Related papers: Asymptotic results for nonparametric regression es…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…
We propose a new class of semiparametric regression models of mean residual life for censored outcome data. The models, which enable us to estimate the expected remaining survival time and generalize commonly used mean residual life models,…
A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…
Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
The research is about a systematic investigation on the following issues. First, we construct different outcome regression-based estimators for conditional average treatment effect under, respectively, true (oracle), parametric,…
This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…
Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
Distributionally robust optimization (DRO) is a widely-used approach to learn models that are robust against distribution shift. Compared with the standard optimization setting, the objective function in DRO is more difficult to optimize,…
Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…
A theory of sufficient dimension reduction (SDR) is developed from an optimizational perspective. In our formulation of the problem, instead of dealing with raw data, we assume that our ground truth includes a mapping ${\mathbf f}: {\mathbb…
We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderate $p/n$ regime, where the number of covariates $p$ grows proportionally with the sample size $n$. Under appropriate regularity conditions, we…
There has been recent interest in extending the ideas of False Discovery Rates (FDR) to variable selection in regression settings. Traditionally the FDR in these settings has been defined in terms of the coefficients of the full regression…