Regression with random design: A minimax study
نویسندگان
چکیده
منابع مشابه
Minimax Fixed-Design Linear Regression
We consider a linear regression game in which the covariates are known in advance: at each round, the learner predicts a real-value, the adversary reveals a label, and the learner incurs a squared error loss. The aim is to minimize the regret with respect to linear predictions. For a variety of constraints on the adversary’s labels, we show that the minimax optimal strategy is linear, with a pa...
متن کاملMinimax exact constant in sup-norm for nonparametric regression with random design
We consider the nonparametric regression model with random design. We study the estimation of a regression function f in the uniform norm assuming that f belongs to a Hölder class. We determine the minimax exact constant and an asymptotically exact estimator. They depend on the minimum value of the design density.
متن کاملSpatial Beta Regression Model with Random Effect
Abstract: In many applications we have to encountered with bounded dependent variables. Beta regression model can be used to deal with these kinds of response variables. In this paper we aim to study spatially correlated responses in the unit interval. Initially we introduce spatial beta generalized linear mixed model in which the spatial correlation is captured through a random effect. T...
متن کاملRobust Minimax Probability Machine Regression Robust Minimax Probability Machine Regression
We formulate regression as maximizing the minimum probability (Ω) that the true regression function is within ±2 of the regression model. Our framework starts by posing regression as a binary classification problem, such that a solution to this single classification problem directly solves the original regression problem. Minimax probability machine classification (Lanckriet et al., 2002a) is u...
متن کاملDesign-adaptive Minimax Local Linear Regression for Longitudinal/clustered Data
This paper studies a weighted local linear regression smoother for longitudinal/clustered data, which takes a form similar to the classical weighted least squares estimate. As a hybrid of the methods of Chen and Jin (2005) and Wang (2003), the proposed local linear smoother maintains the advantages of both methods in computational and theoretical simplicity, variance minimization and bias reduc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2007
ISSN: 0167-7152
DOI: 10.1016/j.spl.2006.05.010