Related papers: Deviation inequalities and moderate deviations for…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
Blind methods often separate or identify signals or signal subspaces up to an unknown scaling factor. Sometimes it is necessary to cope with the scaling ambiguity, which can be done through reconstructing signals as they are received by…
We are concerned with random ordinary differential equations (RODEs). Our main question of interest is how uncertainties in system parameters propagate through the possibly highly nonlinear dynamical system and affect the system's…
The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a…
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…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…
Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…
For normal canonical models, and more generally a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide…
The $L^p$ maximal inequalities for martingales are one of the classical results in the theory of stochastic processes. Here we establish the sharp moderate maximal inequalities for one-dimensional diffusion processes, which include the…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
Ewens-Pitman model has been successfully applied to various fields including Bayesian statistics. There are four important estimators $K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n}, M_{1,m}^{(n)}$ are related to…
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order…
We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…
When estimating the directed information between two jointly stationary Markov processes, it is typically assumed that the recipient of the directed information is itself Markov of the same order as the joint process. While this assumption…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The…
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…