Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T04:28:14.006Z Has data issue: false hasContentIssue false
  • English
  • Français

UNIFORM CONVERGENCE RATES FOR KERNEL ESTIMATION WITH DEPENDENT DATA

Published online by Cambridge University Press:  26 February 2008

Bruce E. Hansen
Bruce E. Hansen*
Affiliation:
University of Wisconsin
*
Address correspondence to Bruce E. Hansen, Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706-1393, USA; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 3 , June 2008 , pp. 726 - 748
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrews, D.W.K. (1995) Nonparametric kernel estimation for semiparametric models. Econometric Theory 11, 560–596.CrossRefGoogle Scholar
Ango Nze, P. ’ Doukhan, P. (2004) Weak dependence: Models and applications to econometrics. Econometric Theory 20, 995–1045.Google Scholar
Bosq, D. (1998) Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, 2nd ed. Lecture Notes in Statistics 110. Springer-Verlag.CrossRefGoogle Scholar
Fan, J. (1992) Design-adaptive nonparametric regression. Journal of the American Statistical Association 87, 998–1004.CrossRefGoogle Scholar
Fan, J. (1993) Local linear regression smoothers and their minimax efficiency. Annals of Statistics 21, 196–216.CrossRefGoogle Scholar
Fan, J. ’ Yao, Q. (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer-Verlag.CrossRefGoogle Scholar
Granovsky, B.L. ’ Müller, H.-G. (1991) Optimizing kernel methods: A unifying variational principle. International Statistical Review 59, 373–388.CrossRefGoogle Scholar
Liebscher, E. (1996) Strong convergence of sums of α-mixing random variables with applications to density estimation. Stochastic Processes and Their Applications 65, 69–80.CrossRefGoogle Scholar
Mack, Y.P. ’ Silverman, B.W. (1982) Weak and strong uniform consistency of kernel regression estimates. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 405–415.CrossRefGoogle Scholar
Marron, J.S. ’ Wand, M.P. (1992) Exact mean integrated squared error. Annals of Statistics 20, 712–736.CrossRefGoogle Scholar
Masry, E. (1996) Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17, 571–599.CrossRefGoogle Scholar
Müller, H.-G. (1984) Smooth optimum kernel estimators of densities, regression curves and modes. Annals of Statistics 12, 766–774.CrossRefGoogle Scholar
Nadaraya, E.A. (1964) On estimating regression. Theory of Probability and Its Applications 9, 141–142.CrossRefGoogle Scholar
Newey, W.K. (1994) Kernel estimation of partial means and a generalized variance estimator. Econometric Theory 10, 233–253.CrossRefGoogle Scholar
Peligrad, M. (1991) Properties of uniform consistency of the kernel estimators of density and of regression functions under dependence conditions. Stochastics and Stochastic Reports 40, 147–168.CrossRefGoogle Scholar
Rio, E. (1995) The functional law of the iterated logarithm for stationary strongly mixing sequences. Annals of Probability 23, 1188–1203.CrossRefGoogle Scholar
Rosenblatt, M. (1956) Remarks on some non-parametric estimates of a density function. Annals of Mathematical Statistics 27, 832–837.CrossRefGoogle Scholar
Stone, C.J. (1977) Consistent nonparametric regression. Annals of Statistics 5, 595–645.CrossRefGoogle Scholar
Stone, C.J. (1982) Optimal global rates of convergence for nonparametric regression. Annals of Statistics 10, 1040–1053.CrossRefGoogle Scholar
Tran, L.T. (1994) Density estimation for time series by histograms. Journal of Statistical Planning and Inference 40, 61–79.CrossRefGoogle Scholar
Wand, M.P. ’ Schucany, W.R. (1990) Gaussian-based kernels. Canadian Journal of Statistics 18, 197–204.CrossRefGoogle Scholar
Watson, G.S. (1964) Smooth regression analysis. Sankya, Series A 26, 359–372.Google Scholar