相关论文: Universal Codes as a Basis for Time Series Testing

We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…

We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…

In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and…

We consider a stationary and ergodic source $p$ generated symbols $x_1 ... x_t$ from some finite set $A$ and a null hypothesis $H_0$ that $p$ is Markovian source with memory (or connectivity) not larger than $m, (m >= 0).$ The alternative…

We consider nonparametric or universal sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are…

In this paper, we present a general framework for testing relevant hypotheses in functional time series. Our unified approach covers one-sample, two-sample, and change point problems under contaminated observations with arbitrary sampling…

We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides…

In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…

We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…

Given a discrete-valued sample $X_1,...,X_n$ we wish to decide whether it was generated by a distribution belonging to a family $H_0$, or it was generated by a distribution belonging to a family $H_1$. In this work we assume that all…

We describe and experimentally investigate a method to construct forecasting algorithms for stationary and ergodic processes based on universal measures (or so-called universal data compressors). Using some geophysical and economical time…

We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…

There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…

Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…

In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…

We consider the problem of the construction of the goodness-of-fit tests for diffusion processes with small noise. The basic hypothesis is composite parametric and our goal is to obtain asymptotically distribution free tests. We propose two…

Given a finite-valued sample $X_1,...,X_n$ we wish to test whether it was generated by a stationary ergodic process belonging to a family $H_0$, or it was generated by a stationary ergodic process outside $H_0$. We require the Type I error…

We consider the goodness of fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We…

We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…