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Simulated Minimum Quadratic Distance Methods Using Grouped Data for Some Bivariate Continuous Models

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Document pages: 28 pages

Abstract: Quadratic distance methodsbased on a special distance which make use of survival functions are developedfor inferences for bivariate continuous models using selected points on thenonegative quadrant. A related version which can be viewed as a simulatedversion is also developed and appears to be suitable for bivariatedistributions with no closed form expressions and numerically not tractable butit is easy to simulate from these distributions. The notion of an adaptive basis is introduced andthe estimators can be viewed as quasilikelihood estimators using the projectedscore functions on an adaptive basis and they are closely related to minimumchi-square estimators with random cells which can also be viewed asquasilikeliood estimators using a projected score functions on a specialadaptive basis but the elements of such a basis were linearly dependent. A rule for selecting points on the nonnegativequadrant which make use of quasi Monte Carlo (QMC) numbers and two samplequantiles of the two marginal distributions is proposed if complete data isavailable and like minimum chi-square methods; the quadratic distance methods also offerchi-square statistics which appear to be useful in practice for model testing.

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