By allowing the numbers appearing in a continued fraction to be random, one gets what are called random continued fractions. Under fairly general conditions, including the case when the random variables are i.i.d. non-negative, random continued fractions converge with probability one. A...

We obtain the rates of pointwise and uniform convergence of kernel density estimators using random bandwidths under i.i.d. as well as strongly mixing dependence assumptions. Pointwise rates are faster and not affected by the tail of the density.

In this note, we establish the convergence properties for a broad class of random variables of the form Sn = [integral operator]Fn(Tn - s)[nu]n(ds) where Tn is some random variable, Fn is an empirical distribution function based on an independent sample of size n, and [nu]n is some measure.

It is well known that symmetric statistics based on a kernel with finite second moment have a limit law which can be described by a multiple Wiener-Ito integral. However, if the kernel has less than second moments, no weak limit law holds in general. In the present paper we show that by a...

In this paper a stationary finite-state process is constructed that satisfies the ø-mixing condition but is not very weak Bernoulli with rate O(1/n). ø-mixing is implied by very weak Bernoulli with rate O(1/n), so this example shows very weak Bernoulli with rate O(1/n) is a strictly stronger...

We show consistency and asymptotic normality of certain estimators for expected exponential growth rates under i.i.d. observations. These statistical functionals are of the formT(F)=[integral operator]log[integral operator]h(x,y)F(dx)F(dy)and are applicable to dimension estimates (information...

A necessary and sufficient condition for the weak convergence of partial sums of strongly mixing random sequences towards p-stable distributions is established and applied to recent work of Davis (1983) and Jakubowski and Kobus (1987).