A nonparametric assessment of model adequacy based on Kullback-Leibler divergence
A discrepancy measure to assess model fitness against a nonparametric alternative is proposed. First, a Polya tree prior is constructed so that the centering distribution is the null. Second, the prior is updated in the light of data to obtain the posterior centering distribution as the alternative. Third, a Kullback-Leibler divergence type of test statistic is derived to assess the discrepancy between the two centering distributions. The properties of the test statistic are derived, and a power comparison with several well-known test statistics is conducted. The use of the test statistic is illustrated using network traffic data.
KeywordsGoodness of fit Nonparametric alternative Packet train Polya tree Teletraffic data
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- Carota, C., Parmigiani, G.: On Bayes factors for nonparametric alternatives. In: Bernardo, J.M., Berger, J.O., David, A.P., Smith, A.F.M. (eds.) Bayesian Statistics 5, pp. 507–511. Clarendon Press, Oxford (1996) Google Scholar
- d’Agostino, R.B., Stephens, M.A.: Goodnesso-of-fit techniques. Statistics: Textbooks and Monographs, vol. 68. Marcel Dekker, New York (1986) Google Scholar
- Mengerson, K., Robert, C.: Testing for mixtures: a Bayesian entropic approach. In: Bernardo, J.M., Berger, J.O., David, A.P., Smith, A.F.M. (eds.) Bayesian Statistics 5, pp. 255–276. Clarendon Press, Oxford (1996) Google Scholar
- Viele, K.: Evaluating fit using Dirichlet processes. Technical Report 384, Department of Statistics, University of Kentucky (http://web.as.uky.edu/statistics/techreports/techreports.html) (2000)
- Willinger, W., Paxson, V., Taqqu, M.S.: Self-similarity and heavy tails: structural modeling of network traffic. In: Adler, R., Feldman, R., Taqqu, M.S. (eds.) A Practical Guide to Heavy Tails: Statistical Techniques and Applications, pp. 27–53. Birkhäuser, Boston (1998) Google Scholar