ENTROPY-BASED GOODNESS OF FIT TEST FOR A COMPOSITE HYPOTHESIS

Sangyeol Lee
2016 Bulletin of the Korean Mathematical Society  
In this paper, we consider the entropy-based goodness of fit test (Vasicek's test) for a composite hypothesis. The test measures the discrepancy between the nonparametric entropy estimate and the parametric entropy estimate obtained from an assumed parametric family of distributions. It is shown that the proposed test is asymptotically normal under regularity conditions, but is affected by parameter estimates. As a remedy, a bootstrap version of Vasicek's test is proposed. Simulation results
more » ... mulation results are provided for illustration. AD Size Laplace(0,1) 20 4 0.064 0.052 0.052 0.048 20 5 0.050 0.052 0.056 0.054 20 6 0.058 0.050 0.052 0.050 20 7 0.064 0.056 0.058 0.054 50 6 0.048 0.048 0.072 0.062 50 7 0.046 0.048 0.046 0.044 50 8 0.036 0.056 0.068 0.064 50 9 0.058 0.036 0.038 0.042 100 8 0.046 0.058 0.054 0.046 100 9 0.056 0.056 0.038 0.046 100 10 0.050 0.060 0.040 0.048 100 11 0.042 0.052 0.050 0.052 Power Normal(0,1) 20 4 0.195 0.076 0.084 0.078 20 5 0.222 0.096 0.076 0.068 20 6 0.252 0.096 0.094 0.082 20 7 0.240 0.088 0.094 0.082 50 6 0.442 0.180 0.170 0.164 50 7 0.482 0.168 0.152 0.138 50 8 0.492 0.180 0.158 0.142 50 9 0.568 0.212 0.192 0.152 100 8 0.690 0.364 0.404 0.342 100 9 0.692 0.386 0.420 0.370 100 10 0.696 0.420 0.420 0.378 100 11 0.718 0.406 0.396 0.348 Power t(3) 20 4 0.070 0.058 0.058 0.072 20 5 0.080 0.064 0.072 0.092 20 6 0.048 0.060 0.058 0.066 20 7 0.072 0.078 0.062 0.066 50 6 0.078 0.068 0.064 0.076 50 7 0.060 0.074 0.058 0.068 50 8 0.082 0.098 0.100 0.011 50 9 0.056 0.086 0.076 0.009 100 8 0.046 0.104 0.092 0.110 100 9 0.064 0.098 0.088 0.100
doi:10.4134/bkms.2016.53.2.351 fatcat:ajya3yvzkvg77o6uc4i4ax4bie