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Nonparametric Estimation and Symmetry Tests for Conditional Density Functions

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  • Hyndman, R.J.
  • Yao, Q.

Abstract

We suggest two new methods for conditional density estimation. The first is based on locally fitting a log-linear model, and is in the spirit of recent work on locally parametric techniques in density estimation. The second method is a constrained local polynomial estimator. Both methods always produce non-negative estimators. We propose an algorithm suitable for selecting the two bandwidths for either estimator. We also develop a new bootstrap test for the symmetry of conditional density functions. The proposed methods are illustrated by both simulation and application to a real data set.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/1998/wp17-98.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 17/98.

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Length: 15 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:msh:ebswps:1998-17

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Keywords: TESTING ; STATISTICAL ANALYSIS ; ESTIMATION OF PARAMETERS;

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References

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  1. Bashtannyk, D.M. & Hyndman, R.J., 1998. "Bandwidth Selection for Kernel Conditional Density Estimation," Monash Econometrics and Business Statistics Working Papers 16/98, Monash University, Department of Econometrics and Business Statistics.
  2. Peter Hall & Rodney C. L. Wolff & Qiwei Yao, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
  3. Wolfgang Polonik & Qiwei Yao, 2000. "Conditional minimum volume predictive regions for stochastic processes," LSE Research Online Documents on Economics 6311, London School of Economics and Political Science, LSE Library.
  4. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
  5. Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
  6. Gooijer, Jan G. De & Gannoun, Ali, 2000. "Nonparametric conditional predictive regions for time series," Computational Statistics & Data Analysis, Elsevier, vol. 33(3), pages 259-275, May.
  7. Jianqing Fan & Qiwei Yao & Howell Tong, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
  8. Howell Tong & Qiwei Yao, 2000. "Nonparametric estimation of ratios of noise to signal in stochastic regression," LSE Research Online Documents on Economics 6324, London School of Economics and Political Science, LSE Library.
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