Improved Hoeffding’s Lemma and Hoeffding’s Tail Bounds

The purpose of this article is to improve Hoeffding's lemma and consequently Hoeffding's tail bounds. The improvement pertains to left skewed zero mean random variables X\in[a,b], where a<0 and -a>b. The proof of Hoeffding's improved lemma uses Taylor's expansion, the convexity of \exp(sx), s\in \RR, and an unnoticed observation since Hoeffding's publication in 1963 that for -a>b the maximum of  the intermediate function \tau(1-\tau) appearing in Hoeffding's proof is attained at an endpoint rather than at \tau=0.5 as in the case b>-a. Using Hoeffding's  improved lemma we obtain one sided and two sided  tail bounds  for \PP(S_n\ge t) and \PP(|S_n|\ge t), respectively, where S_n=\sum_{i=1}^nX_i and the X_i\in[a_i,b_i],i=1,...,n are independent zero mean  random variables (not necessarily identically distributed). It is interesting to note that we  could  also improve Hoeffding's two sided bound for all \{X_i:  -a_i\ne b_i,i=1,...,n\}. This is  so because here the one sided bound should be  increased by \PP(-S_n\ge t),  wherein the left skewed intervals become right skewed and vice versa.

DOA Estimation in Heteroscedastic Noise with sparse Bayesian Learning

We consider direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e., source powers), leading to stochastic maximum likelihood (ML) DOA estimation. The DOAs are estimated from multi-snapshot array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots.

ANALYSIS OF SPACE FRAMES WITH GENERALIZED SEMI-RIGID CONNECTIONS

A mechanical model and analytic method are proposed, in which, the axial, the shearing and the bending semi-rigid characteristics of space frames are taken into account. An independent zero-length connection element comprising six translational and rotational springs is used to simulate the beam-to-column connection. The model, namely six-spring mechanical model, has an advantage that the element number of structure does not increase. The matrix displacement method is used to analyze mechanism of the model, including element analysis and structural analysis. The stiffness matrix of the element is derived. Some reaction forces at the end of the element are obtained when it is subjected to two kinds of different loads respectively. The obtained stiffness matrix gets the characteristics of symmetry and singularity and that makes the size of total stiffness matrix for semi-rigid frame the same as that for frame with rigid joints.