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We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…

We develop a new model selection method for the adaptive robust efficient nonparametric signal estimation observed with impulse noise which is defined by the general non Gaussian L\'evy processes. On the basis of the developed method, we…

We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…

Autoregressive neural network models have been used successfully for sequence generation, feature extraction, and hypothesis scoring. This paper presents yet another use for these models: allocating more computation to more difficult…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

This work deals with the ill-posed inverse problem of reconstructing a function $f$ given implicitly as the solution of $g = Af$, where $A$ is a compact linear operator with unknown singular values and known eigenfunctions. We observe the…

We investigate the problem of estimating a function $f$ based on observations from its noisy convolution when the noise exhibits long-range dependence. We construct an adaptive estimator based on the kernel method, derive minimax lower…

We estimate convex polytopes and general convex sets in $\mathbb R^d,d\geq 2$ in the regression framework. We measure the risk of our estimators using a $L^1$-type loss function and prove upper bounds on these risks. We show that, in the…

We consider the problem of threshold estimation for autoregressive time series with a "space switching" in the situation, when the regression is nonlinear and the innovations have a smooth, possibly non Gaussian, probability density.…

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…

This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…

We consider the model $Z_i=X_i+\varepsilon_i$, for i.i.d. $X_i$'s and $\varepsilon_i$'s and independent sequences $(X_i)_{i\in{\mathbb{N}}}$ and $(\varepsilon_i)_{i\in{\mathbb{N}}}$. The density $f_{\varepsilon}$ of $\varepsilon_1$ is…

We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…

This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method…

In the linear regression model with possibly autoregressive errors, we propose a family of nonparametric tests for regression under a nuisance autoregression. The tests avoid the estimation of nuisance parameters, in contrast to the tests…

Autoregressive models are typically applied to sequences of discrete tokens, but recent research indicates that generating sequences of continuous embeddings in an autoregressive manner is also feasible. However, such Continuous…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…