Related papers: Adaptive estimation for the nonparametric bivariat…

In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In…

Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…

In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…

A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of…

The paper considers two-phase random design linear regression models. The errors and the regressors are stationary long-range dependent Gaussian. The regression parameters, the scale parameters and the change-point are estimated using a…

Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

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…

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…

Difficulties may arise when analyzing longitudinal data using mixed-effects models if there are nonparametric functions present in the linear predictor component. This study extends the use of semiparametric mixed-effects modeling in cases…

We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori "testimation" procedure of Abramovich et al. (2007) for recovering…

We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…

In this paper, we propose a novel method for estimating the long-memory parameter in time series. By combining the multi-resolution framework of wavelets with the robustness of the Least Absolute Deviations (LAD) criterion, we introduce a…

We study the problem of choosing algorithm hyper-parameters in unsupervised domain adaptation, i.e., with labeled data in a source domain and unlabeled data in a target domain, drawn from a different input distribution. We follow the…

In this paper we develop the James - Stein improved estimation method for a nonparametric periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure based on the improved weighted least square…

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…

We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…

Long-term causal inference has drawn increasing attention in many scientific domains. Existing methods mainly focus on estimating average long-term causal effects by combining long-term observational data and short-term experimental data.…

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…