منابع مشابه
Local Linear Regression Smoothers and Their Minimax Efficiencies
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متن کاملSupplement to “Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers”
where, recall, we denote by m = |E| the number of edges in the grid. In the second line we used the 1-Lipschitz property of f , and in the third we used that multi-indices corresponding to adjacent locations on the grid are exactly 1 apart, in `∞ distance. Thus we see that setting C ′ n = √ m/` gives the desired containment Sd(C ′ n) ⊇ Hd(1). It is always true that m n for a d-dimensional grid ...
متن کاملTotal Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers
We consider the problem of estimating a function defined over n locations on a d-dimensional grid (having all side lengths equal to n). When the function is constrained to have discrete total variation bounded by Cn, we derive the minimax optimal (squared) `2 estimation error rate, parametrized by n,Cn. Total variation denoising, also known as the fused lasso, is seen to be rate optimal. Severa...
متن کاملVariable Bandwidth and Local Linear Regression Smoothers
In this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal cho...
متن کاملLocal Linear Smoothers in Regression Function Estimation
A method based on local linear approximation is used to estimate the mean regression function. The proposed local linear smoother has several advantages in comparison with other linear smoothers. Motivated by this fact, we follow this approach to estimate more general functions, among which, conditional median and conditional quantile functions. A further generalization involves the estimation ...
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ژورنال
عنوان ژورنال: Scandinavian Journal of Statistics
سال: 2001
ISSN: 0303-6898,1467-9469
DOI: 10.1111/1467-9469.00229