Qian, Lianfen

This thesis uses Bangladesh Demographic and Health Survey 2014 data to identify the important determinants due to which women justification towards intimate partner violence (IPV) varies. Statistical analyses reveal that among the individual-level independent variables age at first marriage, respondent's education, decision score, religion, NGO membership, access to information, husband's education, normalized wealth score, and division indicator have significant effects on the women's attitude towards IPV. It shows that other than religion, NGO membership, and division indicator, the higher the value of the variable, the lower the likelihood of justifying IPV. However, being a Muslim, NGO member, and resident of other divisions, women are found more tolerant of IPV from their respective counterparts. Among the three community-level variables, only the mean decision score is found significant in lowering the likelihood. The thesis concludes with some policy recommendations and a proposal for future research.

Analyzing life-time data with long-term survivors is an important topic in
medical application. Cure models are usually used to analyze survival data with the
proportion of cure subjects or long-term survivors. In order to include the propor-
tion of cure subjects, mixture and non-mixture cure models are considered. In this
dissertation, we utilize both maximum likelihood and Bayesian methods to estimate
model parameters. Simulation studies are carried out to verify the nite sample per-
formance of the estimation methods. Real data analyses are reported to illustrate
the goodness-of- t via Fr echet, Weibull and Exponentiated Exponential susceptible
distributions. Among the three parametric susceptible distributions, Fr echet is the
most promising.
Next, we extend the non-mixture cure model to include a change point in a covariate
for right censored data. The smoothed likelihood approach is used to address the
problem of a log-likelihood function which is not di erentiable with respect to the
change point. The simulation study is based on the non-mixture change point cure
model with an exponential distribution for the susceptible subjects. The simulation
results revealed a convincing performance of the proposed method of estimation.

Microarray technology is a powerful approach for genomic research, which allows the monitoring of expressing profiles for tens of thousands genes in parallel and is already producing huge amounts of data. This thesis is motivated by a special microarray dataset for the bacteria Yersinia Pestis. It contains more than four thousands genes and each gene has different number of observations. The main purpose of this thesis is to detect essentially functional genes. Gene level adjusted multiple t‐test is proposed to handle the problem of unequal number of observations. Furthermore, a comparation study of our method with two other existing methods (Behrens‐Fisher method and Hotelling t‐square method) are presented. The comparison results show that our proposed methods is the best for identifying essential genes.

This thesis contains two parts. The first part derives the Bayesian estimator of
the parameters in a piecewise exponential Cox proportional hazard regression model,
with one unknown change point for a right censored survival data. The second part
surveys the applications of change point problems to various types of data, such as
long-term survival data, longitudinal data and time series data. Furthermore, the
proposed method is then used to analyse a real survival data.

Change-point detection in hazard rate function is an important research topic in survival
analysis. In this dissertation, we firstly review existing methods for single change-point detection in
piecewise exponential hazard model. Then we consider the problem of estimating the change point in
the presence of right censoring and long-term survivors while using Kaplan-Meier estimator for the
susceptible proportion. The maximum likelihood estimators are shown to be consistent. Taking one
step further, we propose an counting process based and least squares based change-point detection
algorithm. For single change-point case, consistency results are obtained. We then consider the
detection of multiple change-points in the presence of long-term survivors via maximum likelihood
based and counting process based method. Last but not least, we use a weighted least squares based
and counting process based method for detection of multiple change-points with long-term survivors
and covariates. For multiple change-points detection, simulation studies show good performances of
our estimators under various parameters settings for both methods. All methods are applied to real
data analyses.

Meta-analysis is a statistical method of combining many individual analyses. This thesis reviews the need for meta-analysis; the many statistical consideration facing the meta-analyst; and some of Hedges' results concerning the combined estimate of effect size with unequal weights from his 1981 and 1982 papers. Unequal weights used to combine estimates of effect size in meta-analysis are derived using the variances given by the large sample, normal approximation of the distribution of Hedges' unbiased estimates of effect sizes. These variances depend on the effect size and the sample sizes of both experimental and control groups. This creates circular definitions and calls for further estimates. This thesis analyzes the limiting normal approximation to derive a variance which is not dependent on effect size, and it provides guidelines for its use.

In this thesis, we analyze wind speeds collected by South Florida Water Management District at stations L001, L005, L006 and LZ40 in Lake Okeechobee from January 1995 to December 2000. There are many missing values and out-liers in this data. To impute the missing values, three different methods are used: Nearby window average imputation, Jones imputation using Kalman filter, and EM algorithm imputation. To detect outliers and remove impacts, we use ARIMA models of time series. Innovational and additive outliers are considered. It turns out that EM algorithm imputation is the best method for our wind speed data set. After imputing missing values, detecting outliers and removing the impacts, we obtain the best models for all four stations. They are all in the form of seasonal ARIMA(2, 0, 0) x (1, 0, 0)24 for the hourly wind speed data.