# Murray Burke

#### Professor Emeritus

Department of Mathematics and Statistics

#### PhD

Carleton University, 1976

#### MA

York University, 1973

#### BSc

Concordia University, 1972

## Contact information

#### Email

mdburke@ucalgary.ca

## Research and teaching

### Research areas

• Asymptotic theory for goodness-of-fit-type statistics
• Application of bootstrap techniques to approximate unknown limit distributions
• Survival analysis and randomly censored data
• Tests for semi-parametric models

## Publications

### Book

• Burke, Murray. Testing regression models: a strong martingale approach 44. Fields Institute Communications Series, 2004. 351-365. Print.
• Burke, Murray. Tests for a general two-sample problem using weighted spacings J\'anos Bolyai Math. Soc., 2002. 249-268. Print.
• Burke, Murray. A {G}aussian bootstrap approach to estimation and tests North-Holland, 1998. 697-706. Print.
• Burke, Murray. Bootstrapping sums of weighted spacings for composite goodness-of-fit North-Holland, 1992. 3-15. Print.
• Burke, Murray. Independence tests for randomly censored bivariate data 45. North-Holland, 1987. 59-69. Print.
• Burke, Murray. Tests for exponentiality based on randomly censored data 32. North-Holland, 1982. 89-101. Print.
• Cs{\"o}rg{\H{o}}, M. and Burke, Murray. Weak approximations of the empirical process when parameters are estimated Springer, 1976. 1-16. Lecture Notes in Math., Vol. 566. Print.

### Conference proceedings

• Burke, Murray. A Gaussian bootstrap approach to estimation and tests. In: \it{Asymptotic Methods in Probability and Statistics} North Holland, Amsterdam, 1998. 697-706.
• Burke, Murray and Gombay, Edit. Bootstrapped parameter estimated quantile processes -- L-estimation case North-Holland, 1990. 69-81.

### Journal article

• Burke, Murray. "Nonparametric estimation of a survival function under progressive Type-I multistage censoring". Journal of Statistical Planning and Inference 141.2 (2011): 910 - 923. Print.
• Burke, Murray. "Approximations for a Multivariate Hybrid Process with Applications to Change-Point Detection". Mathematical Methods of Statistics 19.2 (2010): 121 - 135. Print.
• Burke, Murray and Lu, Xuewen. "Nonparametric estimation of linear functionals of a bivariate distribution under univariate censoring". Journal of Statistical Planning and Inference 138.10 (2008): 3238-3256. Print.
• Burke, Murray. "Limit theorems for change-point detection in nonparametric regression models". Acta Sci. Math. (Szeged) 73. (2007): 865-882. Print.
• Burke, Murray and Feng, Dandong D. "The proportional hazards regression model with staggered entries: a strong martingale approach". Stochastic Processes and their Applications 116. (2006): 1195-1214. Print.
• Lu, Xuewen and Burke, Murray. "Censored multiple regression by the method of average derivatives". Journal of Multivariate Analysis 95.1 (2005): 182-205. Print.
• Burke, Murray. "Multivariate tests-of-fit and uniform confidence bands using a weighted bootstrap". Statistics \& Probability Letters 46.1 (2000): 13-20. Print.
• Yuen, K. C. and Burke, Murray. "A test of fit for a semiparametric additive risk model". Biometrika 84.3 (1997): 631-639. Print.
• Burke, Murray and K.C. Yuen. "Goodness-of-fit tests for the Cox model via bootstrap method.". Journal of Statistical Planning and Inference 47.3 (1995): 237-256. Print.
• Burke, Murray and Edit Gombay. "Tests of fit for Cox's regression model.". Probab. Math. Statist. 13.1 (1992): 127-137. Print.
• Burke, Murray and Gombay, Edit. "The bootstrapped maximum likelihood estimator with an application". Statistics \& Probability Letters 12.5 (1991): 421-427. Print.
• Burke, Murray and Horv{\'a}th, Lajos. "Large sample properties of kernel-type score function estimators". Journal of Statistical Planning and Inference 22.3 (1989): 307-321. Print.
• Burke, Murray. "Estimation of a bivariate distribution function under random censorship". Biometrika 75.2 (1988): 379-382. Print.
• Burke, Murray and Gombay, Edit. "On goodness-of-fit and the bootstrap". Statistics \& Probability Letters 6.5 (1988): 287-293. Print.
• Burke, Murray. "An almost-sure approximation of a multivariate product-limit estimator under random censorship". Statistics \& Decisions. Journal for Statistical Theory and Related Fields 6.1-2 (1988): 89-108. Print.
• Burke, Murray. "Quadratic measures of fit for estimates of the partial derivatives of a survival function and the hazard gradient". Statistics \& Decisions. Journal for Statistical Theory and Related Fields 6.1-2 (1988): 1-19. Print.
• Burke, Murray, Cs{\"o}rg{\H{o}}, S and Horv{\'a}th, Lajos. "A correction to and improvement of: {S}trong approximations of some biometric estimates under random censorship'' [{Z}. {W}ahrsch.\ {V}erw.\ {G}ebiete {\bf 56} (1981), no.\ 1, 87-112; \refmr {MR}0612162 (83a:62102)\endrefmr]". Probability Theory and Related Fields 79.1 (1988): 51-57. Print.
• Burke, Murray and Horv{\'a}th, L.. "Erratum: {E}stimation of influence functions'' [{S}tatist.\ {P}robab.\ {L}ett.\ {\bf 4} (1986), no.\ 2, 81-85; \refmr {MR}0829438 (87f:62058)\endrefmr]". Statistics \& Probability Letters 5.2 (1987): 161. Print.
• Burke, Murray and Horv{\'a}th, Lajos. "Estimation of influence functions". Statistics \& Probability Letters 4.2 (1986): 81-85. Print.
• Burke, Murray and Horv{\'a}th, Lajos. "Density and failure rate estimation in a competing risks model". Sankhy\=a Ser. A 46.1 (1984): 135-154. Print.
• Burke, Murray. "Approximation of some hazard rate estimators in a competing risks model". Stochastic Processes and their Applications 14.2 (1983): 157-174. Print.
• Burke, Murray, Cs{\"o}rg{\H{o}}, S and Horv{\'a}th, Lajos. "Strong approximations of some biometric estimates under random censorship". Zeitschrift f\"ur Wahrscheinlichkeitstheorie und Verwandte Gebiete 56.1 (1981): 87-112. Print.
• Burke, Murray, Cs{\"o}rg{\H{o}}, M., Cs{\"o}rg{\H{o}}, S. and R{\'e}v{\'e}sz, P.. "Approximations of the empirical process when parameters are estimated". The Annals of Probability 7.5 (1979): 790-810. Print.
• Burke, Murray. "On the asymptotic power of some {$k$}-sample statistics based on the multivariate empirical process". Journal of Multivariate Analysis 9.2 (1979): 183-205. Print.
• Burke, Murray. "On the multivariate two-sample problem using strong approximations of the {EDF}". Journal of Multivariate Analysis 7.4 (1977): 491-511. Print.