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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…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Statistics Theory · Mathematics 2022-07-05 Yuliana Linke , Igor Borisov , Pavel Ruzankin , Vladimir Kutsenko , Elena Yarovaya , Svetlana Shalnova

This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…

Statistics Theory · Mathematics 2015-03-13 Emilio Seijo , Bodhisattva Sen

We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…

Methodology · Statistics 2025-05-09 Kyunghee Han , Yeonjoo Park , Soo-Young Kim

A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…

Optimization and Control · Mathematics 2024-05-16 Naoki Marumo , Takayuki Okuno , Akiko Takeda

Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…

Statistics Theory · Mathematics 2025-02-20 Vladimir Spokoiny

The main result of this article is that we obtain an elementwise error bound for the Fused Lasso estimator for any general convex loss function $\rho$. We then focus on the special cases when either $\rho$ is the square loss function (for…

Statistics Theory · Mathematics 2022-03-21 Teng Zhang , Sabyasachi Chatterjee

We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment with them on several small…

Machine Learning · Computer Science 2026-03-02 Filippo Portera

Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…

Methodology · Statistics 2022-12-06 Yeonjoo Park , Kyunghee Han , Douglas G. Simpson

We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system…

Statistics Theory · Mathematics 2025-10-02 Hemant Tyagi , Denis Efimov

Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…

Methodology · Statistics 2023-01-25 Anupam Kundu , Mohsen Pourahmadi

We construct bootstrap confidence intervals for a monotone regression function. It has been shown that the ordinary nonparametric bootstrap, based on the nonparametric least squares estimator (LSE) $\hat f_n$ is inconsistent in this…

Statistics Theory · Mathematics 2023-05-24 Piet Groeneboom , Geurt Jongbloed

Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…

Statistics Theory · Mathematics 2019-10-16 Arun K. Kuchibhotla , Lawrence D. Brown , Andreas Buja , Junhui Cai

The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…

Methodology · Statistics 2024-03-28 Lu Lin , Ze Chen

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…

Information Theory · Computer Science 2017-04-05 Abbas Kazemipour , Sina Miran , Piya Pal , Behtash Babadi , Min Wu

The present paper solves the problem of local linear approximation of the Fr\'echet conditional mean in an extrinsic and intrinsic way from time correlated bivariate curve data evaluated in a manifold (see Torres et al, 2025, on global…

Statistics Theory · Mathematics 2025-10-06 M. D. Ruiz-Medina , A. Torres-Signes

Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods based on the empirical characteristic…

Computation · Statistics 2018-11-06 J. Martin van Zyl

Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria for $\ell_0$-penalized regression. Although similar in spirit…

Machine Learning · Statistics 2025-05-21 Sabyasachi Chatterjee , Subhajit Goswami , Soumendu Sundar Mukherjee

We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler…

Statistics Theory · Mathematics 2008-06-20 Piet Groeneboom , Marloes H. Maathuis , Jon A. Wellner

We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…

Machine Learning · Computer Science 2019-02-06 Tianyang Li , Anastasios Kyrillidis , Liu Liu , Constantine Caramanis