Develops a nonparametric method to estimate isotropic covariance functions efficiently.
problem Estimating isotropic covariance functions without assuming a specific parametric form.
method Uses Bernstein polynomials and sieve maximum likelihood estimation.
result Consistent estimator with improved performance compared to parametric and nonparametric alternatives.
Study nonparametric covariance function estimation for noisy data.
problem Estimating covariance function from discrete noisy data in high dimensions.
method Adaptive learning-based estimators, including deep learning.
result Established oracle inequality and convergence rates for deep learning estimators.
Improves tensor regression convergence rate with Bayesian estimation.
problem Nonlinear tensor regression in high dimensions.
method Low-rank tensor decomposition and Bayesian Gaussian process estimation.
result Significantly improved convergence rate compared to naive methods.
Optimal nonparametric regression estimator adapts to unknown smoothness.
problem Nonparametric regression with unknown smoothness.
method Constructs an interpolating estimator that adapts to unknown smoothness.
result Minimax optimal rates achieved on Hölder classes.
Study on Q-function estimation for continuous state-action MDPs, deriving rates and conditions.
problem Estimating Q-function in off-policy evaluation for continuous state-action Markov decision processes. method Reformulated as nonparametric instrumental variables (NPIV) problem, derived minimax lower bounds, proposed sieve two-stage least squares estimator.
result First minimax lower bounds for Q-function and its derivatives in sup-norm and L2-norm, same as classical nonparametric regression. Study on distributed nonparametric function estimation with optimal rate and cost of adaptation.
problem Optimal rate of convergence and cost of adaptation in distributed nonparametric function estimation.
method Distributed minimax estimation and adaptive estimation under communication constraints for Gaussian sequence model and white noise model.
result Established minimax rate of convergence and exact communication cost for adaptation.
Paper designs an online algorithm for nonparametric Hawkes processes estimation.
problem Estimating triggering functions of multivariate Hawkes processes.
method NPOLE-MHP algorithm with online estimation and stability guarantees.
result NPOLE-MHP achieves O(1/T) regret and stability. Paper develops PGMM framework for debiased inference on nonparametric IV estimators.
problem Automatic debiased inference on nonparametric IV functionals.
method Penalized GMM (PGMM) framework for functionals of IV estimators.
result PGMM-based debiased estimator performs well, achieving near-nominal coverage.
We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping be…
Estimates personalized treatment response curves using covariates.
problem Flexible estimation of personalized treatment response curves.
method Sieve based nonparametric estimator of smoothed regimen-response curve function.
result Asymptotic linearity and undersmoothing criteria for efficient estimation.
Paper optimizes estimation of quadratic functionals in nonparametric IV models.
problem Optimal estimation of a nonlinear functional in ill-posed inverse regression.
method Adaptive, minimax estimation using leave-one-out, sieve NPIV estimator with data-driven sieve dimension selection.
result Adaptive estimator achieves minimax optimal rate in various ill-posed cases.
Boosts hazard estimation with time-varying covariates using gradient boosting.
problem Estimating nonparametric hazard functions with time-dependent covariates.
method Gradient boosting procedure for nonparametric hazard estimation.
result Step-size restriction prevents overfitting and ensures convergence.
New nonparametric estimators improve causal effect estimation.
problem Estimation of causal effects with selection bias.
method Undersmoothing of the highly adaptive lasso for estimating the weighting mechanism.
result Asymptotic efficiency and convergence to nonparametric efficiency bound.
We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonpa…
New method stabilizes IF-based estimators for causal mediation analysis with continuous mediators.
problem Stability issues in IF-based estimators for continuous mediators.
method Nonparametric weighted balancing method to estimate nuisance functions.
result Significant reductions in bias and variance compared to existing methods.
Develops nonparametric regression for non-smooth functions using fractional Laplacian.
problem Non-smooth regression functions in high dimensions.
method Fractional Laplacian eigenmaps for L2-fractional Sobolev spaces. result Upper bound on estimation error of $n^{- rac{2s}{2s+d}}$.
