Related papers: Autoregressive Functions Estimation in Nonlinear B…

In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…

A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, nearly non-stationary process, unit root process, mildly…

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

For a class of martingales, this paper provides a framework on the uniform consistency with broad applicability. The main condition imposed is only related to the conditional variance of the martingale, which holds true for stationary…

In this article, we study the statistical and asymptotic properties of break-point estimators in nonstationary autoregressive and predictive regression models for testing the presence of a single structural break at an unknown location in…

The non-autoregressive models have boosted the efficiency of neural machine translation through parallelized decoding at the cost of effectiveness when comparing with the autoregressive counterparts. In this paper, we claim that the…

We present symmetry tests for bifurcating autoregressive processes (BAR) when some data are missing. BAR processes typically model cell division data. Each cell can be of one of two types \emph{odd} or \emph{even}. The goal of this paper is…

This paper deals with a nonparametric Nadaraya-Watson estimator $\hat b$ of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on $\hat b$ and its discrete-time approximation are…

This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

The autoregressive (AR) models, such as attention-based encoder-decoder models and RNN-Transducer, have achieved great success in speech recognition. They predict the output sequence conditioned on the previous tokens and acoustic encoded…

This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…

Spectral estimation is a fundamental problem for time series analysis, which is widely applied in economics, speech analysis, seismology, and control systems. The asymptotic convergence theory for classical, non-parametric estimators, is…

Route alignment design in surveying and transportation engineering frequently involves fixed waypoint constraints, where a path must precisely traverse specific coordinates. While existing literature primarily relies on geometric…

In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of…

A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…

In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…