The G statistic and its local version have been used extensively in spatial data analysis. The paper proves the asymptotic normality of the G statistic. Theorems in this paper imply the regular permutation test for the G statistic is valid.

We establish the asymptotic normality of the number of upper records in a sequence of iid geometric random variables. Large deviations and local limit theorems as well as approximation theorems for the number of lower records are also derived.

This paper considers a class of semiparametric models being the sum of a nonparametric trend function g and a FARIMA-GARCH error process. Estimation of g( ), the th derivative of g, by local polynomial tting is investigated. The focus is on the derivation of the asymptotic normality of ĝ( ). At rst a central limit theorem based on martingale theory is developed and asymptotic normality of the s...

Limit distribution results on quadratic and higher order variation quantities are derived for certain types of continuous local martingales, in particular for a class of OU-based stochastic volatility models. Some key words: Mixed asymptotic normality; Realised volatility; Quadratic variation.

Computer-aided detection systems aim at the automatic detection of diseases using different medical imaging modalities. In this paper, a novel approach to detecting normality/pathology in digital chest radiographs is proposed. The problem tackled is complicated since it is not focused on particular diseases but anything that differs from what is considered as normality. First, the areas of inte...