Science, Technology and Engineering

Department of Mathematics and Statistics

RESEARCH

The main research interests of Paul Kabaila are: (a) time series analysis, (b) statistical model selection, (c) the creation of new variants of the bootstrap which are specially suited to particular situations (e.g. discrete data), (d) confidence limits from discrete data, (e) the foundations of statistical inference and (f) the rigorous analysis of Monte Carlo simulations.

a. Time series analysis

Paul has a long-standing research interest in times series analysis. His specific research interests in this area have been inference in the context of misspecified time series models and bounds on the performance of inferential procedures based on time series data. These research interests have resulted in 15 publications, in a variety of journals including Annals Statist., J. Roy. Statist. Soc. Ser. B, J. Time Series Analysis and IEEE Trans. Autom. Control, prior to 1993.

More recently, Paul's research interests have widened to include the application of bootstrap type techniques to the analysis of time series and the foundations of time series predictive inference. His time series publications from 1993 onwards are:

a1. Kabaila, P. (1993). "On bootstrap predictive inference for autoregressive processes", Journal of Time Series Analysis, 14, 473-484.

a2. Kabaila, P. (1994) "The detection of a single additive outlier of unknown position", Journal of Time Series Analysis, 15, 507-522.

a3. Kabaila, P. (1999). "An efficient simulation method for the computation of a class of conditional expectations", Australian & New Zealand Journal of Statistics, 41, 331-336.

a4. Kabaila, P. & He, Z. (1999). "On assessing prediction error in autoregressive models", Journal of Time Series Analysis, 20, 663-670.

a5. Kabaila, P. (1999). "The relevance property for prediction intervals", Journal of Time Series Analysis, 20, 655 - 662.

a6. Kabaila, P. & He, Z. (2001). "On prediction intervals for conditionally heteroscedastic processes", Journal of Time Series Analysis, 22, 725 - 731.

a7. Kabaila, P. & He, Z. (2004). "The adjustment of prediction intervals to account for errors in parameter estimation", Journal of Time Series Analysis, 25, 351-358.

a8. Kabaila, P. & Syuhada, K. (2007). "The relative efficiency of prediction intervals", Communications in Statistics: Theory and Methods, 36, 2673-2686.

a9. Kabaila, P. & Syuhada, K. (2007). "Improved prediction limits for AR(p) and ARCH(p) processes", Journal of Time Series Analysis, 29, 213-223.

b. Statistical model selection

Statistical model selection has attracted a vast amount of research, not only by statisticians but also by control engineers and econometricians. As pointed out in the papers b1 and b2, the analysis of the effect of statistical model selection on subsequent inference needs to be carried out with great care. This has led to the development of an approach to finding valid confidence intervals after variable selection - see paper b4.

b1. Kabaila, P. (1995) "The effect of model selection on confidence regions and prediction regions", Econometric Theory, 11, 537-549. See also Poetscher, B.M. (1995) "Comment on 'The effect of model selection on confidence regions and prediction regions' by P. Kabaila", Econometric Theory, 11, 550-559.

b2. Kabaila, P. (1996) "The evaluation of model selection criteria: pointwise limits in the parameter space", in Information, Statistics and Induction in Science (D. Dowe et al eds.), World Scientific, pp. 114-118.

b3. Kabaila, P. (1997) "Admissible variable-selection procedures when fitting misspecified models by least squares", Communications in Statistics: Theory and Methods, 26, 2303-2306.

b4. Kabaila, P. (1998) "Valid confidence intervals in regression after variable selection", Econometric Theory, 14, 463-482.

b5. Kabaila, P. (2002) "On variable selection in linear regression", Econometric Theory, 18, 913-925.

b6. Kabaila, P. (2005) "Assessment of a preliminary F-test solution to the Behrens-Fisher problem", Communications in Statistics: Theory and Methods, 34, 291-302.

An S-Plus program for calculating the adjusted Welch confidence interval is available HERE.

b7. Kabaila, P. (2005) "On the coverage probability of confidence intervals in regression after variable selection", Australian & New Zealand Journal of Statistics, 47, 549-562.

b8. Kabaila, P. and Leeb, H. (2006), "On the large-sample minimal coverage probability of confidence intervals after model selection", Journal of the American Statistical Association, 101, 619-629.

b9. Giri, K. and Kabaila, P. (2007), "The coverage probability of confidence intervals in 2^r factorial experiments after preliminary hypothesis testing", Australian and New Zealand Journal of Statistics, 50, 69-79.

b10. Farchione, D. and Kabaila, P. (2008), "Confidence intervals for the normal mean utilizing prior information", Statistics & Probability Letters, 78, 1094-1100.

b11. Kabaila, P. and Tuck J. (2008), "Confidence intervals utilizing prior information in the Beherens-Fisher problem". To appear in Australian & New Zeland Journal of Statistics.

b12. Kabaila, P. and Giri, K. (2008), "Upper bounds on the minimum coverage probability of confidence intervals in regression after model selection" To appear in Australian & New Zeland Journal of Statistics

c. New variants of the bootstrap

The bootstrap has many variants and the comparison of these variants requires the use of Edgeworth expansions, among others. This provides the motivation for paper c2. Paul's interest is in finding new variants of the bootstrap which are successful for certain situations in which the usual variants perform poorly or even fail completely. One such variant is described in paper c1. All the usual bootstrap variants fail for discrete data. Paper c3 describes a method which is related to the bootstrap and which is successful for such data.

