Related papers: Exact test for Markov order
The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the…
Variable-order Markov models generate sequences over a finite alphabet by conditioning each symbol on the longest available suffix of the generated history. Regular constraints, by contrast, describe finite-horizon control requirements by…
Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…
Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, $\mathsf{Q}$, since $\exp…
The Importance Markov chain is a novel algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…
We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…
We introduce the concept of asymptotic period for an irreducible and aperiodic, discrete-time Markov chain X on a countable state space, and develop the theory leading to its formal definition. The asymptotic period of X equals one - its…
We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
We study the rate of convergence of the Markov chain on $S_n$ which starts with a random $(n-k)$-cycle for a fixed $k \geq 1$, followed by random transpositions. The convergence to the stationary distribution turns out to be of order $n$.…
We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
The conventional perspective on Markov chains considers decision problems concerning the probabilities of temporal properties being satisfied by traces of visited states. However, consider the following query made of a stochastic system…
The score test statistic using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the…
For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic…
We describe a suite of validation metrics that assess the credibility of a given automatic spike sorting algorithm applied to a given electrophysiological recording, when ground-truth is unavailable. By rerunning the spike sorter two or…
We prove several results concerning classifications, based on successive observations $(X_1,..., X_n)$ of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov…
This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time nonhomogeneous Markov process with a finite state space. The proposed tests are…
It is shown how a natural representation of perpetuities as asymptotically homogeneous in space Markov chains allows to prove various asymptotic tail results for stable perpetuities and limit theorems for unstable ones. Some of these…