Related papers: Penalized Spline M-Estimators for Discretely Sampl…
This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is…
This work proposes new estimators for discrete optimal transport plans that enjoy Gaussian limits centered at the true solution. This behavior stands in stark contrast with the performance of existing estimators, including those based on…
Linear regression models have been extensively considered in the literature. However, in some practical applications they may not be appropriate all over the range of the covariate. In this paper, a more flexible model is introduced by…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
This paper investigates the partial linear model by Least Absolute Deviation (LAD) regression. We parameterize the nonparametric term using Deep Neural Networks (DNNs) and formulate a penalized LAD problem for estimation. Specifically, our…
In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…
This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n…
We study non-parametric estimation of choice models, which were introduced to alleviate unreasonable assumptions in traditional parametric models, and are prevalent in several application areas. Existing literature focuses only on the…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
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…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space.…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Longitudinal binary or count functional data are common in neuroscience, but are often too large to analyze with existing functional regression methods. We propose one-step penalized generalized estimating equations that supports…
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…
Predicting scalar outcomes using functional predictors is a classic problem in functional data analysis. In many applications, however, only specific locations or time-points of the functional predictors have an impact on the outcome. Such…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…