98,624 research outputs found
On Multiple Hypothesis Testing with Rejection Option
We study the problem of multiple hypothesis testing (HT) in view of a
rejection option. That model of HT has many different applications. Errors in
testing of M hypotheses regarding the source distribution with an option of
rejecting all those hypotheses are considered. The source is discrete and
arbitrarily varying (AVS). The tradeoffs among error probability
exponents/reliabilities associated with false acceptance of rejection decision
and false rejection of true distribution are investigated and the optimal
decision strategies are outlined. The main result is specialized for discrete
memoryless sources (DMS) and studied further. An interesting insight that the
analysis implies is the phenomenon (comprehensible in terms of
supervised/unsupervised learning) that in optimal discrimination within M
hypothetical distributions one permits always lower error than in deciding to
decline the set of hypotheses. Geometric interpretations of the optimal
decision schemes are given for the current and known bounds in multi-HT for
AVS's.Comment: 5 pages, 3 figures, submitted to IEEE Information Theory Workshop
201
Testing Universality in Critical Exponents: the Case of Rainfall
One of the key clues to consider rainfall as a self-organized critical
phenomenon is the existence of power-law distributions for rain-event sizes. We
have studied the problem of universality in the exponents of these
distributions by means of a suitable statistic whose distribution is inferred
by several variations of a permutational test. In contrast to more common
approaches, our procedure does not suffer from the difficulties of multiple
testing and does not require the precise knowledge of the uncertainties
associated to the power-law exponents. When applied to seven sites monitored by
the Atmospheric Radiation Measurement Program the test lead to the rejection of
the universality hypothesis, despite the fact that the exponents are rather
close to each other
A Random Attention Model
This paper illustrates how one can deduce preference from observed choices
when attention is not only limited but also random. In contrast to earlier
approaches, we introduce a Random Attention Model (RAM) where we abstain from
any particular attention formation, and instead consider a large class of
nonparametric random attention rules. Our model imposes one intuitive
condition, termed Monotonic Attention, which captures the idea that each
consideration set competes for the decision-maker's attention. We then develop
revealed preference theory within RAM and obtain precise testable implications
for observable choice probabilities. Based on these theoretical findings, we
propose econometric methods for identification, estimation, and inference of
the decision maker's preferences. To illustrate the applicability of our
results and their concrete empirical content in specific settings, we also
develop revealed preference theory and accompanying econometric methods under
additional nonparametric assumptions on the consideration set for binary choice
problems. Finally, we provide general purpose software implementation of our
estimation and inference results, and showcase their performance using
simulations
Testing Monotonicity of Pricing Kernels
The behaviour of market agents has always been extensively covered in the literature. Risk averse behaviour, described by von Neumann and Morgenstern (1944) via a concave utility function, is considered to be a cornerstone of classical economics. Agents prefer a fixed profit over uncertain choice with the same expected value, however lately there has been a lot of discussion about the reliability of this approach. Some authors have shown that there is a reference point where market utility functions are convex. In this paper we have constructed a test to verify uncertainty about the concavity of agents’ utility function by testing the monotonicity of empirical pricing kernels (EPKs). A monotone decreasing EPK corresponds to a concave utility function while non-monotone decreasing EPK means non-averse pattern on one or more intervals of the utility function. We investigated the EPK for German DAX data for years 2000, 2002 and 2004 and found the evidence of non-concave utility functions: H0 hypothesis of monotone decreasing pricing kernel was rejected at 5% and 10% significance level in 2002 and at 10% significance level in 2000.Risk Aversion, Pricing kernel
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