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Activity Number:
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412
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 1, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #308604 |
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Title:
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Kernel Estimation of Multivariate Cumulative Distribution Function
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Author(s):
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Rong Liu*+ and Lijian Yang
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Companies:
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Michigan State University and Michigan State University
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Address:
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Department of Statistics and Probability, East Lansing, MI, 48824,
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Keywords:
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Berry-Esseen bound ; GDP ; kernel ; rate of convergence ; strongly mixing ; survival function
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Abstract:
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A kernel estimator is proposed for multivariate cumulative distribution function, extending the work on Yamato (1973) on univariate distribution function estimation. Under assumptions of strict stationarity and geometrically strong mixing, we establish that the proposed estimator follows the same pointwise asymptotically normal distribution of the empirical cdf, while the new estimator is a smooth instead of a step function as the empirical cdf. Under stronger assumptions the smooth kernel estimator converges to the true cdf uniformly almost surely. Simulated examples are provided to illustrate the theoretical properties. Using the smooth estimator, survival curves for US GDP growth are estimated conditional on the unemployment growth rate to examine how GDP growth rate depends on the unemployment policy.
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