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A goodnessofit test for semiparametric copula models for bivariate censored dataShin, Jimin 07 August 2020 (has links)
In this thesis, we suggest a goodnessofit test for semiparametric copula models. We extended the pseudo inandoutsample (PIOS) test proposed in [17], which is based on the PIOS test in [28]. The PIOS test is constructed by comparing the pseudo "insample" likelihood and pseudo "outofsample" likelihood. Our contribution is twoold. First, we use the approximate test statistics instead of the exact test statistics to alleviate the computational burden of calculating the test statistics. Secondly, we propose a parametric bootstrap procedure to approximate the distribution of the test statistic. Unlike the nonparametric bootstrap which resamples from the original data, the parametric procedure resamples the data from the copula model under the null hypothesis. We conduct simulation studies to investigate the performance of the approximate test statistic and parametric bootstrap. The results show that the parametric bootstrap presents higher test power with a wellcontrolled type I error compared to the nonparametric bootstrap.

2 
GoodnessOfFit Test for Hazard RateVital, Ralph Antoine 14 December 2018 (has links)
In certain areas such as Pharmacokinetic(PK) and Pharmacodynamic(PD), the hazard rate function, denoted by ??, plays a central role in modeling the instantaneous risk of failure time data. In the context of assessing the appropriateness of a given parametric hazard rate model, Huh and Hutmacher [22] showed that their hazardbased visual predictive check is as good as a visual predictive check based on the survival function. Even though Huh and Hutmacher’s visual method is simple to implement and interpret, the final decision reached there depends on the personal experience of the user. In this thesis, our primary aim is to develop nonparametric goodnessofit tests for hazard rate functions to help bring objectivity in hazard rate model selections or to augment subjective procedures like Huh and Hutmacher’s visual predictive check. Toward that aim two nonparametric goodnessofit (go) test statistics are proposed and they are referred to as chisquare go test and kernelbased nonparametric goodnessofit test for hazard rate functions, respectively. On one hand, the asymptotic distribution of the chisquare goodnessofit test for hazard rate functions is derived under the null hypothesis ??0 : ??(??) = ??0(??) ??? ? R + as well as under the fixed alternative hypothesis ??1 : ??(??) = ??1(??) ??? ? R +. The results as expected are asymptotically similar to those of the usual Pearson chisquare test. That is, under the null hypothesis the proposed test converges to a chisquare distribution and under the fixed alternative hypothesis it converges to a noncentral chisquare distribution. On the other hand, we showed that the power properties of the kernelbased nonparametric goodnessofit test for hazard rate functions are equivalent to those of the Bickel and Rosenblatt test, meaning the proposed kernelbased nonparametric goodnessofit test can detect alternatives converging to the null at the rate of ???? , ?? < 1/2, where ?? is the sample size. Unlike the latter, the convergence rate of the kernelbase nonparametric go test is much greater; that is, one does not need a very large sample size for able to use the asymptotic distribution of the test in practice.

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