Related papers: Universal Codes as a Basis for Nonparametric Testi…
We consider the problem of constructing sequential power-one tests where the null and alternative classes are specified indirectly through historical or offline data. More specifically, given an offline dataset consisting of observations…
In this paper, we consider the hypothesis testing of correlation between two $m$-uniform hypergraphs on $n$ unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperdges…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
An important assumption in the work on testing for structural breaks in time series consists in the fact that the model is formulated such that the stochastic process under the null hypothesis of "no change-point" is stationary. This…
Bailey showed that the general pointwise forecasting for stationary and ergodic time series has a negative solution. However, it is known that for Markov chains the problem can be solved. Morvai showed that there is a stopping time sequence…
Given the importance of the claim, we want to start by exposing the following consideration: this claim comes out more than a year after the article "Practical applications of Set Shaping Theory in Huffman coding" which reports the program…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
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…
We construct a statistic and null test for examining the stationarity of time-series of discrete symbols: whether two data streams appear to originate from the same underlying unknown dynamical system, and if any difference is statistically…
A system is data-independent with respect to a data type X iff the operations it can perform on values of type X are restricted to just equality testing. The system may also store, input and output values of type X. We study model checking…
Hypothesis testing based on surrogate data has emerged as a popular way to test the null hypothesis that a signal is a realization of a linear stochastic process. Typically, this is done by generating surrogates which are made to conform to…
Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual…
In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
As it is known, universal codes, which estimate the entropy rate consistently, exist for stationary ergodic sources over finite alphabets but not over countably infinite ones. We generalize universal coding as the problem of universal…
For ordinal outcomes, we construct sequences of alternative hypotheses in increasing departures from the sharp null hypothesis of zero treatment effect on each experimental unit, to help assess the powers of randomization tests in…
The use of ordinal patterns (OPs) for analyzing the dependence structure of univariate and continuously distributed processes has gained popularity in recent years. This research goes one step further and considers the transcripts being…
We address the recently suggested problem of causal lossless coding of a randomly arriving source samples. We construct variable-to-fixed coding schemes and show that they outperform the previously considered fixed-to-variable schemes when…
We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type I error control and…