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In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking…
In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite ($\alpha N$) and sampled under two different random times. Based on…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Majority-vote ensembles achieve variance reduction by averaging over diverse, approximately independent base learners. When training data exhibits Markov dependence, as in time-series forecasting, reinforcement learning (RL) replay buffers,…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…
For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…
Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…
The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…
We noisily observe solutions of an ordinary differential equation $\dot u = f(u)$ at given times, where $u$ lives in a $d$-dimensional state space. The model function $f$ is unknown and belongs to a H\"older-type smoothness class with…
This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information…
In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…
This paper is concerned with the detection of multiple change-points in the joint distribution of independent categorical variables. The procedures introduced rely on model selection and are based on a penalized least-squares criterion.…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…