Related papers: A Large Deviation Inequality for $\beta$-mixing Ti…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common distribution $F$, where $F(x+\Delta)=F((x, x+T])$ is an $\mathcal{O}$-regularly varying…
We consider $\alpha$-mixing observations and deal with the estimation of the conditional mode of a scalar response variable $Y$ given a random variable $X$ taking values in a semi-metric space. We provide a convergence rate in $L^p$ norm of…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
Economic inequalities referring to specific regions are crucial in deepening spatial heterogeneity. Income surveys are generally planned to produce reliable estimates at countries or macroregion levels, thus we implement a small area model…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…
In the analysis of binary longitudinal data, it is of interest to model a dynamic relationship between a response and covariates as a function of time, while also investigating similar patterns of time-dependent interactions. We present a…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
We prove a concentration inequality for sequential dynamical systems of the unit interval enjoying an exponential loss of memory in the BV norm, and we investigate several of its consequences. In particular, this covers compositions of…
We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…
Suppose $ E$ is a space with a null-recurrent Markov kernel $ P$. Furthermore, suppose there are infinite particles with variable weights on $ E$ performing a random walk following $ P$. Let $ X_{t}$ be a weighted functional of the position…
Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…