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Early Detection Techniques for Market Risk Failure
The implementation of appropriate statistical techniques for monitoring conditional VaR models, i.e, backtesting, reported by institutions is fundamental to determine their exposure to market risk. Backtesting techniques are important since the severity of the departures of the VaR model from market results determine the penalties imposed for inadequate VaR models. In this paper we make six contributions to backtesting techniques. In particular, we show that the Kupiec test can be viewed as a combination of CUSUM change point tests; we detail the lack of power of CUSUM methods in detecting violations of VaR as soon as these occur; we develop an alternative technique based on weighted U-statistic type processes that have power against wrong specifications of the risk measure and early detection; we show these new backtesting techniques are robust to the presence of estimation risk; we construct a new class of weight functions that can be used to weight our processes; and our methods are applicable both under conditional and unconditional VaR settings
Brownian Polymers in Poissonian Environment: a survey
We consider a space-time continuous directed polymer in random environment.
The path is Brownian and the medium is Poissonian. We review many results
obtained in the last decade, and also we present new ones. In this fundamental
setup, we can make use of fine formulas and strong tools from stochastic
analysis for Gaussian or Poisson measure, together with martingale techniques.
These notes cover the matter of a course presented during the Jean-Morlet chair
2017 of CIRM "Random Structures in Statistical Mechanics and Mathematical
Physics" in Marseille.Comment: 64 pages. 4 figure
The Overlooked Potential of Generalized Linear Models in Astronomy - I: Binomial Regression
Revealing hidden patterns in astronomical data is often the path to
fundamental scientific breakthroughs; meanwhile the complexity of scientific
inquiry increases as more subtle relationships are sought. Contemporary data
analysis problems often elude the capabilities of classical statistical
techniques, suggesting the use of cutting edge statistical methods. In this
light, astronomers have overlooked a whole family of statistical techniques for
exploratory data analysis and robust regression, the so-called Generalized
Linear Models (GLMs). In this paper -- the first in a series aimed at
illustrating the power of these methods in astronomical applications -- we
elucidate the potential of a particular class of GLMs for handling
binary/binomial data, the so-called logit and probit regression techniques,
from both a maximum likelihood and a Bayesian perspective. As a case in point,
we present the use of these GLMs to explore the conditions of star formation
activity and metal enrichment in primordial minihaloes from cosmological
hydro-simulations including detailed chemistry, gas physics, and stellar
feedback. We predict that for a dark mini-halo with metallicity , an increase of in the gas
molecular fraction, increases the probability of star formation occurrence by a
factor of 75%. Finally, we highlight the use of receiver operating
characteristic curves as a diagnostic for binary classifiers, and ultimately we
use these to demonstrate the competitive predictive performance of GLMs against
the popular technique of artificial neural networks.Comment: 20 pages, 10 figures, 3 tables, accepted for publication in Astronomy
and Computin
On the Design of LIL Tests for (Pseudo) Random Generators and Some Experimental Results
NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo)
random generators to detect deviations of a binary sequence from randomness. On
the one hand, as a counter example to NIST SP800-22 test suite, it is easy to
construct functions that are considered as GOOD pseudorandom generators by NIST
SP800-22 test suite though the output of these functions are easily
distinguishable from the uniform distribution. Thus these functions are not
pseudorandom generators by definition. On the other hand, NIST SP800-22 does
not cover some of the important laws for randomness. Two fundamental limit
theorems about random binary strings are the central limit theorem and the law
of the iterated logarithm (LIL). Several frequency related tests in NIST
SP800-22 cover the central limit theorem while no NIST SP800-22 test covers
LIL.
This paper proposes techniques to address the above challenges that NIST
SP800-22 testing suite faces. Firstly, we propose statistical distance based
testing techniques for (pseudo) random generators to reduce the above mentioned
Type II errors in NIST SP800-22 test suite. Secondly, we propose LIL based
statistical testing techniques, calculate the probabilities, and carry out
experimental tests on widely used pseudorandom generators by generating around
30TB of pseudorandom sequences. The experimental results show that for a sample
size of 1000 sequences (2TB), the statistical distance between the generated
sequences and the uniform distribution is around 0.07 (with for
statistically indistinguishable and for completely distinguishable) and the
root-mean-square deviation is around 0.005
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