Skip to main content
×
Home
    • Aa
    • Aa

UNIFORM CONVERGENCE RATES FOR KERNEL ESTIMATION WITH DEPENDENT DATA

  • Bruce E. Hansen (a1)
Abstract

This paper presents a set of rate of uniform consistency results for kernel estimators of density functions and regressions functions. We generalize the existing literature by allowing for stationary strong mixing multivariate data with infinite support, kernels with unbounded support, and general bandwidth sequences. These results are useful for semiparametric estimation based on a first-stage nonparametric estimator.

Copyright
Corresponding author
Address correspondence to Bruce E. Hansen, Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706-1393, USA; e-mail: bhansen@ssc.wisc.edu.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

D. Bosq (1998) Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, 2nd ed. Lecture Notes in Statistics 110. Springer-Verlag.

J. Fan (1992) Design-adaptive nonparametric regression. Journal of the American Statistical Association 87, 9981004.

J. Fan (1993) Local linear regression smoothers and their minimax efficiency. Annals of Statistics 21, 196216.

B.L. Granovsky H.-G. Müller (1991) Optimizing kernel methods: A unifying variational principle. International Statistical Review 59, 373388.

E. Liebscher (1996) Strong convergence of sums of α-mixing random variables with applications to density estimation. Stochastic Processes and Their Applications 65, 6980.

Y.P. Mack B.W. Silverman (1982) Weak and strong uniform consistency of kernel regression estimates. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 405415.

J.S. Marron M.P. Wand (1992) Exact mean integrated squared error. Annals of Statistics 20, 712736.

E. Masry (1996) Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17, 571599.

H.-G. Müller (1984) Smooth optimum kernel estimators of densities, regression curves and modes. Annals of Statistics 12, 766774.

E.A. Nadaraya (1964) On estimating regression. Theory of Probability and Its Applications 9, 141142.

W.K. Newey (1994) Kernel estimation of partial means and a generalized variance estimator. Econometric Theory 10, 233253.

M. Peligrad (1991) Properties of uniform consistency of the kernel estimators of density and of regression functions under dependence conditions. Stochastics and Stochastic Reports 40, 147168.

E. Rio (1995) The functional law of the iterated logarithm for stationary strongly mixing sequences. Annals of Probability 23, 11881203.

M. Rosenblatt (1956) Remarks on some non-parametric estimates of a density function. Annals of Mathematical Statistics 27, 832837.

C.J. Stone (1977) Consistent nonparametric regression. Annals of Statistics 5, 595645.

C.J. Stone (1982) Optimal global rates of convergence for nonparametric regression. Annals of Statistics 10, 10401053.

L.T. Tran (1994) Density estimation for time series by histograms. Journal of Statistical Planning and Inference 40, 6179.

M.P. Wand W.R. Schucany (1990) Gaussian-based kernels. Canadian Journal of Statistics 18, 197204.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Altmetric attention score