Richard Lockhart's Goodness-of-fit Work

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.

Other goodness-of-fit co-authors include Gemai Chen, Vartan Choulakian, Alberto Contreras, Christian Genest, Dan Jeske, Reg Kulperger, Graham McLaren, Steve Meester, Federico O'Reilly, Chandanie Perera, John Spinelli, Zheng Sun, and Tim Swartz.

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 PDF

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

Chen, Gemai, Lockhart, R.A. and Stephens, M.A. (2002). Large Sample Theory for Box-Cox Transformations in Linear Models (With discussion. Read March 22, 2002, in the read paper series of The Canadian Journal of Statistics). The Canadian Journal of Statistics, 30, 177-—234. PDF

Anderson, T.W., Lockhart, R. A. and Stephens, M. A. (2004). An Omnibus Test for the Time Series Model AR(1). Journal of Econometrics , 118, 111-—127. PDF

Lockhart, R. A. and Perera, C. W. (2006). Testing normality in designs with many parameters. Technometrics , 48, 436-—444. PDF

Lockhart, R.A., Spinelli, J. J. and Stephens, M.A. (2007). Cramér-von Mises statistics for discrete distributions with unknown parameters. The Canadian Journal of Statistics, 35, 125–133. No PDF

Jeske, D., Lockhart, R., Stephens, M.A., and Zhang, Q. (2008). Cramer-von Mises tests for the Compatibility of Two Software Environments. Technometrics, 50, 53--60. PDF

Lockhart, R. A., O'Reilly, F.J. & Stephens, M.A. (2009). Exact conditional tests and approximate bootstrap tests for the von Mises distribution. Journal of Statistical Theory and Practice, 3 543--554. No PDF

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. PDF

McLaren, C. G. and Lockhart, R. A. (1987). On the asymptotic efficiency of certain correlation tests of fit. Can. J. Statist., 15 159--167. PDF

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. PDF

Lockhart, R.A. (1991). Overweight tails are inefficient. Ann. Statist., 19 2254-2258. PDF PDF

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

Chen, Gemai and Lockhart, R.A. (2001). Weak convergence of the empirical process of residuals in linear models with many parameters. Ann. Statist., 19 2254-2258. PDF

Lockhart, R. A. and O'Reilly, F. J. (2005). A note on Moore's Conjecture. Statistics and probability Letters , 74, 212-—220. PDF

Lockhart, R. A., O'Reilly, F.J. and Stephens, M.A. (2007). Use of the Gibbs Sampler to obtain conditional tests, with applications. Biometrika, 94, 992-998. PDF

Lockhart, R. A. (2012). Conditional Limit Laws for Goodness-of-Fit Tests. Bernoulli , 18, 857-—882. PDF

Email comments or suggestions to Richard Lockhart (lockhart@sfu.ca)