22,472 research outputs found
Two Rank Order Tests for \u3cem\u3eM\u3c/em\u3e-ary Detection
We consider a general M-ary detection problem where, given M groups of L samples each, the problem is to identify which unique group of L samples have come from the signal hypothesis. The optimal likelihood ratio test is unrealizable, when the joint distribution of ML samples is not completely known. In this paper we consider two rank order types of tests termed as the modified rank test (MRT) and the modified rank test with row sort (MRTRS). We examine through simulation, the small sample probability of error performances of MRT and MRTRS for detecting a signal among contaminants. Numerically computable closed –form error expressions are derived for some special cases. Asymptotic (large sample) error rate of MRT is also derived. The results indicate that MRTRS provides improved performance over other previously known rank tests
A modified Corrado test for assessing abnormal security returns
Event studies typically use the methodology developed by Fama et al. [19699. Fama , E. , Fisher , L. , Jensen , M. and Roll , R. 1969 . The adjustment of stock prices to new information . International Economic Review , 10 ( 1 ) : 1 – 21 . [CrossRef] View all references. The adjustment of stock prices to new information. International Economic Review 10, no. 1: 1–21] to segregate a stock's return into expected and unexpected components. Moreover, conventional practice assumes that abnormal returns evolve in terms of a normal distribution. There is, however, an increasing tendency for event studies to employ non-parametric testing procedures due to the mounting empirical evidence which shows that stock returns are incompatible with the normal distribution. This paper focuses on the widely used non-parametric ranking procedure developed by Corrado [19896. Corrado , C. 1989 . A nonparametric test for abnormal security price performance in event studies . Journal of Financial Economics , 23 ( 2 ) : 385 – 95 . [CrossRef], [Web of Science ®] View all references. A nonparametric test for abnormal security price performance in event studies. Journal of Financial Economics 23, no. 2: 385–95] for assessing the significance of abnormal security returns. In particular, we develop a consistent estimator for the variance of the sum of ranks of the abnormal returns, and show how this leads to a more efficient test statistic (as well as to less cumbersome computational procedures) than the test originally proposed by Corrado (19896. Corrado , C. 1989 . A nonparametric test for abnormal security price performance in event studies . Journal of Financial Economics , 23 ( 2 ) : 385 – 95 . [CrossRef], [Web of Science ®] View all references). We also use the theorem of Berry [19413. Berry , A. 1941 . The accuracy of the Gaussian approximation to the sum of independent variates . Transactions of the American Mathematical Society , 49 ( 1 ) : 122 – 36 . [CrossRef] View all references. The accuracy of the Gaussian approximation to the sum of independent variates. Transactions of the American Mathematical Society 49, no. 1: 122–36] and Esseen [19458. Esseen , C. 1945 . Fourier analysis of distribution functions: A mathematical study of the Laplace–Gaussian law . Acta Mathematica , 77 ( 1 ) : 1 – 125 . [CrossRef] View all references. Fourier analysis of distribution functions: A mathematical study of the Laplace–Gaussian law. Acta Mathematica 77, no. 1: 1–125] to demonstrate how the distribution of the modified Corrado test statistic developed here asymptotically converges towards the normal distribution. This shows that describing the distributional properties of the sum of the ranks in terms of the normal distribution is highly problematic for small sample sizes and small event windows. In these circumstances, we show that a second-order Edgeworth expansion provides a good approximation to the actual probability distribution of the modified Corrado test statistic. The application of the modified Corrado test developed here is illustrated using data for the purchase and sale by UK directors of shares in their own companies
Planting trees in graphs, and finding them back
In this paper we study detection and reconstruction of planted structures in
Erd\H{o}s-R\'enyi random graphs. Motivated by a problem of communication
security, we focus on planted structures that consist in a tree graph. For
planted line graphs, we establish the following phase diagram. In a low density
region where the average degree of the initial graph is below some
critical value , detection and reconstruction go from impossible
to easy as the line length crosses some critical value ,
where is the number of nodes in the graph. In the high density region
, detection goes from impossible to easy as goes from
to , and reconstruction remains impossible so
long as . For -ary trees of varying depth and ,
we identify a low-density region , such that the following
holds. There is a threshold with the following properties.
Detection goes from feasible to impossible as crosses . We also show
that only partial reconstruction is feasible at best for . We
conjecture a similar picture to hold for -ary trees as for lines in the
high-density region , but confirm only the following part of
this picture: Detection is easy for -ary trees of size ,
while at best only partial reconstruction is feasible for -ary trees of any
size . These results are in contrast with the corresponding picture for
detection and reconstruction of {\em low rank} planted structures, such as
dense subgraphs and block communities: We observe a discrepancy between
detection and reconstruction, the latter being impossible for a wide range of
parameters where detection is easy. This property does not hold for previously
studied low rank planted structures
Detection of Sparse Positive Dependence
In a bivariate setting, we consider the problem of detecting a sparse
contamination or mixture component, where the effect manifests itself as a
positive dependence between the variables, which are otherwise independent in
the main component. We first look at this problem in the context of a normal
mixture model. In essence, the situation reduces to a univariate setting where
the effect is a decrease in variance. In particular, a higher criticism test
based on the pairwise differences is shown to achieve the detection boundary
defined by the (oracle) likelihood ratio test. We then turn to a Gaussian
copula model where the marginal distributions are unknown. Standard invariance
considerations lead us to consider rank tests. In fact, a higher criticism test
based on the pairwise rank differences achieves the detection boundary in the
normal mixture model, although not in the very sparse regime. We do not know of
any rank test that has any power in that regime
The TAOS Project: Statistical Analysis of Multi-Telescope Time Series Data
The Taiwanese-American Occultation Survey (TAOS) monitors fields of up to
~1000 stars at 5 Hz simultaneously with four small telescopes to detect
occultation events from small (~1 km) Kuiper Belt Objects (KBOs). The survey
presents a number of challenges, in particular the fact that the occultation
events we are searching for are extremely rare and are typically manifested as
slight flux drops for only one or two consecutive time series measurements. We
have developed a statistical analysis technique to search the multi-telescope
data set for simultaneous flux drops which provides a robust false positive
rejection and calculation of event significance. In this paper, we describe in
detail this statistical technique and its application to the TAOS data set.Comment: 15 pages, 14 figures. Submitted to PAS
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