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This paper studies simultaneous inference of conditional distributions in nonlinear time series from a sieve M-regression perspective. Existing literature on sieve M-regression has primarily focused on pointwise asymptotics, leaving the…

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

Multi-fidelity methods that use an ensemble of models to compute a Monte Carlo estimator of the expectation of a high-fidelity model can significantly reduce computational costs compared to single-model approaches. These methods use oracle…

In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold…

Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical challenges, such as personalized medicine and optimal resource allocation. In this paper, we develop a general class of two-step algorithms for…

This paper studies the non-parametric estimation and uniform inference for the conditional quantile regression function (CQRF) with covariates exposed to measurement errors. We consider the case that the distribution of the measurement…

We prove some efficient inference results concerning estimation of a Ornstein-Uhlenbeck regression model, which is driven by a non-Gaussian stable Levy process and where the output process is observed at high-frequency over a fixed time…

In this paper, we are interested in nonparametric kernel estimation of a generalized regression function, including conditional cumulative distribution and conditional quantile functions, based on an incomplete sample $(X_t, Y_t,…

The robust distributed state estimation for a class of continuous-time linear time-invariant systems is achieved by a novel kernel-based distributed observer, which, for the first time, ensures fixed-time convergence properties. The…

When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…

This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…

We study distribution free, nonparametric prediction bands with a special focus on their finite sample behavior. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band…

Nonlinear autoregressive models are very useful for modeling many natural processes, however, the size of the class of these models is large. Functional-coefficient autoregressive models (FCAR) are useful structures for reducing the size of…

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator…

In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear…

The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset…

In this paper, we consider estimation of the conditional mode of an outcome variable given regressors. To this end, we propose and analyze a computationally scalable estimator derived from a linear quantile regression model and develop…