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We investigate the application of sufficient dimension reduction (SDR) to a noiseless data set derived from a deterministic function of several variables. In this context, SDR provides a framework for ridge recovery. In this second part, we…

Numerical Analysis · Mathematics 2018-08-10 Andrew Glaws , Paul G. Constantine , R. Dennis Cook

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…

Machine Learning · Statistics 2020-07-01 Yuhao Zhou , Jiaxin Shi , Jun Zhu

We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…

Statistics Theory · Mathematics 2018-10-26 Ursula U. Müller , Anton Schick , Wolfgang Wefelmeyer

Nonparametric estimators of a regression function with circular response and Rd-valued predictor are considered in this work. Local polynomial type estimators are proposed and studied. Expressions for their asymptotic biases and variances…

Given a random sample from a parametric model, we show how indirect inference estimators based on appropriate nonparametric density estimators (i.e., simulation-based minimum distance estimators) can be constructed that, under mild…

Statistics Theory · Mathematics 2011-01-10 Richard Nickl , Benedikt M. Pötscher

In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth…

Statistics Theory · Mathematics 2023-07-03 Tien Dat Nguyen , Thanh Mai Pham Ngoc , Vincent Rivoirard

No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…

Applications · Statistics 2020-09-01 María Alonso-Pena , Jose Ameijeiras-Alonso , Rosa M. Crujeiras

In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…

Statistics Theory · Mathematics 2008-12-18 Jean-Michel Loubes , Anne-Françoise Yao

Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…

Methodology · Statistics 2024-06-18 Chunlei Ge , W. John Braun

Estimating the effective dimension reduction (EDR) space, related to the semiparametric regression model introduced by Li \cite{sir}, is based on the estimation of the covariance matrix $\Lambda$ of the conditional expectation of the vector…

Statistics Theory · Mathematics 2018-11-08 Emmanuel De Dieu Nkou , Guy Martial Nkiet

In this paper, we use the stochastic approximation method to estimate Sliced Average Variance Estimation (SAVE). This method is known for its efficiency in recursive estimation. Stochastic approximation is particularly effective for…

Statistics Theory · Mathematics 2024-06-25 Emmanuel De Dieu Nkou

This paper provides the theory about the convergence rate of the tilted version of linear smoother. We study tilted linear smoother, a nonparametric regression function estimator, which is obtained by minimizing the distance to an infinite…

We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and…

Machine Learning · Statistics 2023-08-29 Zejian Liu , Meng Li

A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…

Methodology · Statistics 2024-07-24 Yin Jin , Wei Luo

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…

Statistics Theory · Mathematics 2013-08-07 Aboubacar Amiri , Christophe Crambes , Baba Thiam

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

Machine Learning · Computer Science 2012-06-22 Samuel Gershman , Matt Hoffman , David Blei

We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…

Statistics Theory · Mathematics 2025-08-19 Rahul Singh , Suhas Vijaykumar

In this work, we develop and study an empirical projection operator scheme for solving nonparametric regression problems. This scheme is based on an approximate projection of the regression function over a suitable reproducing kernel…

Statistics Theory · Mathematics 2020-02-04 Bilel Bousselmi , Jean-François Dupuy , Abderrazek Karoui

Semi-implicit variational inference (SIVI) is a powerful framework for approximating complex posterior distributions, but training with the Kullback-Leibler (KL) divergence can be challenging due to high variance and bias in…

Machine Learning · Computer Science 2025-06-06 Tobias Pielok , Bernd Bischl , David Rügamer

We propose a new method, semi-penalized inference with direct false discovery rate control (SPIDR), for variable selection and confidence interval construction in high-dimensional linear regression. SPIDR first uses a semi-penalized…

Methodology · Statistics 2013-12-02 Jian Huang , Shuangge Ma , Cun-Hui Zhang , Yong Zhou