Smoothed Bootstrap Methods for
Right-Censored Data and Bivariate Data

Abstract

This thesis introduces a smoothed bootstrap method for univariate right-censored
data and investigates this bootstrap method for the coverage probability and survival
function inferences through simulations. The bootstrap method relies on the
right-censoring A(n) assumption, which was proposed by Coolen and Yan [21]. This
assumption allows sampling from the whole data range and avoids the complication
in computation that occurs due to ties and right-censored observations which often
occur in the samples created by Efron's bootstrap method [31]. The performance
of the proposed bootstrap method is studied on finite and infinite data ranges, and
compared to the performance of Efron's bootstrap method through simulations. It
is found that the smoothed bootstrap method mostly outperforms Efron's bootstrap
method, in particular when the sample size is small. Also, the smoothed bootstrap
method and Efron's bootstrap method are compared through simulations to compute
the actual Type 1 error rates of quartiles tests and two sample medians test.
For bivariate data, three smoothed bootstrap methods are introduced. Two
of them are based on the generalization of Nonparametric Predictive Inference for
random quantities (X,Y) with copulas, proposed by Coolen-Maturi et al. [22] and
Muhammad et al. [65]. The third one is by using uniform kernels. These smoothed
bootstrap methods are compared to Efron's bootstrap method [33] through simulations.
It is found that the smoothed bootstrap methods mostly outperform Efron's
bootstrap method in terms of the coverage probabilities for Pearson correlation and
the means of T1 = X + Y and T2 = XY^2 when the data distribution is symmetric. Also, these bootstrap methods are compared to compute the Type 1 error rates
of the Pearson and Kendall correlation tests to provide insight into the methods'
performances. For the Pearson correlation test, the smoothed bootstrap methods
mostly perform better than Efron's method, but Efron's method provides better
results for the Kendall correlation test.