A note on prediction for discrete time series

Gusztáv Morvai; Benjamin Weiss

Displaying similar documents to “A note on prediction for discrete time series”

Inferring the residual waiting time for binary stationary time series

Gusztáv Morvai, Benjamin Weiss (2014)

Kybernetika

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For a binary stationary time series define $σ_{n}$ to be the number of consecutive ones up to the first zero encountered after time $n$ , and consider the problem of estimating the conditional distribution and conditional expectation of $σ_{n}$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the...

About stability of risk-seeking optimal stopping

Raúl Montes-de-Oca, Elena Zaitseva (2014)

Kybernetika

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We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space $X$ . It is supposed that the transition probability $p (\cdot | x)$ , $x \in X$ is approximated by the transition probability $\tilde{p} (\cdot | x)$ , $x \in X$ , and that the stopping rule ${\tilde{f}}_{*}$ , which is optimal for the process with the transition probability $\tilde{p}$ is applied to the process with the transition probability $p$ . We give an upper bound (expressed in term of the total variation distance:...

On an algorithm for testing T4 solvability of max-plus interval systems

Helena Myšková (2012)

Kybernetika

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In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$ , where $a \oplus b = max {a, b}$ , $a \otimes b = a + b$ . The notation $𝔸 \otimes x = 𝕓$ represents an interval system of linear equations, where $𝔸 = [\bar{b}, \bar{A}]$ and $𝕓 = [\underset{̲}{b}, \bar{b}]$ are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and...

Equivalence of compositional expressions and independence relations in compositional models

Francesco M. Malvestuto (2014)

Kybernetika

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We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system $ℋ$ is star-like with...

Universally typical sets for ergodic sources of multidimensional data

Tyll Krüger, Guido F. Montúfar, Ruedi Seiler, Rainer Siegmund-Schultze (2013)

Kybernetika

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We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below...