Publications of Axel Gandy


[1] Axel Gandy and Georg Hahn. A framework for Monte-Carlo based multiple testing. arXiv:1402.3019, 2014. [ bib | http ]
[2] Axel Gandy and Georg Hahn. QuickMMCTest - higher accuracy for multiple testing corrections. arXiv:1402.2706, 2014. [ bib | http ]
[3] Ragnhild C. Noven, Almut E. D. Veraart, and Axel Gandy. A Lévy-driven rainfall model with applications to futures pricing. arXiv:1403.7406 [stat.ME], 2014. [ bib | http ]
[4] F. Din-Houn Lau and Axel Gandy. Rolling Markov chain Monte Carlo - a system for sequential updating. arXiv:1307.0742 [stat.ME], 2013. [ bib | http ]
[5] Axel Gandy and Nils Lid Hjort. Focussed information criteria for semiparametric linear hazard regression. Submitted, 2009. [ bib ]
The semiparametric linear hazard regression model introduced by McKeague and Sasieni (1994) is an extension of the linear hazard regression model developed by Aalen (1980). Methods of model selection for this type of model are still underdeveloped. In the process of fitting a semiparametric linear hazard regression model one usually starts with a given set of covariates. For each covariate one has at least the following three choices: allow it to have time-varying effect; allow it to have constant effect over time; or exclude it from the model. In this paper we discuss focused information criteria (FIC) to help with this choice. In the spirit of Claeskens and Hjort (2003), `focused' means that one is interested in one specific quantity, e.g. the probability of survival of a patient with a certain set of covariates up to a given time. The FIC involves estimating the mean squared error of the estimator of the quantity one is interested in, and the chosen model is the one minimising this estimated mean squared error. The focused model selection machinery is extended to allow for weighted versions, leading to a suitable wFIC method that aims at finding models that lead to good estimates of a given list of parameters, such as survival probabilities for a subset of patients or for a specified region of covariate vectors. In addition to developing model selection criteria, methods associated with averaging across the best models are also discussed. We illustrate these methods of model selection in a real data situation.

Peer Reviewed Publications

[1] Axel Gandy and Georg Hahn. MMCTest - a safe algorithm for implementing multiple Monte Carlo tests. Scandinavian Journal of Statistics, 2014. Early View. Also available via arXiv:1209.3963 [stat.ME]. [ bib | DOI | http ]
[2] F. Din-Houn Lau and Axel Gandy. Optimality of non-restarting cusum charts. Sequential Analysis, 32(4):458-468, 2013. [ bib | DOI ]
[3] Ioannis Phinikettos and Axel Gandy. An omnibus cusum chart for monitoring time to event data. Lifetime Data Analysis, pages 1-14, 2013. [ bib | DOI ]
Keywords: Omnibus; CUSUM; Control chart; Kolmogorov–Smirnov
[4] Marc Henrion, David J. Hand, Axel Gandy, and Daniel J. Mortlock. CASOS: a subspace method for anomaly detection in high dimensional astronomical databases. Statistical Analysis and Data Mining, 6(1):53-72, 2013. [ bib | DOI ]
[5] Axel Gandy and Patrick Rubin-Delanchy. An algorithm to compute the power of Monte Carlo tests with guaranteed precision. Annals of Statistics, 41(1):125-142, 2013. [ bib | DOI ]
[6] Axel Gandy and F. Din-Houn Lau. Non-restarting CUSUM charts and control of the false discovery rate. Biometrika, 100, 2013. [ bib | DOI ]
[7] Axel Gandy and Jan Terje Kvaløy. Guaranteed conditional performance of control charts via bootstrap methods. Scandinavian Journal of Statistics, 40:647-668, 2013. [ bib | DOI ]
[8] Axel Gandy. Performance monitoring of credit portfolios using survival analysis. International Journal of Forecasting, 28:139-144, 2012. [ bib | DOI ]
[9] Axel Gandy and Luitgard A. M. Veraart. The effect of estimation in high-dimensional portfolios. Mathematical Finance, 2012. [ bib | DOI ]
[10] Marc Henrion, Daniel J. Mortlock, David J. Hand, and Axel Gandy. A Bayesian approach to star-galaxy classification. Monthly Notices of the Royal Astronomical Society, 412(4):2286-2302, 2011. [ bib | DOI ]
Keywords: methods: statistical, surveys
[11] Ioannis Phinikettos and Axel Gandy. Fast computation of high-dimensional multivariate normal probabilities. Computational Statistics & Data Analysis, 55(4):1521 - 1529, 2011. [ bib | DOI ]
Keywords: Multivariate normal distribution
[12] A. Gandy, J. T. Kvaloy, A. Bottle, and F. Zhou. Risk-adjusted monitoring of time to event. Biometrika, 97(2):375-388, 2010. [ bib | DOI ]
Recently there has been interest in risk-adjusted cumulative sum charts, CUSUMS, to monitor the performance of e.g. hospitals, taking into account the heterogeneity of patients. Even though many outcomes involve time, only conventional regression models are commonly used. In this article we investigate how time to event models may be used for monitoring purposes. We consider monitoring using CUSUMS based on the partial likelihood ratio between an out-of-control state and an in-control state. We consider both proportional and non-proportional alternatives, as well as a head start. Against proportional alternatives, we present an analytic method of computing the expected number of observed events before stopping or the probability of stopping before a given observed number of events. In a stationary set-up, the former is roughly proportional to the average run length in calendar time. Adding a head start changes the threshold only slightly if the expected number of events until hitting is used as a criterion. However, it changes the threshold substantially if a false alarm probability is used. In simulation studies, charts based on survival analysis perform better than simpler monitoring schemes. We present one example from retail finance and one medical application.

