131 research outputs found
Strategies for sequential prediction of stationary time series
We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combination of several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. We offer an analog result for the prediction of stationary gaussian processes.Sequential prediction, ergodic process, individual sequence, gaussian process
Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum
In this paper, we revisit the classical results on the generalized St.
Petersburg sums. We determine the limit distribution of the St. Petersburg sum
conditioning on its maximum, and we analyze how the limit depends on the value
of the maximum. As an application, we obtain an infinite sum representation of
the distribution function of the possible semistable limits. In the
representation, each term corresponds to a given maximum, in particular this
result explains that the semistable behavior is caused by the typical values of
the maximum.Comment: Published at http://dx.doi.org/10.3150/14-BEJ685 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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Detecting ineffective features for pattern recognition
For a binary classification problem, the hypothesis testing is studied, that a component of the observation vector is not effective, i.e., that component carries no information for the classification. We introduce nearest neighbor and partitioning estimates of the Bayes error probability, which result in a strongly consistent test
On rate optimal private regression under local differential privacy
We consider the problem of estimating a regression function from anonymized
data in the framework of local differential privacy. We propose a novel
partitioning estimate of the regression function, derive a rate of convergence
for the excess prediction risk over H\"older classes, and prove a matching
lower bound. In contrast to the existing literature on the problem the
so-called strong density assumption on the design distribution is obsolete.Comment: Revised versio
Poisson limit of an inhomogeneous nearly critical INAR(1) model
An inhomogeneous first--order integer--valued autoregressive (INAR(1))
process is investigated, where the autoregressive type coefficient slowly
converges to one. It is shown that the process converges weakly to a Poisson or
a compound Poisson distribution.Comment: Latex2e pdfeTex Version 3, 22 pages, submitted to ACTA Sci. Math.
(Szeged
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