Two models, one random the other periodic, are described which exhibit splay rigidity but are not rigid with respect to compression. The random model is based on a periodic lattice of rhombuses whose sides consist of central-force springs, which is perturbed in the following way: rhombuses can have diagonal central force struts with probability y or they can have one of the horizontal springs r...

Abstract: We study the asymptotic properties of Lasso+mLS and Lasso+ Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+ mLS and Lasso+Ridge. Second, we der...

Abstract—In this work, we provide non-asymptotic, probabilistic guarantees for successful sparse support recovery by the multiple sparse Bayesian learning (M-SBL) algorithm in the multiple measurement vector (MMV) framework. For joint sparse Gaussian sources, we show that M-SBL perfectly recovers their common nonzero support with arbitrarily high probability using only finitely many MMVs. In fa...

Linkage analysis (either parametric or nonparametric) is commonly applied to identify chromosomal regions using related individuals affected by disease. In complex disease the incomplete relationship between phenotype and genotype can be modeled using a phenocopy parameter, the probability that an individual is affected given they do not carry the disease mutation of interest, and a nonpenetran...

The buyer’s type is his value  ∈ [ ] and the seller’s type is his cost  ∈ [ ]. The buyer’s value is drawn from a distribution (·) whose density (·) is nonzero on [ ], while the seller’s cost is drawn from the distribution  (·) whose density (·) is nonzero on [ ]. A trader observes his own type but not the type of the other trader. The buyer’s ex post utility from acquiring the...

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the cova...

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the cova...

We calculate the probability amplitude for tree-level elastic electron-muon scattering in Minkowski spacetime with carefully prepared initial and final wave packets. The obtained nonzero implies a nonvanishing detecting recoil electron outside light-cone of muon. Transposing this Minkowski-spacetime result to near-horizon region massive Schwarzschild black hole referring previously proposed Ged...

this paper considers the search problem, introduced by srivastava cite{sr}. this is a model discrimination problem. in the context of search linear models, discrimination ability of search designs has been studied by several researchers. some criteria have been developed to measure this capability, however, they are restricted in a sense of being able to work for searching only one possible non...

We study the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We consider variable selection using the adaptive Lasso, where the L1 norms in the penalty are re-weighted by data-dependent weights. We show that, if a reasonable initial estimator is available, under appropri...