Deep neural networks improve mean function estimation for functional data.
problem Estimating mean functions of functional data.
method Deep neural networks with ReLU activation, sparsely connected.
result Achieves optimal nonparametric convergence rate in empirical norm.
A new clustering method uses nonparametric smoothing to estimate cluster membership functions.
problem Clustering with flexible, nonparametric estimation.
method Nonparametric smoothing to estimate cluster membership functions without explicit modelling assumptions.
result The method automatically determines the number of clusters and level of flexibility.
Estimates long-term effects using past experiments as instruments with many weak instruments.
problem Estimating long-term causal effects with limited short-term outcomes and many weak instruments.
method Nonparametric instrumental variable inference with many weak instruments, using past experiments as instruments.
result Automatic debiased machine learning estimators for linear functionals of the structural function and its minimum-norm projection are efficient in the many-weak-instruments regime.
New estimators for probability density functions, minimizing bias and variance.
problem Lack of practical estimators for Sobolev quantities of unknown probability density functions.
method Proposed and analyzed a family of estimators for Sobolev quantities of unknown probability density functions.
result Our estimators are minimax rate-optimal and computationally tractable, adapting to computational constraints.
Proposes a method for selecting variables in nonparametric learning using power series kernels.
problem Variable selection in nonparametric learning with power series kernels.
method Two-stage estimation: consistent function approximation followed by l1-type penalized variable selection.
result The method achieves variable selection consistency for power series kernels.
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics literature. We show that estimators based either on data-splitting or a leave-one-out t…
Improved nonparametric regression with debiasing for root-n consistency.
problem Challenges in achieving root-n consistency and normal distribution for nonparametric estimators.
method Debiasing technique by adding a correction term to nonparametric estimators.
result Achieves root-n consistency and asymptotic normality.
New methods for estimating and inferring nonparametric structural functions and elasticities.
problem Estimating and inferring nonparametric structural functions and their derivatives.
method Data-driven sieve dimension choice and uniform confidence bands construction.
result Optimal estimation and inference procedures with minimax rates of convergence.
Improves MARS for nonparametric multivariate regression with dimension reduction.
problem High number of basis functions in MARS for high-order interactions.
method Linear combinations of covariates for dimension reduction, facilitating gradient calculation and eigen-analysis for estimation.
result Asymptotic theory and numerical studies show improved performance over MARS.
Improves RL efficiency with nonparametric methods.
problem High sample complexity in policy gradient algorithms.
method Nonparametric regression and density estimation for value function estimation.
result Better sample efficiency compared to existing methods.
We extend nonparametric models to handle extrapolation, providing bounds for inference.
problem Challenges in nonparametric statistical inference when evaluating outside the conditioning variable's support.
method Introduced a class of extrapolation assumptions and a consistent estimation procedure to handle extrapolation.
result Validated extrapolation-aware conclusions through various applications and real-world data.
Estimates nonlinear Hawkes processes using RKHSs with ReLU rectification.
problem Nonlinear multivariate Hawkes processes with complex interaction functions.
method Nonparametric estimation using RKHSs with approximations for ReLU and integral operators.
result Proposes an estimation method with bounds on approximation errors.
Paper introduces a new histogram estimator for nonparametric density estimation that improves performance.
problem Smoothness-based nonparametric density estimators are not optimal for all types of data.
method Incorporates a multi-view latent variable model into histogram-style estimators.
result A new histogram estimator converges faster to multi-view models in L1 error. Bayesian method with Gaussian process priors achieves optimal convergence rates for regression function and its derivatives.
problem Estimating the regression function and its derivatives in nonparametric regression.
method Bayesian approach with Gaussian process priors, focusing on convergence rates and plug-in property.
result Equivalence of convergence rates of posterior distributions and Bayes estimators for regression function and its derivatives.
We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate dynamic programming and applied probability in general. We incorporate "soft in…
New method calibrates multivariate Lévy processes using neural networks.
problem Calibrating multivariate Lévy processes with less smooth densities.
method Approximate Lévy density with parametrized functional form, estimate characteristic function using numerical integration with deep neural networks.
result Deep neural networks robustly capture sharp transitions in Lévy densities.
