Rates of convergence of nearest neighbor estimation under arbitrary sampling

By Sanjeev R. Kulkarni, S. Posner. 1995

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Citations in the corpus

Distributed learning in wireless sensor networks (2005, background): “Many efforts have extended this result to address the consistency of Stone-type learning rules under various sampling processes; for example, [23], [34] and references therein, [19], [32], [45], [48], [49], [58], [65], [66], [67], [85], [90], [103], and [104].”
On the Kernel Rule for Function Classification (2006, background): “Note also that a similar requirement is imposed by Kulkarni and Posner [18] who study the problem of nearest neighbor estimation under arbitrary sampling in a general separable metric space.”
On the Rate of Convergence of the Bagged Nearest Neighbor Estimate (2010, background): “This result sharpens the constant of Theorem 1, page 1032 in Kulkarni and Posner [12] and of Proposition 2.2 in the case of the nearest neighbor.”
Choice of neighbor order in nearest-neighbor classification (2008, background): “ral dimension, and Snapp and Venkatesh (1998) further extended the results to the case of multiple classes. Bax (2000) gave probabilistic bounds for the conditional error rate in the case where k= 1. Kulkarni and Posner (1995) addressed nearest-neighbor methods for quite general dependent data, and ”
A Distribution-Free Theory of Nonparametric Regression (2002, background): “(1993), Bosq (1996), Bosq and Lecoutre (1987), Breiman et al.”
Fast, smooth and adaptive regression in metric spaces (2009, result): “[9]) was shown in an earlier work [10] to control the risk of nearest neighbor regression, although adaptivity was not a subject of that result.”
A deterministic approach to throughput scaling in wireless networks (2002, result): “The deterministic view taken in this paper is in line with recent work on individual sequences in information theory, statistics and learning theory (cf. [6, 9 , 15, 14]).”