Spatial scan statistics are well-known methods for cluster detection and widely used in epidemiology medical studies detecting evaluating the statistical significance of disease hotspots. For sake simplicity, classical spatial statistic assumes that observations outcome variable different locations independent, while practice data may exhibit a correlation. In this article, we use autoregressiv...

Abstract When assessing the oil reserves of a given region, often the statistic S = R/P is used, where R denotes the amount of proven reserves in the region and P is the current rate of production. This statistic can be misleading because the rate of production typically varies over time. We investigate a general framework for oil discovery and production and find the limit of S as time tends t...

In a randomized clinical trial, a statistic that measures the proportion of treatment effect on the primary clinical outcome that is explained by the treatment effect on a surrogate outcome is a useful concept. We investigate whether a statistic proposed to estimate this proportion can be given a causal interpretation as defined by models of counterfactual variables. For the situation of binary...

A match statistic considered by Khidr (1981) is interpreted in terms of crossings of the empirical and true distribution functions and a simpler alternate derivation of its distribution provided. This approach can also be used to obtain the distribution of a two-sample match statistic, considered earlier by Tak~tcs (1971).

The multivariate nonlinear Granger causality developed by Bai et al. (2010) (Mathematics and Computers in simulation. 2010; 81: 5-17) plays an important role in detecting the dynamic interrelationships between two groups of variables. Following the idea of Hiemstra-Jones (HJ) test proposed by Hiemstra and Jones (1994) (Journal of Finance. 1994; 49(5): 1639-1664), they attempt to establish a cen...

Let X1, X2, . . . be independent copies of a random variable X whose distribution function is denoted by F. There have been many studies on characterizations of F via linear regression relations of one order statistic on one or two other order statistics. See Wesolowski & Ahsanullah (1997) for references and the most complete results. Similarly, the regression of one record value on another has...