Statistical problems about the use of the ordinary least-squares method in astrometry - Application to the Paris-Astrolabe data

Details Statistical problems about the use of the ordinary least-squares method in astrometry - Application to the Paris-Astrolabe data Statistical problems about the use of the ordinary least-squares method in astrometry - Application to the Paris-Astrolabe data

Sep 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...183..156b&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 183, no. 1, Sept. 1987, p. 156-166. Research supported by D.A.N.O.F. and CNRS.

Physics

4

Astrolabes, Astrometry, Least Squares Method, Statistical Analysis, Data Reduction, Error Analysis, Linear Equations, Stellar Physics

Scientific paper

In this paper, the implicit assumptions under which the ordinary least-squares (OLS) fit is valid are discussed, with an application to the Paris-Astrolabe data. Nonzero mean of the computer residuals, serial dependence of the errors, heteroscedasticity, and nonnormality of the disturbance term in the model are also discussed. The suggested tests and remedies run into the problems of internal corrections, detection of omitted variables in the linear model such as sidereal time of passage, magnitude, and color effects, and into the problem of unequal variances of the errors in global reductions. Finally, the discussion of nonnormality of the 'statistical' residuals leads to the thorough study of the problem of the detection of suspicious stars and outliers in the OLS regressions, such as stars of the FK-4 supp. catalog which have systematically ill-behaved residuals in the program (Bougeard, 1986). This statistical analysis may be extended, through slight modifications, to many other astronomical data.

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