The asymptotics of waiting times between stationary processes, allowing distortion

The First Order Asymptotics of Waiting Times between Stationary Processes under Nonstandard Conditions

We give necessary and sufficient conditions for the almost sure convergence of − 1 n logQ(B(X 1 ,D)) when (Xn)n≥1 is stationary and ergodic and when Q is stationary and satisfies certain strong mixing conditions. B(x1 ,D) is the single letter, additive distortion ball of radius D at the point x1 := (x1, . . . , xn). The asymptotic behavior of this quantity arises frequently in rate distortion t...

The first-order asymptotic of waiting times with distortion between stationary processes

Asymptotic Recurrence and Waiting times for Stationary Processes

Let X = fX n ; n 2 Zg be a discrete-valued stationary ergodic process distributed according to P and let x = of the recurrence time R n deened as the rst time that the initial n-block x n 1 = (x 1 ; x 2 ; : : : ; x n) reappears in the past of x. We identify an associated random walk, ? log P (X n 1); on the same probability space as X, and we prove a strong approximation theorem between log R n...

Gradient estimation for quantiles of stationary waiting times

Quantiles of customer based performance characteristics have been adopted in many areas for measuring the quality of service. Recently, sensitivity analysis of quantiles has attracted quite some attention. Sensitivity analysis of quantiles is particularly challenging as quantiles cannot be expressed as the expected value of some sample performance function, and it is therefore not evident how s...

The effect of practice budgets on patient waiting times: allowing for selection bias.

Under the UK fundholding scheme, general practices could elect to hold a budget to meet the costs of some types of elective surgery (chargeable admissions) for their patients. It was alleged that patients of fundholding practices had shorter waits for elective surgery than the patients of non-fundholders. Comparison of waiting times between fundholding and non-fundholding practices are potentia...