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Testing for linear regression relationships in randomly right-censored varying-coefficient models. (English) Zbl 1195.62051

Summary: A test statistic is constructed to test linear relationships in randomly right-censored varying-coefficient models. A residual-based bootstrap procedure is employed to derive the \(p\)-value of the test. The performance of the test is examined by extensive simulations. The simulation results show that the bootstrap estimate of the null distribution of the test statistic is approximately valid and the test method with the residual-based bootstrap works satisfactorily for at least moderate censoring rates of the response. Furthermore, the proposed test is applied to the Stanford heart transplant data for exploring a linear regression relationship between the logarithm of the survival time and the age of the patients.

MSC:

62G10 Nonparametric hypothesis testing
62N01 Censored data models
62J05 Linear regression; mixed models
62G09 Nonparametric statistical resampling methods
65C60 Computational problems in statistics (MSC2010)
62N03 Testing in survival analysis and censored data
62G08 Nonparametric regression and quantile regression
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References:

[1] Bao Y. C., Computational Statistics and Data Analysis 51 pp 6488– (2007) · Zbl 1445.62160 · doi:10.1016/j.csda.2007.02.025
[2] Brumback B., Journal of the American Statistical Association 93 pp 961– (1998) · doi:10.1080/01621459.1998.10473755
[3] Buckley J., Biometrika 66 pp 429– (1979) · Zbl 0425.62051 · doi:10.1093/biomet/66.3.429
[4] Cai Z. W., Journal of Econometrics 136 pp 163– (2007) · Zbl 1418.62306 · doi:10.1016/j.jeconom.2005.08.004
[5] Cai Z. W., Journal of the American Statistical Association 95 pp 941– (2000) · doi:10.1080/01621459.2000.10474284
[6] Cai Z. W., Journal of the American Statistical Association 95 pp 888– (2000) · doi:10.1080/01621459.2000.10474280
[7] Carroll R. J., Journal of the American Statistical Association 92 pp 477– (1997) · doi:10.1080/01621459.1997.10474001
[8] Chen R., Journal of the American Statistical Association 88 pp 298– (1993)
[9] Chiang C. T., Journal of the American Statistical Association 96 pp 605– (2001) · Zbl 1018.62034 · doi:10.1198/016214501753168280
[10] Cleveland W. S., Statistical Models in S pp 309– (1991)
[11] Cox D. R., Journal of the Royal Statistical Society B 34 pp 187– (1972)
[12] Engel R. F., Journal of the American Statistical Association 81 pp 310– (1986) · doi:10.1080/01621459.1986.10478274
[13] Fan J., Journal of the American Statistical Association 89 pp 560– (1994) · doi:10.1080/01621459.1994.10476781
[14] Fan J., Bernoulli 11 pp 1031– (2005) · Zbl 1098.62077 · doi:10.3150/bj/1137421639
[15] Fan J., Journal of the American Statistical Association 100 pp 890– (2005) · Zbl 1117.62328 · doi:10.1198/016214504000001439
[16] Fan J., The Annals of Statistics 27 pp 1491– (1999) · Zbl 0977.62039 · doi:10.1214/aos/1017939139
[17] Fan J., The Annals of Statistics 29 pp 153– (2001) · Zbl 1029.62042 · doi:10.1214/aos/996986505
[18] Friedman J. H., The Annals of Statistics 19 pp 1– (1991) · Zbl 0765.62064 · doi:10.1214/aos/1176347963
[19] Gu C., Journal of Computational Graphics and Statistics 2 pp 97– (1993)
[20] Härdle W., Journal of Financial Econometrics 1 pp 55– (2003) · doi:10.1093/jjfinec/nbg005
[21] Härdle W., Partially Linear Models (2000) · Zbl 0968.62006 · doi:10.1007/978-3-642-57700-0
[22] Härdle W., Journal of the American Statistical Association 84 pp 986– (1989)
[23] Hart J. D., Nonparametric Smoothing and Lack-of-Fit Tests (1997) · Zbl 0886.62043 · doi:10.1007/978-1-4757-2722-7
[24] Hastie T. J., Generalized Additive Models (1990) · Zbl 0747.62061
[25] Hastie T. J., Journal of the Royal Statistical Society B 55 pp 757– (1993)
[26] Hoover D. R., Biometrika 85 pp 809– (1998) · Zbl 0921.62045 · doi:10.1093/biomet/85.4.809
[27] Huang J. Z., Statistica Sinica 14 pp 763– (2004)
[28] Koul H., The Annals of Statistics 9 pp 1276– (1981) · Zbl 0477.62046 · doi:10.1214/aos/1176345644
[29] Kaplan E. L., Journal of the American Statistical Association 53 pp 457– (1958) · doi:10.1080/01621459.1958.10501452
[30] Lai T. L., Survival Analysis (1993)
[31] Lai T. L., Journal of Multivariate Analysis 52 pp 259– (1995) · Zbl 0817.62008 · doi:10.1006/jmva.1995.1013
[32] Luo X. H., Acta Mathematica Applicatae Sinica 29 pp 415– (2006)
[33] Mercurio D., The Annals of Statistics 32 pp 577– (2004) · Zbl 1091.62103 · doi:10.1214/009053604000000102
[34] Miller R., Biometrika 63 pp 449– (1976) · Zbl 0344.62058 · doi:10.1093/biomet/63.3.449
[35] Miller R., Biometrika 69 pp 521– (1982) · Zbl 0503.62091 · doi:10.1093/biomet/69.3.521
[36] Pardo-Fernández J. C., Canadian Journal of Statistics 35 pp 249– (2007) · Zbl 1129.62036 · doi:10.1002/cjs.5550350204
[37] Qin G. S., Journal of Statistical Planning and Inference 84 pp 95– (2000) · Zbl 0968.62043 · doi:10.1016/S0378-3758(99)00141-X
[38] Stute W., Journal of the American Statistical Association 93 pp 141– (1998) · doi:10.1080/01621459.1998.10474096
[39] Wang Q. H., Science China Series A 39 pp 163– (1996)
[40] Wu C. O., Journal of the American Statistical Association 93 pp 1388– (1998) · doi:10.1080/01621459.1998.10473800
[41] Zhang C. X., Computational Statistics and Data Analysis 51 pp 6543– (2007) · Zbl 1445.62257 · doi:10.1016/j.csda.2007.03.005
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