Grant: Discovery Grants Program - Individual

How accurate is a given statistic? This might be the first question that a researcher asks once a statistic is used to estimate a parameter of interest. Obtaining accuracy measures of a given statistic, such as the variance, is not always easy through analytical methods. That is why resampling methods, such as the bootstrap, have been widely used in the literature to estimate such measurements. In my research program, I intend to study the theoretical developments and practical applications of bootstrap methods in order to establish new ideas.******Statistics Canada provides researchers with access to data files containing columns of bootstrap weights. These weights account for sampling variability in the observations and can be easily used to compute the variance of estimators or construct confidence intervals. Unfortunately, life is rarely that simple and one important practical problem in statistical surveys is the presence of item non-response in most data files. Item non-response is usually compensated using imputation which fills the empty cells in the data file. Treating the imputed values as if they were observed values may lead to serious underestimation of the variance of point estimators since bootstrap methods for full response survey data take into account neither the variability due to item non-response, nor imputation. I plan to build bootstrap methods for imputed survey data assuming the cases of unequal response probabilities and complex survey designs. ******The bootstrap is widely applied in different statistical areas. The generalized bootstrap for estimating equations is applied to estimate the variance of model parameter estimates. Under this approach, we intend to find optimal bootstrap weights in the case of a semi-parametric regression model for autocorrelated time series of count data with applications in finance and epidemiology.******In another application, I intend to develop a bootstrap method for prevalent cohort survival data. A special case of such data is length-biased right censored data. Interest mostly stems from challenges that some Canadian statisticians were faced with while analyzing survival with dementia data collected as part of the Canadian Study of Health and Aging survey. The existing bootstrap methods for such survival data do not consider the extra available information in the left truncation distribution. Thus, such bootstrap methodologies are not efficient. I plan to develop an efficient bootstrap method tailored for such data. Studying jackknife resampling methods in such settings is also a part of my research. The jackknife methods are usually aim at reducing bias where the plug-in estimators are often biased due to right censoring and/or biased sampling. ******These projects will improve current statistical techniques and produce new practical approaches while training strong statisticians who will work in academia or industry in Canada.