A new method improves the DNN estimator for mean regression, achieving optimal convergence rates.
problem Lack of distributional results and suboptimal convergence rates for DNN estimator.
method Two-scale distributional nearest neighbors (TDNN) estimator, combining two DNN estimators with different subsampling scales.
result The two-scale DNN estimator achieves the optimal nonparametric convergence rate under fourth-order smoothness.
Deep neural networks with adversarial training achieve sup-norm convergence for nonparametric regression.
problem Achieving sup-norm convergence for deep neural network estimators in nonparametric regression.
method Developed an adversarial training scheme to address the sup-norm convergence issue.
result Deep neural network estimators achieve optimal sup-norm convergence with the proposed adversarial training.
New estimators improve density functional estimation with faster convergence rates.
problem Estimating functionals of nonparametric densities efficiently.
method Fixing k in k-nearest neighbor statistics for bias correction.
result Faster convergence rates for certain functionals.
Bayesian neural networks with nonparametric noise models for system identification.
problem Estimating parameters and noise processes in stochastic dynamic systems.
method Bayesian nonparametric approach using neural networks and Gibbs sampler.
result The method converges to full nonparametric Bayesian regression model.
Study uniform consistency in nonparametric mixture models and mixed regression.
problem Uniform consistency in nonparametric mixture models and mixed regression models.
method Construct uniformly consistent estimators under general conditions, develop novel technical tools.
result Prove uniform consistency results for nonparametric mixtures and mixed regression models.
A new method debiases multiple target parameters without IFs.
problem Debiasing multiple target parameters in nonparametric models.
method Kernel Debiased Plug-in Estimation (KDPE) using TMLE and reproducing kernel Hilbert spaces.
result KDPE simultaneously debiases all pathwise differentiable target parameters.
New estimator for estimating derivatives in nonparametric regression.
problem Estimating derivatives of regression functions.
method Plug-in kernel ridge regression (KRR) estimator.
result Plug-in property for derivatives estimation, optimal rate of convergence.
Develops EM algorithm for analyzing multi-curve data with switching nonparametric regression models.
problem Analyzing multi-curve data with switching latent state processes.
method Switching nonparametric regression models and an EM algorithm for parameter estimation.
result Frequentist properties of parameter estimates validated through simulation studies and real data application.
Paper proposes a new ML estimator for BL pdfs.
problem Estimating probability density functions (pdfs) of unknown form.
method Nonparametric maximum likelihood (ML) estimator for band-limited (BL) pdfs.
result BLML estimator outperforms KDE algorithms in mean integrated squared error.
Study minimax rates for nonparametric density estimation with adversarial losses.
problem Estimating densities under various adversarial loss functions.
method General framework for analyzing minimax rates with different loss functions.
result Determines the minimax rate based on loss choice and density smoothness.
Study builds a classifier for diffusions with unknown diffusion but known drifts.
problem Multiclass classification of S.D.E. paths with unknown diffusion coefficient.
method Plug-in classifier using nonparametric estimators of drift and diffusion functions.
result Consistent classification procedure with rate of convergence under different assumptions.
Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, …
A new interpolation-based method for nonparametric regression.
problem Nonparametric regression challenges in computational complexity and experimental design.
method Reconstruction approach using interpolators and regularized least squares.
result Effective surrogates for complex methods with reduced computational burden.
Estimates precision matrix with confounding, improving over baselines.
problem Precision matrix estimation with extraneous confounding.
method Joint nonparametric estimator inspired by neuroscientific research.
result Consistent and efficient estimation of precision matrix with improved performance over baselines.
Paper develops a spectral algorithm for nonparametric HMMs with smooth emission densities.
problem Estimating hidden Markov models with nonparametric emission densities.
method Spectral decomposition of continuous matrices for nonparametric density estimation.
result Computational efficiency and competitive performance on synthetic and real problems.
Deep neural networks with ReLU activation achieve optimal nonparametric regression rates.
problem Nonparametric regression with general composition assumptions.
method Sparsely connected deep neural networks with ReLU activation function.
result Achieve minimax rates of convergence under general composition assumption.