We study the asymptotic properties of bridge estimators in sparse, highdimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero. We show that under appropriate conditio...

We study the asymptotic properties of bridge estimators in sparse, highdimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero. We show that under appropriate conditio...

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different probability of being nonzero. We propose a...

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different probability of being nonzero. We propose a...

Longitudinal or repeated measures data with clumping at zero occur in many applications in biometrics, including health policy research, epidemiology, nutrition, and meteorology. These data exhibit correlation because they are measured on the same subject over time or because subjects may be considered repeated measures within a larger unit such as a family. They present special challenges beca...

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

Simple Stochastic Game nondeterminism nondeterminism probability probability nondeterminism nondeterminism probability 1 Definitions Markov Chain (MC) Definition 1. A Markov Chain ((S, E), δ) is a graph (S, E) with a function δ : S → D(S) that maps every state to a probability distribution of successor states. There is an edge between two states s, t in S iff the probability of going from s to ...

Consider repeated measures data with many zeros. For the case with one grouping factor and one repeated measure, we examine several models, assuming that the nonzero data are roughly lognormal. One of the simplest approaches is to model the zeros as left-censored observations from the lognormal distribution. A random effect is assumed for subjects. The censored model makes a strong assumption a...

We consider the problem of reconstructing a sparse signal x0 ∈ R from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an orthonormal matrix, we show that 1 minimization recovers x0 exactly when the number of measurements exceeds m const · μ(U) · S · log n, where S is the number of nonzero components in x0 and μ is the largest entry in U properly nor...