Investigating Light Curve Modulation via Kernel Smoothing. I. Application to 53 fundamental mode and first-overtone Cepheids in the LMC

Recent studies have revealed a hitherto unknown complexity of Cepheid pulsation. We implement local kernel regression to search for both period and amplitude modulations simultaneously in continuous time and to investigate their detectability, and test this new method on 53 classical Cepheids from the OGLE-III catalog. We determine confidence intervals using parametric and non-parametric bootstrap sampling to estimate significance and investigate multi-periodicity using a modified pre-whitening approach that relies on time-dependent light curve parameters. We find a wide variety of period and amplitude modulations and confirm that first overtone pulsators are less stable than fundamental mode Cepheids. Significant temporal variations in period are more frequently detected than those in amplitude. We find a range of modulation intensities, suggesting that both amplitude and period modulations are ubiquitous among Cepheids. Over the 12-year baseline offered by OGLE-III, we find that period changes are often non-linear, sometimes cyclic, suggesting physical origins beyond secular evolution. Our method more efficiently detects modulations (period and amplitude) than conventional methods reliant on pre-whitening with constant light curve parameters and more accurately pre-whitens time series, removing spurious secondary peaks effectively.Comment: Re-submitted including revisions to Astronomy and Astrophysic

Model misspecification in peaks over threshold analysis

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of the marginal distribution of threshold exceedances and of the mean cluster size, but requires the choice of a threshold and of a run parameter, $K$, that determines how exceedances are declustered. We extend a class of estimators of the reciprocal mean cluster size, known as the extremal index, establish consistency and asymptotic normality, and use the compound Poisson process to derive misspecification tests of model validity and of the choice of run parameter and threshold. Simulated examples and real data on temperatures and rainfall illustrate the ideas, both for estimating the extremal index in nonstandard situations and for assessing the validity of extremal models.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS292 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Likelihood estimation of the extremal index

The article develops the approach of Ferro and Segers (J.R. Stat. Soc., Ser. B 65:545, 2003) to the estimation of the extremal index, and proposes the use of a new variable decreasing the bias of the likelihood based on the point process character of the exceedances. Two estimators are discussed: a maximum likelihood estimator and an iterative least squares estimator based on the normalized gaps between clusters. The first provides a flexible tool for use with smoothing methods. A diagnostic is given for condition $D^{(2)}(u_n)$ , under which maximum likelihood is valid. The performance of the new estimators were tested by extensive simulations. An application to the Central England temperature series demonstrates the use of the maximum likelihood estimator together with smoothing method