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The estimation of regression parameters in one dimensional broken stick models is a research area of statistics with an extensive literature. We are interested in extending such models by aiming to recover two or more intersecting…

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…

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…

We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the function are proven. By the estimation the well known…

We consider the residual-based or naive bootstrap for functional autoregressions of order 1 and prove that it is asymptotically valid for, e.g., the sample mean and for empirical covariance operator estimates. As a crucial auxiliary result,…

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

We propose a novel method for estimating nonseparable selection models. We show that, for a given selection function, the potential outcome distributions are nonparametrically identified from the selected outcome distributions and can be…

This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this…

We study a Markov matching market involving a planner and a set of strategic agents on the two sides of the market. At each step, the agents are presented with a dynamical context, where the contexts determine the utilities. The planner…

We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems, one of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the…

This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…

We propose a Markov Chain Monte Carlo (MCMC) algorithm based on Gibbs sampling with parallel tempering to solve nonlinear optimal control problems. The algorithm is applicable to nonlinear systems with dynamics that can be approximately…

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…

Linear time series modelling is dominated by the use of purely autoregressive models even though incorporating moving average components can greatly improve parsimony. We present a convex formulation for vector-ARMA system identification…

We develop a recursion for hidden Markov model of any order h, which allows us to obtain the posterior distribution of the latent state at every occasion, given the previous h states and the observed data. With respect to the well-known…

This paper investigates the role of high-dimensional information sets in the context of Markov switching models with time varying transition probabilities. Markov switching models are commonly employed in empirical macroeconomic research…

We present a novel methodology utilizing Recurrent Neural Networks (RNNs) to classify Markovian and non-Markovian quantum processes, leveraging time series data derived from Choi states. The model exhibits exceptional accuracy, surpassing…

In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a…

This article studies identification and estimation for the network vector autoregressive model with nonstationary regressors. In particular, network dependence is characterized by a nonstochastic adjacency matrix. The information set…