[13] Axel Gandy. Sequential implementation of Monte Carlo tests with uniformly bounded resampling risk. Journal of the American Statistical Association, 104(488):1504-1511, 2009. [ bib | DOI ]
This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical p-value, is uniformly bounded by an arbitrarily small constant. Previously suggested sequential or nonsequential algorithms, using a bounded sample size, do not have this property. Although the algorithm is open-ended, the expected number of steps is finite, except when the p-value is on the threshold between rejecting and not rejecting. The algorithm is suitable as standard for implementing tests that require (re)sampling. It can also be used in other situations: to check whether a test is conservative, iteratively to implement double bootstrap tests, and to determine the sample size required for a certain power. An R-package implementing the sequential algorithm is available online.

[14] Axel Gandy and Uwe Jensen. Model checks for Cox-type regression models based on optimally weighted martingale residuals. Lifetime Data Analysis, 15(4):534-557, 2009. [ bib | DOI ]
We introduce directed goodness-of-fit tests for Cox-type regression models in survival analysis. 'Directed' means that one may choose against which alternatives the tests are particularly powerful. The tests are based on sums of weighted martingale residuals and their asymptotic distributions. We derive optimal tests against certain competing models which include Cox-type regression models with different covariates and/or a different link function. We report results from several simulation studies and apply our test to a real dataset.

[15] Axel Gandy, Terry M. Therneau, and Odd O. Aalen. Global tests in the additive hazards regression model. Statistics in Medicine, 27:831-844, 2008. [ bib | DOI ]
In this article, we discuss testing for the effect of several covariates in the additive hazards regression model. Bhattacharyya and Klein (Statist. Med. 2005; 24(14):2235-2240) note that an ad hoc weight function suggested by Aalen (Statist. Med. 1989; 8:907-925) is inconsistent when used as a global test for comparing groups since the test statistic depends on which group is used as the baseline group. We will suggest a simple alternative test that does not exhibit this problem. This test is a natural extension of the logrank test. We shall also discuss an alternative covariance estimator. The tests are applied to a data set and a simulation study is performed.

