46,152 research outputs found
Expectiles for subordinated Gaussian processes with applications
In this paper, we introduce a new class of estimators of the Hurst exponent
of the fractional Brownian motion (fBm) process. These estimators are based on
sample expectiles of discrete variations of a sample path of the fBm process.
In order to derive the statistical properties of the proposed estimators, we
establish asymptotic results for sample expectiles of subordinated stationary
Gaussian processes with unit variance and correlation function satisfying
(\kappa\in \RR) with . Via a
simulation study, we demonstrate the relevance of the expectile-based
estimation method and show that the suggested estimators are more robust to
data rounding than their sample quantile-based counterparts
How the instability of ranks under long memory affects large-sample inference
Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue that a rank other than one is unstable, whereas, a rank equal to one is stable. We provide empirical evidence supporting this argument. This has important consequences. Assuming a higher-order rank when it is not really there usually results in underestimating the order of the fluctuations of the statistic of interest. We illustrate this through various examples involving the sample variance, the empirical processes and the Whittle estimator.Accepted manuscrip
How the instability of ranks under long memory affects large-sample inference
Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue that a rank other than one is unstable, whereas, a rank equal to one is stable. We provide empirical evidence supporting this argument. This has important consequences. Assuming a higher-order rank when it is not really there usually results in underestimating the order of the fluctuations of the statistic of interest. We illustrate this through various examples involving the sample variance, the empirical processes and the Whittle estimator.Accepted manuscrip
Probability and Statistics for Particle Physicists
Lectures presented at the 1st CERN Asia-Europe-Pacific School of High-Energy
Physics, Fukuoka, Japan, 14-27 October 2012. A pedagogical selection of topics
in probability and statistics is presented. Choice and emphasis are driven by
the author's personal experience, predominantly in the context of physics
analyses using experimental data from high-energy physics detectors.Comment: Updated version of lectures given at the First Asia-Europe-Pacific
School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. Published
as a CERN Yellow Report (CERN-2014-001) and KEK report
(KEK-Proceedings-2013-8), K. Kawagoe and M. Mulders (eds.), 2014, p. 219.
Total 28 pages, 36 figure
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