448,044 research outputs found
Notes on sum-tests and independence tests
We study statistical sum-tests and independence tests, in particular for computably enumerable semimeasures on a discrete domain. Among other things, we prove that for universal semimeasures every Sigma0/1-sum-test is bounded, but unbounded Pi0/1-sum-tests exist, and we study to what extent the latter can be universal. For universal semimeasures, in the unary case of sum-test we leave open whether universal Pi0/1-sum-tests exist, whereas in the binary case of independence tests we prove that they do not exist
Influence tests I: ideal composite hypothesis tests, and causal semimeasures
Ratios of universal enumerable semimeasures corresponding to hypotheses are
investigated as a solution for statistical composite hypotheses testing if an
unbounded amount of computation time can be assumed.
Influence testing for discrete time series is defined using generalized
structural equations. Several ideal tests are introduced, and it is argued that
when Halting information is transmitted, in some cases, instantaneous cause and
consequence can be inferred where this is not possible classically.
The approach is contrasted with Bayesian definitions of influence, where it
is left open whether all Bayesian causal associations of universal semimeasures
are equal within a constant. Finally the approach is also contrasted with
existing engineering procedures for influence and theoretical definitions of
causation.Comment: 29 pages, 3 figures, draf
Statistics of the electromagnetic response of a chaotic reverberation chamber
This article presents a study of the electromagnetic response of a chaotic
reverberation chamber (RC) in the presence of losses. By means of simulations
and of experiments, the fluctuations in the maxima of the field obtained in a
conventional mode-stirred RC are compared with those in a chaotic RC in the
neighborhood of the Lowest Useable Frequency (LUF). The present work
illustrates that the universal spectral and spatial statistical properties of
chaotic RCs allow to meet more adequately the criteria required by the Standard
IEC 61000-4-21 to perform tests of electromagnetic compatibility.Comment: 6 pages, 9 figure
Sub-computable Boundedness Randomness
This paper defines a new notion of bounded computable randomness for certain
classes of sub-computable functions which lack a universal machine. In
particular, we define such versions of randomness for primitive recursive
functions and for PSPACE functions. These new notions are robust in that there
are equivalent formulations in terms of (1) Martin-L\"of tests, (2) Kolmogorov
complexity, and (3) martingales. We show these notions can be equivalently
defined with prefix-free Kolmogorov complexity. We prove that one direction of
van Lambalgen's theorem holds for relative computability, but the other
direction fails. We discuss statistical properties of these notions of
randomness
On high-dimensional sign tests
Sign tests are among the most successful procedures in multivariate
nonparametric statistics. In this paper, we consider several testing problems
in multivariate analysis, directional statistics and multivariate time series
analysis, and we show that, under appropriate symmetry assumptions, the
fixed- multivariate sign tests remain valid in the high-dimensional case.
Remarkably, our asymptotic results are universal, in the sense that, unlike in
most previous works in high-dimensional statistics, may go to infinity in
an arbitrary way as does. We conduct simulations that (i) confirm our
asymptotic results, (ii) reveal that, even for relatively large , chi-square
critical values are to be favoured over the (asymptotically equivalent)
Gaussian ones and (iii) show that, for testing i.i.d.-ness against serial
dependence in the high-dimensional case, Portmanteau sign tests outperform
their competitors in terms of validity-robustness.Comment: Published at http://dx.doi.org/10.3150/15-BEJ710 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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