Search results for "tail"

Author response: Individual differences in selective attention predict speech identification at a cocktail party

2016

Transitivity in coherence-based probability logic

2016

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the squa…

The Psychological Science Accelerator’s COVID-19 rapid-response dataset

2023

Funder: Amazon Web Services (AWS) Imagine Grant

Weighted bounded mean oscillation applied to backward stochastic differential equations

2015

Abstract We deduce conditional L p -estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the solution ( Y , Z ) on subintervals of [ 0 , T ] . Some new results for the decoupling technique introduced in Geiss and Ylinen (2019) are obtained as well and some applications of the tail estimates are given.

Incorporating big microdata in life table construction: A hypothesis-free estimator

2019

Abstract The IT revolution, now more than ever, offers a cheaper and faster way to collect, store, transmit and process data. Detailed microdata of dates of death, migration and birth are already becoming available for general populations. In this paper, we develop within the family of period-based estimators a new, assumption-free estimator for constructing life tables. The estimator proposed exploits all the detailed data available and is free of the theoretical inconsistencies that the estimators currently used by most official statistical agencies have. We compute the proposed estimator for a real database and test the suitability of the hypotheses on which the estimators used so far re…

Power laws and the market structure of tourism industry

2013

In this article, we use both graphical and analytical methods to investigate the market structure of one of the world’s fastest growing industries. For the German and Italian datasets, we show that the size distribution of tourism industry is heavy-tailed and consistent with a power-law behavior in its upper tail. Such a behavior seems quite persistent over the time horizon covered by our study, provided that during the period 2004–2009, the shape parameter is always in the vicinity of 2.5 for Germany and 2.6 for Italy. Size of the tourism industry has been proxied by the lodging capacity of hotel establishments: hotels, boarding houses, inns, lodging houses, motels, apartment hotels, touri…

Large deviations results for subexponential tails, with applications to insurance risk

1996

AbstractConsider a random walk or Lévy process {St} and let τ(u) = inf {t⩾0 : St > u}, P(u)(·) = P(· | τ(u) < ∞). Assuming that the upwards jumps are heavy-tailed, say subexponential (e.g. Pareto, Weibull or lognormal), the asymptotic form of the P(u)-distribution of the process {St} up to time τ(u) is described as u → ∞. Essentially, the results confirm the folklore that level crossing occurs as result of one big jump. Particular sharp conclusions are obtained for downwards skip-free processes like the classical compound Poisson insurance risk process where the formulation is in terms of total variation convergence. The ideas of the proof involve excursions and path decompositions for Mark…

k-Step shape estimators based on spatial signs and ranks

2010

In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in Dümbgen (1998) and Oja and Randles (2004) and further studied for example in Sirkiä et al. (2009). The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the es…

Fractional calculus approach to the statistical characterization of random variables and vectors

2009

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…

Understanding the determinants of volatility clustering in terms of stationary Markovian processes

2016

Abstract Volatility is a key variable in the modeling of financial markets. The most striking feature of volatility is that it is a long-range correlated stochastic variable, i.e. its autocorrelation function decays like a power-law τ − β for large time lags. In the present work we investigate the determinants of such feature, starting from the empirical observation that the exponent β of a certain stock’s volatility is a linear function of the average correlation of such stock’s volatility with all other volatilities. We propose a simple approach consisting in diagonalizing the cross-correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still kee…