A Goodness-of-Fit Test for Additivity

다국어 초록 (Multilingual Abstract)

In this research, we propose a testing procedure for the goodness-of-fit test to investigate whether the assumption of the additivity between two distributions holds or not. In order to apply this test to the survival analysis, we allow the data to contain the possibly right censored observations. We construct statistics with computing the difference between two different consistent interval estimates from the partitioned the positive half real line, which has been used by Akritas (1988). Also we obtain another consistent estimate of the additivity parameter as byproduct during the construction of test statistics. Then we obtain the limiting distribution of the proposed statistics using the large sample approximation theorem with a consistently estimated covariance matrix when the additivity assumption holds with some additional conditions. Then we exemplify our proposed goodness-of-test with a numerical example and comment briefly some interesting features related to the goodness-of-fit test as concluding remarks.

참고문헌 (Reference)

1 Huffer, F. W., "Weighted test squares estimation for Aalen's additive risk model" 86 : 114-129, 1991

2 홍승만, "Two Sample Nonparametric Test under the Additive Hazards Model" 한국자료분석학회 11 (11): 43-51, 2009

3 박효일, "Test Procedure for the Multivariate Data under the Additive Hazards Assumption" 한국자료분석학회 12 (12): 625-639, 2010

4 Embury, S. H., "Remission maintenance therapy in acute myelogenous leukemia" 126 : 267-272, 1977

5 Grambsch, P. M., "Proportional hazards tests and diagnostics based on weighted residuals" 81 : 515-526, 1994

6 Billingsley, P, "Probability and Measure" Wiley 1986

7 Akritas, M. G., "Pearson-type goodness-of-fit tests : the univariate case" 83 : 222-230, 1988

8 Schott, J. R., "Matrix Analysis for Statistics" Wiley 1997

9 Aalen, O. O., "Mathematical Statistics and Probability Theory" 1-25, 1980

10 Therneau, T. M., "Martingale-based residuals for survival model" 77 : 147-160, 1990

11 Gill, R. D., "Large sample behaviour of the product-limit estimator on the whole line" 11 : 49-58, 1983

12 Hjort, N. L., "Goodness of fit tests in models for life history data based on the cumulative hazard rates" 18 : 1221-1258, 1990

13 이성원, "Goodness of fit Test for the Proportional Hazards Model using the Relative Risk" 한국자료분석학회 8 (8): 31-42, 2006

14 Shorack, G. R., "Empirical Processes with Applications to Statistics" Wiley 1986

15 Neuhaus, G., "Conditional rank tests for the two-sample problem under random censorship" 21 : 1760-1779, 1993

16 Efron, B., "Bootstrap methods: Another look at the jackknife" 7 : 1-26, 1979

17 Serfling,R.J, "Approximation Theorems of Mathematical Statistics" Wiley 1980

18 박효일, "An Estimation of Treatment Effect under the Additive Model" 한국자료분석학회 18 (18): 2329-2336, 2016

19 Yin, G., "Additive hazards model with multivariate failure time data" 91 : 801-818, 2004

20 Choi, J. H., "A nonparametric test for diagnosis of the proportionality assumption" 48 : 467-477, 2007

21 Aalen, O. O., "A linear regression model for the analysis of life times" 8 : 907-925, 1989

22 홍승만, "A Note on a Test Procedure under the Proportional Hazards Model" 한국자료분석학회 18 (18): 2889-2896, 2016