Goodness of Fit Based on Integrated Squared Errors in Characteristic Functions or Densities.
RENSSELAER POLYTECHNIC INST TROY NY SCHOOL OF MANAGEMENT
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This paper is concerned mainly with tests of goodness of fit that a random sample x sub 1, x sub 2,..., x sub n is from a completely specified distribution function. The test is based on the integral of the weighted squared modulus of the difference between sample and population characteristic functions. This integral expression is equivalent to the integral of the squared difference between a density and its Parzen kernel estimate. The asymptotic null distribution of the statistic is that of an infinite weighted sum of mutually independent chi squared variates. An approximation to the asymptotic null distribution is given and applied to give the percentage points of a test of fit of p-variate normality. The test of fit is consistent under mild regularity conditions. Keyword Multivariate normality Parametric density estimation.
- Statistics and Probability