We consider dependent multidimensionally indexed random variables whose dependence is determined by the distance of their indices. This provides a generalization of the well-known notion of m-dependence. For the partial sum of a collection of such variables we prove a central limit theorem.

This paper addresses some of the questions raised in a debate between (Deaton and Paxson, 1998) and (Deaton and Paxson, 2003) and Gan and Vernon (2003) in the Journal of Political Economy. At issue is what, on the basis of theory, the behaviour of households should be in relation to expenditure...

In this paper two Kolmogorov inequalities are presented for the sample average of independent (but not necessarily identically distributed) Bernoulli random variables.

In this paper a Kolmogorov probability inequality for weighted U-statistics based on Bernoulli kernels is presented. This inequality which extends the results of [Turner, D.W., Young, D.M., Seaman, J.W., 1995. A Kolmogorov inequality for the sum of independent Bernoulli random variables with...