22,248 research outputs found
Continuous testing for Poisson process intensities: A new perspective on scanning statistics
We propose a novel continuous testing framework to test the intensities of
Poisson Processes. This framework allows a rigorous definition of the complete
testing procedure, from an infinite number of hypothesis to joint error rates.
Our work extends traditional procedures based on scanning windows, by
controlling the family-wise error rate and the false discovery rate in a
non-asymptotic manner and in a continuous way. The decision rule is based on a
\pvalue process that can be estimated by a Monte-Carlo procedure. We also
propose new test statistics based on kernels. Our method is applied in
Neurosciences and Genomics through the standard test of homogeneity, and the
two-sample test
Distributed Hypothesis Testing with Privacy Constraints
We revisit the distributed hypothesis testing (or hypothesis testing with
communication constraints) problem from the viewpoint of privacy. Instead of
observing the raw data directly, the transmitter observes a sanitized or
randomized version of it. We impose an upper bound on the mutual information
between the raw and randomized data. Under this scenario, the receiver, which
is also provided with side information, is required to make a decision on
whether the null or alternative hypothesis is in effect. We first provide a
general lower bound on the type-II exponent for an arbitrary pair of
hypotheses. Next, we show that if the distribution under the alternative
hypothesis is the product of the marginals of the distribution under the null
(i.e., testing against independence), then the exponent is known exactly.
Moreover, we show that the strong converse property holds. Using ideas from
Euclidean information theory, we also provide an approximate expression for the
exponent when the communication rate is low and the privacy level is high.
Finally, we illustrate our results with a binary and a Gaussian example
On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection
The distributed hypothesis testing problem with full side-information is
studied. The trade-off (reliability function) between the two types of error
exponents under limited rate is studied in the following way. First, the
problem is reduced to the problem of determining the reliability function of
channel codes designed for detection (in analogy to a similar result which
connects the reliability function of distributed lossless compression and
ordinary channel codes). Second, a single-letter random-coding bound based on a
hierarchical ensemble, as well as a single-letter expurgated bound, are derived
for the reliability of channel-detection codes. Both bounds are derived for a
system which employs the optimal detection rule. We conjecture that the
resulting random-coding bound is ensemble-tight, and consequently optimal
within the class of quantization-and-binning schemes
Caste Based Discrimination: Evidence and Policy
Caste-based quotas in hiring have existed in the public sector in India for decades. Recently there has been debate about introducing similar quotas in private sector jobs. This paper uses an audit study to determine the extent of caste-based discrimination in the Indian private sector. On average low-caste applicants need to send 20 percent more resumes than high-caste applicants to get the same callback. Differences in callback which favor high-caste applicants are particularly large when hiring is done by male recruiters or by Hindu recruiters. This finding suggests that the differences in callback between high and low-caste applicants are not entirely due to statistical discrimination. High-caste applicants are also differentially favored by firms with a smaller scale of operations, while low-caste applicants are favored by firms with a larger scale of operations. This finding is consistent with taste-based theories of discrimination and with commitments made by large firms to hire actively from among low-caste groups.field experiments, discrimination, public policy, human resources
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