Asymptotic properties of sequences iteratively generated by point-to-set maps

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

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Asymptotic properties of M-estimators based on estimating equations and censored data in semi-parametric models with multiple change points

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2020.124883 ◽

2021 ◽

Vol 497 (2) ◽

pp. 124883

Author(s):

Salim Bouzebda ◽

Anouar Abdeldjaoued Ferfache

Keyword(s):

Censored Data ◽

Asymptotic Properties ◽

Estimating Equations ◽

Parametric Models ◽

Change Points

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Opacity from Loops in AdS

Journal of High Energy Physics ◽

10.1007/jhep02(2021)089 ◽

2021 ◽

Vol 2021 (2) ◽

Cited By ~ 1

Author(s):

Alexandria Costantino ◽

Sylvain Fichet

Keyword(s):

Imaginary Part ◽

Quantum Dynamics ◽

Model Building ◽

Asymptotic Properties ◽

The Self ◽

Effective Theory ◽

Self Energy ◽

Higher Dimensional ◽

Timelike Region ◽

Spectral Representations

Abstract We investigate how quantum dynamics affects the propagation of a scalar field in Lorentzian AdS. We work in momentum space, in which the propagator admits two spectral representations (denoted “conformal” and “momentum”) in addition to a closed-form one, and all have a simple split structure. Focusing on scalar bubbles, we compute the imaginary part of the self-energy ImΠ in the three representations, which involves the evaluation of seemingly very different objects. We explicitly prove their equivalence in any dimension, and derive some elementary and asymptotic properties of ImΠ.Using a WKB-like approach in the timelike region, we evaluate the propagator dressed with the imaginary part of the self-energy. We find that the dressing from loops exponentially dampens the propagator when one of the endpoints is in the IR region, rendering this region opaque to propagation. This suppression may have implications for field-theoretical model-building in AdS. We argue that in the effective theory (EFT) paradigm, opacity of the IR region induced by higher dimensional operators censors the region of EFT breakdown. This confirms earlier expectations from the literature. Specializing to AdS5, we determine a universal contribution to opacity from gravity.

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