TITLE:
Simulated Minimum Quadratic Distance Methods Using Grouped Data for Some Bivariate Continuous Models
AUTHORS:
Andrew Luong
KEYWORDS:
Projected Score Functions, Adaptive Basis, Complete Basis, Chi-Square Tests Statistics, Random Cells, Contingency Table
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.2,
April
30,
2018
ABSTRACT: Quadratic distance methods
based on a special distance which make use of survival functions are developed
for inferences for bivariate continuous models using selected points on the
nonegative quadrant. A related version which can be viewed as a simulated
version is also developed and appears to be suitable for bivariate
distributions with no closed form expressions and numerically not tractable but
it is easy to simulate from these distributions. The notion of an adaptive basis is introduced and
the estimators can be viewed as quasilikelihood estimators using the projected
score functions on an adaptive basis and they are closely related to minimum
chi-square estimators with random cells which can also be viewed as
quasilikeliood estimators using a projected score functions on a special
adaptive basis but the elements of such a basis were linearly dependent. A rule for selecting points on the nonnegative
quadrant which make use of quasi Monte Carlo (QMC) numbers and two sample
quantiles of the two marginal distributions is proposed if complete data is
available and like minimum chi-square methods; the quadratic distance methods also offer
chi-square statistics which appear to be useful in practice for model testing.