Estimation of Sample Spacing in Stochastic Processes

Abstract

Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies.

Central limit theorem for mean and variogram estimators in Lévy–based models

“…We show, under mild regularity conditions, that both S and T (h) are asymptotically normally distributed and give explicit expressions for the asymptotic variances. It turns out that the asymptotic variance of T (h) is equal to an approximate variance, earlier derived in [14]. In the latter paper, the approximate variance was used in the assessment of the precision of a section spacing estimator in electron microscopy.…”

“…In the following theorem we give the asymptotic normality ofT . In fact, apart from the scaling, the asymptotic variance is equal to the approximation to the variance suggested in [14].…”

“…This estimator is studied in [13], where an expression for the variance ofT Γ is derived. Furthermore an approximate expression for the variance ofd 0 is found using a Taylor approximation.…”