Bootstrapping the empirical distribution of a stationary process with change-point

© 2019, Institute of Mathematical Statistics. All rights reserved. When detecting a change-point in the marginal distribution of a stationary time series, bootstrap techniques are required to determine critical values for the tests when the pre-change distribution is unknown. In this paper, we propose a sequential moving block bootstrap and demonstrate its validity under a converging alternative. Furthermore, we demonstrate that power is still achieved by the bootstrap under a non-converging alternative. We follow the approach taken by Peligrad in [14], and avoid assumptions of mixing, association or near epoch dependence. These results are applied to a linear process and are shown to be valid under very mild conditions on the existence of any moment of the innovations and a corresponding condition of summability of the coefficients

Change-point detection in the marginal distribution of a linear process

© 2016, Institute of Mathematical Statistics. All rights reserved. The subject of this paper is the detection of a change in the marginal distribution of a stationary linear process. By considering the marginal distribution, the change-point model can simultaneously incorporate any change in the coefficients and/or the innovations of the linear process. Furthermore, the change point can be random and data dependent. The key is an analysis of the asymptotic behaviour of the sequential empirical process, both with and without a change point. Our results hold under very mild conditions on the existence of any moment of the innovations and a corresponding condition of summability of the coefficients

The Quaternary lions of Ukraine and a trend of decreasing size in Panthera spelaea (advance online)

The fossil record of the cave lion, Panthera spelaea, suggests a gradual decrease in body size, the process peaking just before the extinction of the species at the end of the Late Pleistocene. Such an evolutionary trend appears rather unusual for a large felid species and requires further investigation. This study reviews the cave lions of Ukraine, whose fossils are known from 46 localities dated from 800 kyr to 18–17 kyr ago, with a special emphasis on size changes through time. We describe several important finds including those of Panthera spelaea fossilis from Sambir, Panthera spelaea ssp. from Bilykh Stin Cave and Panthera spelaea spelaea from Kryshtaleva Cave. We make subspecific identifications of specimens from the region and focus on their size characteristics. Our analysis of Ukrainian cave lions agrees with the temporal trend of decreasing size, particularly accelerating during MIS 2, as exemplified by the extremely small female skull from Kryshtaleva Cave. We provide a direct AMS date for this specimen (22.0–21.5 cal kyr BP), which suggests that the Kryshtaleva lioness must have belonged to a Panthera spelaea spelaea population forced south by the spreading ice sheet. We discuss some palaeoecological aspects of the evolutionary history and eventual extinction of the cave lion. Finally, we review the subfossil records of the extant lion Panthera leo known from several Ukrainian sites archaeologically dated to 6.4–2.0 kyr BP. These finds most probably represent the Persian lion Panthera leo persica