[1]  Axel Gandy and F. DinHoun Lau. The chopthin algorithm for resampling. arXiv:1502.07532 [stat.CO], 2015. [ bib  http ] 
[2]  Axel Gandy and Georg Hahn. A framework for MonteCarlo based multiple testing. arXiv:1402.3019, 2014. [ bib  http ] 
[3]  Axel Gandy and Georg Hahn. QuickMMCTest  higher accuracy for multiple testing corrections. arXiv:1402.2706, 2014. [ bib  http ] 
[4]  Ragnhild C. Noven, Almut E. D. Veraart, and Axel Gandy. A Lévydriven rainfall model with applications to futures pricing. arXiv:1403.7406 [stat.ME], 2014. [ 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 timevarying 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.

[1]  F. DinHoun Lau and Axel Gandy. RMCMC: A system for updating Bayesian models. Computational Statistics and Data Analysis, 80:99110, 2014. [ bib  DOI  http ] 
[2]  Axel Gandy and Georg Hahn. MMCTest  a safe algorithm for implementing multiple Monte Carlo tests. Scandinavian Journal of Statistics, 41(4):10831101, 2014. [ bib  DOI ] 
[3]  F. DinHoun Lau and Axel Gandy. Optimality of nonrestarting cusum charts. Sequential Analysis, 32(4):458468, 2013. [ bib  DOI ] 
[4] 
Ioannis Phinikettos and Axel Gandy.
An omnibus cusum chart for monitoring time to event data.
Lifetime Data Analysis, pages 114, 2013.
[ bib 
DOI ]
Keywords: Omnibus; CUSUM; Control chart; Kolmogorovâ€“Smirnov 
[5]  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):5372, 2013. [ bib  DOI ] 
[6]  Axel Gandy and Patrick RubinDelanchy. An algorithm to compute the power of Monte Carlo tests with guaranteed precision. Annals of Statistics, 41(1):125142, 2013. [ bib  DOI ] 
[7]  Axel Gandy and F. DinHoun Lau. Nonrestarting CUSUM charts and control of the false discovery rate. Biometrika, 100, 2013. [ bib  DOI ] 
[8]  Axel Gandy and Jan Terje Kvaløy. Guaranteed conditional performance of control charts via bootstrap methods. Scandinavian Journal of Statistics, 40:647668, 2013. [ bib  DOI ] 
[9]  Axel Gandy. Performance monitoring of credit portfolios using survival analysis. International Journal of Forecasting, 28:139144, 2012. [ bib  DOI ] 
[10]  Axel Gandy and Luitgard A. M. Veraart. The effect of estimation in highdimensional portfolios. Mathematical Finance, 2012. [ bib  DOI ] 
[11] 
Marc Henrion, Daniel J. Mortlock, David J. Hand, and Axel Gandy.
A Bayesian approach to stargalaxy classification.
Monthly Notices of the Royal Astronomical Society,
412(4):22862302, 2011.
[ bib 
DOI ]
Keywords: methods: statistical, surveys 
[12] 
Ioannis Phinikettos and Axel Gandy.
Fast computation of highdimensional multivariate normal
probabilities.
Computational Statistics & Data Analysis, 55(4):1521  1529,
2011.
[ bib 
DOI ]
Keywords: Multivariate normal distribution 
[13] 
A. Gandy, J. T. Kvaloy, A. Bottle, and F. Zhou.
Riskadjusted monitoring of time to event.
Biometrika, 97(2):375388, 2010.
[ bib 
DOI ]
Recently there has been interest in riskadjusted 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 outofcontrol state and an incontrol state. We consider both proportional and nonproportional 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 setup, 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.

[14] 
Axel Gandy.
Sequential implementation of Monte Carlo tests with uniformly
bounded resampling risk.
Journal of the American Statistical Association,
104(488):15041511, 2009.
[ bib 
DOI ]
This paper introduces an openended sequential algorithm for computing the pvalue 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 pvalue, 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 openended, the expected number of steps is finite, except when the pvalue 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 Rpackage implementing the sequential algorithm is available online.

[15] 
Axel Gandy and Uwe Jensen.
Model checks for Coxtype regression models based on optimally
weighted martingale residuals.
Lifetime Data Analysis, 15(4):534557, 2009.
[ bib 
DOI ]
We introduce directed goodnessoffit tests for Coxtype 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 Coxtype 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.

[16] 
Axel Gandy, Terry M. Therneau, and Odd O. Aalen.
Global tests in the additive hazards regression model.
Statistics in Medicine, 27:831844, 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):22352240) note that an ad hoc weight function suggested by Aalen (Statist. Med. 1989; 8:907925) 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 
[17]  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):921929, 2007. [ bib  DOI ] 
[18] 
Axel Gandy and Uwe Jensen.
On goodness of fit tests for Aalen's additive risk model.
Scand. J. Statist., 32:425445, 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 http://www.blackwellpublishing.com or http://www.blackwellsynergy.com 
[19]  Axel Gandy and Uwe Jensen. Checking a semiparametric additive risk model. Lifetime Data Anal., 11(4):451472, 2005. [ bib  DOI ] 
[20] 
Axel Gandy, Uwe Jensen, and Constanze Lütkebohmert.
A Cox model with a changepoint applied to an actuarial problem.
Brazilian Journal of Probability and Statistics, 19(2):93109,
2005.
[ bib ]
Available at: http://www.redeabe.org.br/bjpspublishedpapers_volume19_2_pp093109.pdf 
[21]  Axel Gandy. Effects of uncertainties in components on the survival of complex systems with given dependencies. In Alyson Wilson, Sallie KellerMcNulty, 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 ] 
[22]  Axel Gandy and Uwe Jensen. A nonparametric approach to software reliability. Appl. Stoch. Models Bus. Ind., 20:315, 2004. [ bib  DOI ] 
[1]  MeiLing 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):12, 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. SherlawJohnson, 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, 72:458459, 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, 55:589590, 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, http://www.logosverlag.de/cgibin/engbuchmid?isbn=1144&lng=deu&id= 
[8]  Axel Gandy and Uwe Jensen. Checking a semiparametric additive risk model. Technical Report. University of Hohenheim, 2005. [http://www.unihohenheim.de/ jensen/veroeffent.html]. [ bib ] 
[9]  Axel Gandy, Thilo Köder, Uwe Jensen, and Wolfgang Schinköthe. Ausfallverhalten bürstenbehafteter Kleinantriebe. Mechatronik F&M, 1112:1417, 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 VDIBerichte, pages 873898. 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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