In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...

Here, we propose a method of estimation of the derivatives of probability density based wavelets methods for a sequence of m−dependent random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for the such estimators.

We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.

In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.

where N(0, 1) is a standard normal random variable. Later Rempala and Wesolowski (2002) extended such a central limit theorem to general i.i.d. positive random variables. Recently, the central limit theorem for product of sums has also been studied for dependent random variables (c.f., Gonchigdanzan and Rempala (2006)). In this note, we will show that this kind of result follows from the invari...

We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of pairwise negative quadrant dependent random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts st...

we propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of pairwise negative quadrant dependent random variables with a common one-dimensional probability density function. some asymptotic properties of the proposed estimator are investigated. it is found that the estimators have similar properties to their counterparts st...