Much of my work is in the area of model assessment, generally in the form of goodness-of-fit. In this area I work with Michael Stephens developing specific tests for distributional assumptions and with Peter Guttorp providing general large sample theory for quadratic tests.

My approach to theory is that large sample calculations should lead in a natural way to computable probability approximations. In practice this seems to lead to the study of linear or quadratic functionals of asymptotically Guassian processes. I am particularly interested in limit theorems which naturally lead to approximations whose quality is uniform.

Papers Developing Specific Tests

Lockhart, R. A. and McLaren, G. C. (1985). Asymptotic points for a test of symmetry about a specified median. Biometrika, 72 208--210. PDF

Lockhart, R. A. and Stephens, M. A. (1985). Tests of fit for the von Mises distribution. Biometrika, 72 647--652. PDF

Lockhart, R. A., O'Reilly, F. J. and Stephens, M. A. (1986). Tests for the extreme value and Weibull distributions based on normalized spacings. Nav. Res. Logist. Quart., 33 413--421.

Lockhart, R. A., O'Reilly, F. J. and Stephens, M. A. (1986). Tests of fit based on normalised spacings. J. Roy. Statist. Soc., B, 48 344--352. PDF

Meester, S.G. and Lockhart, R. A. (1988). Testing for normal errors in regression models with many blocks. Biometrika, 75 569--575. PDF

Lockhart, R.A. and Stephens, M. A. (1994). Estimation and tests of fit for the three--parameter Weibull distribution. J. Roy. Statist. Soc.. B. 56 491--500. PDF

Choulakian, V., Lockhart, R.A. and Stephens, M. A. (1994). Cram\'er von Mises statistics for discrete distributions. Canad J. Statist., 22, 125--137.

Theoretical papers analyzing the properties of tests

Lockhart, R. A. (1985). The asymptotic distribution of the correlation coefficient in testing fit to the exponential distribution. Can. J. Statist., 13 253--256.
McLaren, C. G. and Lockhart, R. A. (1987). On the asymptotic efficiency of certain correlation tests of fit. Can. J. Statist., 15 159--167.
Guttorp, P. and Lockhart, R. A. (1988). On the asymptotic distribution of quadratic forms in uniform order statistics. Ann. Statist., 16, 433--449. PDF
Guttorp, P. and Lockhart, R.A. (1989). On the asymptotic distribution of high order spacings statistics. Canad. J. Statist., 17 371--378.
Lockhart, R.A. (1991). Overweight tails are inefficient. Ann. Statist., 19 2254-2258. PDF

Lockhart, R.A. and Swartz, T. B. (1992). Computing asymptotic P-values for EDF tests. Statistics and Computing, 2, 137--141.

Email comments or suggestions to Richard Lockhart (