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Optimal convergence rates of high order Parzen windows with unbounded sampling
Institution:1. Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul, 110-745, Republic of Korea;2. Mathematics Department, Tulane University, 6823 St. Charles Avenue, New Orleans, LA 70118, USA;3. Department of Statistics and Operations Research, UNC at Chapel Hill, CB#3260, Hanes Hall, Chapel Hill, NC 27599, USA;1. School of Sciences, Ningbo University of Technology, 201 Fenghua Rd., Ningbo 315211, PR China;2. Department of Mathematics, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, PR China
Abstract:High order Parzen windows are considered with data drawn from unbounded sampling processes. Convergence analysis is established by imposing a moment hypothesis on the unbounded sampling outputs and some decay conditions on the marginal distributions. Our estimate of convergence rate is consistent with the previous result with bounded sampling.
Keywords:Statistical learning theory  Parzen windows  Unbounded sampling  Convergence rate
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