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This paper deals with the conditional quantile estimation based on left-truncated and right-censored data. Assuming that the observations with multivariate covariates form a stationary α-mixing sequence, the authors derive the strong convergence with rate, strong representation as well as asymptotic normality of the conditional quantile estimator. Also, a Berry-Esseen-type bound for the estimator is established. In addition, the finite sample behavior of the estimator is investigated via simulations. [ABSTRACT FROM AUTHOR]

Asymptotic error expansions in the sense of L ∞-norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing technique, and the key point in deriving them is the establishment of the error estimates for the mixed regularized Green’s functions with memory terms presented in R. Ewing at al., Int. J. Numer. Anal. Model 2 (2005), 301–328. As a result of all these higher order numerical approximations, they can be used to generate a posteriori error estimators for this mixed finite element approximation. [ABSTRACT FROM AUTHOR]

For an array of rowwise pairwise negative quadrant dependent, mean 0 random variables, Chandra, Li, and Rosalsky provided conditions under which weighted averages converge in L1 to 0. The Chandra, Li, and Rosalsky result is extended to Lr convergence (1≤r<2) and is shown to hold under weaker conditions by applying a mean convergence result of Sung and an inequality of Adler, Rosalsky, and Taylor. [ABSTRACT FROM AUTHOR]

For arrays of rowwise pairwise negative quadrant dependent random variables, conditions are provided under which weighted averages converge in mean to 0 thereby extending a result of Chandra, and conditions are also provided under which normed and centered row sums converge in mean to 0. These results are new even if the random variables in each row of the array are independent. Examples are provided showing (i) that the results can fail if the rowwise pairwise negative quadrant dependent hypotheses are dispensed with, and (ii) that almost sure convergence does not necessarily hold. [ABSTRACT FROM AUTHOR]

Let X be an observable random variable with unknown distribution function F(x)=P(X≤x), −∞, and let θ=sup{r≥0:E|X|r<∞}. We call θ the power of moments of the random variable X. Let X1,X2,…,Xn be a random sample of size n drawn from F(⋅). In this paper we propose the following simple point estimator of θ and investigate its asymptotic properties: θˆn=lognlogmax1≤k≤n|Xk|, where logx=ln(e∨x), −∞. In particular, we show that θˆn→Pθif and only iflimx→∞xrP(|X|>x)=∞∀r>θ. This means that, under very reasonable conditions on F(⋅), θˆn is actually a consistent estimator of θ. [ABSTRACT FROM AUTHOR]