Related papers: Nonparametric tests of the Markov hypothesis in co…
We propose a sequential nonparametric test for detecting a change in distribution, based on windowed Kolmogorov--Smirnov statistics. The approach is simple, robust, highly computationally efficient, easy to calibrate, and requires no…
In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to…
We propose consistent nonparametric tests of conditional independence for time series data. Our methods are motivated from the difference between joint conditional cumulative distribution function (CDF) and the product of conditional CDFs.…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We study the problem of estimating the coefficients of a diffusion (X_t,t\geq 0); the estimation is based on discrete data X_{n\Delta},n=0,1,...,N. The sampling frequency \Delta^{-1} is constant, and asymptotics are taken as the number N of…
This paper proposes a Kolmogorov-Smirnov type statistic and a Cram\'er-von Mises type statistic to test linearity in semi-functional partially linear regression models. Our test statistics are based on a residual marked empirical process…
This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based…
For Kolmogorov test we find natural conditions of uniform consistency of sets of alternatives approaching to hypothesis. Sets of alternatives can be defined both in terms of distribution functions and in terms of densities.
We derive an asymptotic theory of nonparametric estimation for a time series regression model $Z_t=f(X_t)+W_t$, where \ensuremath\{X_t\} and \ensuremath\{Z_t\} are observed nonstationary processes and $\{W_t\}$ is an unobserved stationary…
We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…
We consider the change-point problem for the marginal distribution of subordinated Gaussian processes that exhibit long-range dependence. The asymptotic distributions of Kolmogorov-Smirnov- and Cram\'{e}r-von Mises type statistics are…
This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain tests statistics for breaks in…
Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…
We study two nonparametric tests of the hypothesis that a sequence of independent observations is identically distributed against the alternative that at a single change point the distribution changes. The tests are based on the Cramer-von…
Consider a continuous time Markov chain with rates Q in the state space \Lambda\cup\{0\} with 0 as an absorbing state. In the associated Fleming-Viot process N particles evolve independently in \Lambda with rates Q until one of them…
This paper considers hidden Markov models where the observations are given as the sum of a latent state which lies in a general state space and some independent noise with unknown distribution. It is shown that these fully nonparametric…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
This paper develops goodness of fit statistics that can be used to formally assess Markov random field models for spatial data, when the model distributions are discrete or continuous and potentially parametric. Test statistics are formed…
We analyzed the effect of the deviation of the exact distribution of the p-values from the uniform distribution on the Kolmogorov-Smirnov (K-S) test that was implemented as the second-level randomness test. We derived an inequality that…