The Annals of statistics, 2007-10, Vol.35 (5), p.2219-2232
2007
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Details
- Autor(en) / Beteiligte
- Titel
- Variance Estimation in Nonparametric Regression via the Difference Sequence Method
- Ist Teil von
- The Annals of statistics, 2007-10, Vol.35 (5), p.2219-2232
- Ort / Verlag
- Hayward, CA: Institute of Mathematical Statistics
- Erscheinungsjahr
- 2007
- Quelle
- Elektronische Zeitschriftenbibliothek (Open access)
- Beschreibungen/Notizen
- Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0090-5364eISSN: 2168-8966DOI: 10.1214/009053607000000145Titel-ID: cdi_projecteuclid_primary_oai_CULeuclid_euclid_aos_1194461728
- Format
- –
- Schlagworte
- 62G08, 62G20, Acceleration of convergence, asymptotic minimaxity, Density, Estimating techniques, Estimation methods, Estimators, Estimators for the mean, Exact sciences and technology, General topics, Linear inference, regression, Linear regression, Mathematical functions, Mathematical models, Mathematical sequences, Mathematics, Minimax, Nonparametric inference, Nonparametric regression, Numerical analysis, Numerical analysis. Scientific computation, Polynomials, Probability and statistics, Sciences and techniques of general use, Statistical analysis, Statistical variance, Statistics, Studies, variance estimation