Let {X,Xn,n≥1} be a sequence of i.i.d. random variables, and set Sn=X1+⋯+Xn. For 1<p≤3/2, if EX=0, EX2=1 and E[|X|2p(log+|X|)−p]<∞, we prove that limε↘0ε1/2∑n≥2np−2P(|Sn|≥(2p−2+ε)nlogn)=2p−1, thus extending a result by Spătaru (2004). For 1<p≤3/2 and δ>0, we establish conditions for the convergence of the related series ∑n≥2np−2P(|Sn|≥(2p−2)nlogn+δn1/2loglogn(2p−2)nlogn), and derive its precise asymptotic as δ↘1/2.

Considering the covariance selection problem of multivariate normal distributions, we show that its Fenchel dual formulation is insightful and allows one to calculate direct estimates under decomposable models. We next generalize the covariance selection to multivariate dependence, which...

It is common in epidemiology and other fields that the analyzing data is collected with error-prone observations and the variances of the measurement errors change across observations. Heteroscedastic measurement error (HME) models have been developed for such data. This paper extends the...

In the present article we are interested in presenting some properties of testing homogeneity of multivariate normal mean vectors against an order restriction for two cases, the covariance matrices are known, and the case that they have an unknown scale factor. This problem of testing with these...