Rates of Uniform Consistency for k-NN Regression
نویسنده
چکیده
We derive high-probability finite-sample uniform rates of consistency for k-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that kNN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the k-NN regression rates to establish new results about estimating the level sets and global maxima of a function from noisy observations.
منابع مشابه
Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression
We obtain uniform consistency results for kernel-weighted sample covariances in a nonstationary multiple regression framework that allows for both fixed design and random design coefficient variation. In the fixed design case these nonparametric sample covariances have different uniform convergence rates depending on direction, a result that differs fundamentally from the random design and stat...
متن کاملمقایسه عملکرد مدل کاکس و روش K ـ نزدیکترین همسایگی در تخمین بقای بیماران پیوند کلیه
Introduction & Objective: Cox model is a common method to estimate survival and validity of the results is dependent on the proportional hazards assumption. K- Nearest neighbor is a nonparametric method for survival probability in heterogeneous communities. The purpose of this study was to compare the performance of k- nearest neighbor method (K-NN) with Cox model. Materials & Methods: This ...
متن کاملMULTIVARIATE LOCAL POLYNOMIAL REGRESSION FOR TIME SERIES: UNIFORM STRONG CONSISTENCY AND RATES by
Local high-order polynomial fitting is employed for the estimation of the multivariate regression function m (x 1 , . . . ,xd) = E [ψ (Yd) | X 1 = x 1 , . . . ,Xd = xd], and of its partial derivatives, for stationary random processes {Yi , Xi}. The function ψ may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency...
متن کاملComparison of Gene Expression Programming (GEP) and Parametric and Non-parametric Regression Methods in the Prediction of the Mean Daily Discharge of Karun River (A case Study: Mollasani Hydrometric Station)
Nowadays, the prediction of river discharge is one of the important issues in hydrology and water resources; the results of daily river discharge pattern could be used in the management of water resources and hydraulic structures and flood prediction. In this research, Gene Expression Programming (GEP), parametric Linear Regression (LR), parametric Nonlinear Regression (NLR) and non-parametric ...
متن کاملUniform in Bandwidth Consistency of Kernel Regression Estimators at a Fixed Point
We consider pointwise consistency properties of kernel regression function type estimators where the bandwidth sequence in not necessarily deterministic. In some recent papers uniform convergence rates over compact sets have been derived for such estimators via empirical process theory. We now show that it is possible to get optimal results in the pointwise case as well. The main new tool for t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1707.06261 شماره
صفحات -
تاریخ انتشار 2017