c1. Kabaila, P. (1993) "Some properties of profile bootstrap confidence intervals", Australian Journal of Statistics, 35, 205-214.

c2. Kabaila, P. (1993) "A method for the computer calculation of Edgeworth expansions for smooth function models", Journal of Computational and Graphical Statistics, 2, 199-207.

c3. Kabaila, P. & Lloyd, C.J. (2000) "A computable confidence upper limit from discrete data with good coverage properties", Statistics & Probability Letters, 47, 189-198.

d. Confidence limits from discrete data

Paul Kabaila was recently awarded an Australian Research Council grant of $155,000 over 3 years (jointly with Prof. Chris Lloyd) for the project New and computationally feasible methods of constructing efficient and exact confidence limits from count data. This project will lead to important advances in the statistical analysis of count data in fields such as epidemiology, reliability, toxicology and finance.

d1. Kabaila, P. & Lloyd, C.J. (1997) "Tight upper confidence limits from discrete data", Australian Journal of Statistics, 37, 193-204.

d2. Kabaila, P. (1998) "The choice of statistic on which to base tight upper confidence limits", Australian & New Zealand Journal of Statistics, 40, 189-196.

d3. Kabaila, P. & Lloyd, C.J. (2000) "Profile upper confidence limits from discrete data", Australian & New Zealand Journal of Statistics, 42, 67-79.

d4. Kabaila, P. & Byrne, J. (2001) "Exact short Poisson confidence intervals", Canadian Journal of Statistics, 29, 99-106. An Splus program for calculating these confidence intervals is available here.

d5. Kabaila, P. & Lloyd, C.J. (2000) "When do best confidence limits exist?", Statistics & Probability Letters, 50, 115-120.

d6. Kabaila, P. & Byrne, J. (2001) "Exact short confidence intervals from discrete data", Australian & New Zealand Journal of Statistics, 43, 303 - 309.

d7. Byrne, J. & Kabaila, P. (2001) "Short exact confidence intervals for the Poisson mean", Communications in Statistics: Theory and Methods, 30, 257 - 261.

d8. Kabaila, P. (2001) "Better Buehler confidence limits", Statistics & Probability Letters, 52, 145-154.

d9. Kabaila, P. and Lloyd, C.J. (2002) "The importance of the designated statistic on Buehler upper limits on a system failure probability", Technometrics, 44, 390-395.

d10. Lloyd, C.J. and Kabaila, P. (2003) "On the optimality and limitations of Buehler bounds", Australian & New Zealand Journal of Statistics, 45, 167-174.

d11. Kabaila, P. (2003) "A large sample approximation to the profile plug-in upper confidence limit", Acta Applicandae Mathematicae, 78, 185-192.

d12. Kabaila, P. and Lloyd, C.J. (2003) "The efficiency of Buehler confidence limits", Statistics & Probability Letters, 65, 21-28.

d13. Kabaila, P. and Lloyd, C.J. (2004) "Buehler confidence limits and nesting", Australian & New Zealand Journal of Statistics, 46, 463-469.

d14. Kabaila, P. and Lloyd, C.J. (2004) "Buehler limits from approximate upper limits; a numerical investigation of the role of nominal coverage", Journal of Applied Statistical Science, 13, 217-230.

d15. Byrne, J. and Kabaila, P. (2005) "Comparison of Poisson confidence intervals", Communications in Statistics: Theory and Methods, 34, 545-556.

d16. Kabaila, P. and Lloyd, C.J. (2005) "A simple measure of the efficiency of a Buehler confidence limit", Communications in Statistics: Theory and Methods, 34, 767-774.

d17. Kabaila, P. (2005) "Computation of exact confidence intervals from discrete data using studentized test statistics", Statistics and Computing, 15, 71-78.

d18. Kabaila, P. (2005) "Computation of exact confidence limits from discrete data", Computational Statistics, 20, 401-414.

d19. Kabaila, P. and Lloyd, C.J. (2006) "Improved Buehler limits based on refined designated statistics", Journal of Statistical Planning and Inference, 136, 3145-3155.

d20. Kabaila, P. (2007) "Comparison of 'tail method' exact confidence limits for the difference of binomial probabilities", Acta Applicandae Mathematicae, 96, 283-291.

d21. Kabaila, P. (2008) "Statistical properties of exact confidence intervals from discrete data using studentized test statistics", Statistics & Probability Letters, 78, 720-727 .

e. Foundations of statistical inference

The papers e1 and e2 concern the sufficiency principle.

e1. Kabaila, P. (1998) "A note on sufficiency and information loss", Statistics & Probability Letters, 37, 111-114.

e2. Kabaila, P. (2001) "On the order of data reductions by ancillarity and by sufficiency", Australian & New Zealand Journal of Statistics, 43, 299 - 301.

f. Rigorous analysis of Monte Carlo simulations

Monte Carlo simulations are usually analysed on the basis of the fiction that the pseudorandom sequences employed are observations of truly random independent and identically distributed variables. This raises the question of the extent to which Monte Carlo simulations can be analysed rigorously i.e. without resort to this fiction. The papers f1 and f2 show how to rigorously analyse Monte Carlo simulations based on a certain sequence of 4-independent random variables when the quantities being estimated are the expectations of, respectively, an indicator function and an arbitrary function of a continuous random vector.

f1. Kabaila, P. (1999) "Confidence intervals from simulations based on 4-independent random variables", Statistics & Probability Letters, 45, 141-147.

f2. Kabaila, P. "A new method of simulation suitable for evaluating the performance of a wide range of statistical procedures", submitted for publication.