Related papers: Jump estimation in inverse regression
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
Our study addresses the inference of jumps (i.e. sets of discontinuities) within multivariate signals from noisy observations in the non-parametric regression setting. Departing from standard analytical approaches, we propose a new…
This paper considers M-estimation of a nonlinear regression model with multiple change-points occuring at unknown times. The multi-phase random design regression model, discontinuous in each change-point, have an arbitrary error $\epsilon$.…
Without measurement errors in predictors, discontinuity of a nonparametric regression function at unknown locations could be estimated using a number of existing approaches. However, it becomes a challenging problem when the predictors…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function…
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…
We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…
Volatility estimation is a central problem in financial econometrics, but becomes particularly challenging when jump activity is high, a phenomenon observed empirically in highly traded financial securities. In this paper, we revisit the…
Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient…
We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
In this article, we consider a jump diffusion process (X_t)observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends to 0 and nDelta tends to infinity. We assume that (X_t) is ergodic, strictly stationary and…
The problem of estimating the baseline signal from multisample noisy curves is investigated. We consider the functional mixed effects model, and we suppose that the functional fixed effect belongs to the Besov class. This framework allows…