Related papers: A Large Deviation Inequality for $\beta$-mixing Ti…

We consider a classical model related to an empirical distribution function $ F_n(t)=\frac{1}{n}\sum_{k=1}^nI_{\{\xi_k\le t\}}$ of $(\xi_k)_{i\ge 1}$ -- i.i.d. sequence of random variables, supported on the interval $[0,1]$, with continuous…

This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…

A Freidlin-Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and…

We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and strong uniform consistency are derived…

Errors in variables (Deming) regression of measurements spanning a wide range of values requires appropriate weighting to reflect nonconstant variance. Precision profile models, mathematical relationships between measurement variance and…

Given a periodic function $f$, we study the convergence almost everywhere and in norm of the series $\sum_{k} c_k f(kx)$. Let $f(x)= \sum_{m=1}^\infty a_m \sin {2\pi m x}$ where $\sum_{m=1}^\infty a_{m }^2d(m) <\infty$ and $d(m)=\sum_{d|m}…

This study develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series (LSFTS). We investigate a kernel-based method to estimate the time-varying covariance operator and the…

Motivated by spectral analysis of replicated brain signal time series, we propose a functional mixed effects approach to model replicate-specific spectral densities as random curves varying about a deterministic population-mean spectrum. In…

Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname…

For Y a subset of the complex plane,a beta ensemble is a sequence of probability measures on Y^n for n=1,2,3...depending on a real-valued continuous function Q and a real positive parameter beta.We consider the associated sequence of…

This study introduces a novel forecasting strategy that leverages the power of fractional differencing (FD) to capture both short- and long-term dependencies in time series data. Unlike traditional integer differencing methods, FD preserves…

In many real-world regression tasks, the data distribution is heavily skewed, and models learn predominantly from abundant majority samples while failing to predict minority labels accurately. While imbalanced classification has been…

Time series modeling techniques based on deep learning have seen many advancements in recent years, especially in data-abundant settings and with the central aim of learning global models that can extract patterns across multiple time…

We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…

Let $\mathbf{W}=(W_1,W_2,...,W_k)$ be a random vector with nonnegative coordinates having nonzero and finite variances. We prove concentration inequalities for $\mathbf{W}$ using size biased couplings that generalize the previous univariate…

For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…

This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null…

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large…