Distribuzione asintotica della statistica V2 nel caso di stime non standard - Carpita, Maurizio (Statistica, 1999)
The asymptotic distribution of the godness-of-fit test statistic V2, recently proposed by Dancelli (1993), is derived when estimators other than the standard maximum likelihood are employed. We prove that in these cases, under the null hypothesis, V2 is non asymptotically distributed as a Chi-Square variate, but his distribution is that of a weighted sum of independent Chi-Square variates, the weights being represented by the non negative eingevalues of a particular matrix depending by the unknown parameters. A similar result was derived by Molinari (1977) for the classical Pearson's X2. Numerical examples are also carried out with the log normal model and the method of moments estimator in order to evaluate the actual size of the V2 and X2 tests when referring to the usual X2 tables. The results indicate that, when the number of the class intervals is sufficiently high (15 or more), the bias for the V2 test is not so serious then that of the X2 test.