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MINIMUM QUADRATIC DISTANCE ESTIMATION FOR A PARAMETRIC FAMILY OF DISCRETE DISTRIBUTIONS DEFINED RECURSIVELY
Author(s) -
Luong Andrew,
Garrido José
Publication year - 1993
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1993.tb01312.x
Subject(s) - mathematics , estimator , independent and identically distributed random variables , parametric statistics , negative binomial distribution , exponential family , poisson distribution , quadratic equation , parametric model , random variable , statistics , geometry
Summary The distribution function of a random sum can easily be computed iteratively when the distribution of the number of independent identically distributed elements in the sum is itself defined recursively. Classical estimation procedures for such recursive parametric families often require specific distributional assumptions (e.g. Poisson, Negative Binomial). The minimum distance estimator proposed here is an estimator within a larger parametric family. The estimator is consistent, efficient when the parametric family is truncated, and can be made either robust or asymptotically efficient when the parametric family has infinite range. Its asymptotic distribution is derived. A brief illustration with Automobile Insurance data is included.