Keywords: survival analysis;additive model;logrank test
[16] Axel Gandy, Patrick Jäger, Bernd Bertsche, and Uwe Jensen. Decision support in early development phases - a case study from machine engineering. Reliability Engineering & System Safety, 92(7):921-929, 2007. [ bib | DOI ]
[17] Axel Gandy and Uwe Jensen. On goodness of fit tests for Aalen's additive risk model. Scand. J. Statist., 32:425-445, 2005. [ bib | DOI | .pdf ]
This is an electronic version of an article published in Scandinavian Journal of Statistics complete citation information for the final version of the paper, as published in the print edition of Scandinavian Journal of Statistics is available on the Blackwell Synergy online delivery service, accessible via the journal's website at or
[18] Axel Gandy and Uwe Jensen. Checking a semiparametric additive risk model. Lifetime Data Anal., 11(4):451-472, 2005. [ bib | DOI ]
[19] Axel Gandy, Uwe Jensen, and Constanze Lütkebohmert. A Cox model with a change-point applied to an actuarial problem. Brazilian Journal of Probability and Statistics, 19(2):93-109, 2005. [ bib ]
Available at:
[20] Axel Gandy. Effects of uncertainties in components on the survival of complex systems with given dependencies. In Alyson Wilson, Sallie Keller-McNulty, Nikolaos Limnios, and Yvonne Armijo, editors, Mathematical and Statistical Methods in Reliability. World Scientific, Singapore, 2005. Proceedings of the Conference “Mathematical Models in Reliability” in Santa Fe, NM, USA, 2004. [ bib ]
[21] Axel Gandy and Uwe Jensen. A nonparametric approach to software reliability. Appl. Stoch. Models Bus. Ind., 20:3-15, 2004. [ bib | DOI ]

Further Publications

[1] Mei-Ling Ting Lee, Mitchell Gail, Ruth Pfeiffer, Glen Satten, Tianxi Cai, and Axel Gandy, editors. Risk Assessment and Evaluation of Predictions. Lecture Notes in Statistics 210. Springer, 2013. [ bib ]
[2] Axel Gandy and Roberto Trotta. Special issue on astrostatistics - editorial. Statistical Analysis and Data Mining, 6(1):1-2, 2013. [ bib | DOI ]
[3] Axel Gandy and Jan Terje Kvaløy. Contribution to the discussion on the article “Statistical methods for healthcare regulation: rating, screening and surveillance” by D. Spiegelhalter, C. Sherlaw-Johnson, M. Bardsley, I. Blunt, C. Wood and O. Grigg. Journal of the Royal Statistical Society, Series A, 175:Early View, 2012. [ bib ]
[4] Axel Gandy. Contribution to the discussion on the article “Stability selection” by N. Meinshausen and P. Bühlmann. Journal of the Royal Statistical Society, Series B, 72:458-459, 2010. [ bib ]
[5] Axel Gandy and Ian W McKeague. Aalen's additive risk model. Encyclopedia of Statistical Sciences, 2008. [ bib ]
[6] Axel Gandy. Contribution to the discussion on the article “Semiparametric analysis of case series data” by C. P. Farrington and H. J. Whitaker. Journal of the Royal Statistical Society, Series C, 55:589-590, 2006. [ bib ]
[7] Axel Gandy. Directed Model Checks for Regression Models from Survival Analysis. Logos Verlag, Berlin, 2006. Dissertation, Universität Ulm. [ bib | .pdf ]
Copyright Logos Verlag Berlin,
Promotionspreis der Universitätsgesellchaft Ulm, siehe, S. 4,7.
[8] Axel Gandy and Uwe Jensen. Checking a semi-parametric additive risk model. Technical Report. University of Hohenheim, 2005. [ jensen/veroeffent.html]. [ bib ]
[9] Axel Gandy, Thilo Köder, Uwe Jensen, and Wolfgang Schinköthe. Ausfallverhalten bürstenbehafteter Kleinantriebe. Mechatronik F&M, 11-12:14-17, 2005. [ bib ]
[10] Patrick Jäger, Michael Wedel, Axel Gandy, Bernd Bertsche, Peter Göhner, and Uwe Jensen. Zuverlässigkeitsbewertung softwareintensiver mechatronischer Systeme in frühen Entwicklungsphasen. In Mechatronik 2005 - Innovative Produktentwicklung, number 1892 in VDI-Berichte, pages 873-898. VDI Verlag, 2005. Contribution to the VDI Konferenz 01./02. Juni 2005, Wiesloch bei Heidelberg. [ bib ]
[11] Axel Gandy. A nonparametric additive risk model with applications in software reliability. Diplomarbeit, Universität Ulm, 2002. [ bib ]

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