This paper is an extension of EbayesThresh (the empirical bayesian thresholding method) under assumption of data with homogeneous standard deviation noises described in Johnstone and Silverman (2004)[1]. We ease this restriction, allowing heterogeneous standard deviation of noises, and provide details in estimating the true effects with posterior estimator, e.g. posterior mean or posterior medi...

Absolute deviation is utilized as a measure of risk and a new function is provided for it. We consider the mean-absolute deviation (MAD) portfolio optimization problem in a frictional market with additional constraints representing the socalled short sales. An algorithm for solving the optimization problem is thus presented, which uses the special structure of the original problem to reduce to ...

We measured the mean plane of the Kuiper belt as a function of semi-major axis. For the classical Kuiper belt as a whole (the non-resonant objects in the semi-major axis range 42–48 au), we find a mean plane of inclination im = 1.8 ◦+0.7 −0.4◦ and longitude of ascending node Ωm = 77 ◦+18 −14◦ (in the J2000 ecliptic-equinox coordinate system), in accord with theoretical expectations of the secul...

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis o...

In this paper, we establish a new coherent risk measure on Lp, which refer to as the monotone mean Lp-deviation measure. Then, related properties are discussed. Furthermore, from perspective of acceptance set, discuss relationship between and Sharpe ratio Finally, extend multivariate setting.

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of L1 regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviatio...

Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based its mean and variance. While tight, has been criticized for only being attained by pathological distributions that abuse unboundedness underlying support are not considered realistic in many applications. We provide alternative tight lower bounds given bounded support, absolute deviation variable. ...