46,152 research outputs found

    Expectiles for subordinated Gaussian processes with applications

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    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 ρ(i)κiα\rho(i)\sim \kappa|i|^{-\alpha} (\kappa\in \RR) with α>0\alpha>0. 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

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    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

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    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

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    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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