful insertion the decisionmaker can dynamically choose the next item based on the remaining capacity and available items,while an unsuccessful insertion terminates the process. We build on a semi-infinite relaxationi...

Chapter 1 Pseudo Generalized Least Squares Regression Estimation with Spatial Data Abstract It is hard to account for all pairwise correlations in the estimation of the mean parameters for a large sample of spatial data. In a linear regression model, a pseudo generalized least squares (PGLS) approach is proposed. Data could be divided into groups according to natural geographic areas, only corr...

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically 12nnΘ(1) pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far. ⋆ Parts of this wo...

In undirected graphical models, each node represents a random variable while the set of edges specifies the conditional independencies of the underlying distribution. When the random variables are jointly Gaussian, the models are called Gaussian graphical models (GGMs) or Gauss Markov random fields. In this thesis, we address several important problems in the study of GGMs. The first problem is...