Robust Estimation in Non-normal Samples with Known Detection Limits

Oral, E.
Accepted Paper, Int. J. Math Stat., 2012, 12(2).

Non-detected values, which are the observations below or above a limit of detection, are almost inevitable in most environmental data sets and in HIV studies. The common approach is replacing the non-detected observations with the LOD values, log-transforming the data and using standard procedures to estimate the parameters of a normally distributed population. In this study, we discuss the case when the data is not necessarily from a lognormal population, which is a more realistic situation from a practical point of view. We derive the modified maximum likelihood estimators of the mean and the standard deviation, and develop procedures for hypothesis testing of the population mean under non-normality. We show that the derived MMLEs are much more precise than those obtained by using the traditional approach. We study the robustness properties of the proposed estimators under plausible deviations from an assumed model, and show that derived estimators are highly robust with respect to data anomalies. We apply the method to the NHANES data.

Binary Regression with Stochastic Covariates

Oral, E.
Communications in Statistics-Theory and Methods, 2006 (35) 1429-1447.

In binary regression the risk factor X has been treated in the literature as a non-stochastic variable. In most situations, however, X is stochastic. We present solutions applicable to such situations. We show that our solutions are more precise
than those obtained by treating X as non-stochastic when, in fact, it is stochastic.

Robust ratio-type estimators in simple random sampling

Oral, E. and Kadilar, C.
Journal of the Korean Stat. Soc., 2011, 40(4), 457-467.

In sampling theory, ratio-type estimators are extensively used to estimate the population mean when the correlation between study and auxiliary variables is positively high. In this study, we incorporate robust modified maximum likelihood estimators (MMLEs) into Kadilar–Cingi estimators and provide their properties theoretically. We support the theoretical results with simulations under numerous super-population models, and study the robustness properties of these modified estimators. We show that utilization of MMLEs in estimating the mean of a finite population leads to robust estimates, which is very advantageous when we have non-normality or other common data anomalies such as
outliers.

IMPROVED RATIO ESTIMATORS VIA MODIFIED MAXIMUM LIKELIHOOD

Oral, E. and Kadilar, C.
Pak. J. Statist. 2011 Vol. 27 (3), 269-282

We consider ratio estimators in simple random sampling under data anomalies. We specifically focus on the situations where the error term is not normally distributed, and exploit Tiku’s modified maximum likelihood estimators in the ratio method of
estimation. We derive the mean square errors of the proposed ratio estimators theoretically and obtain the conditions where the proposed ratio estimators have less mean square errors than the traditional ratio-type estimators. We support our theoretical results with two different real-life examples.

STOCHASTIC COVARIATES IN BINARY REGRESSION

Oral, E. and Gunay, S.
Hacettepe Journal of Mathematics and Statistics, 2004, 33, 93-109.

Binary regression has many medical applications. In applying the technique, the tradition is to assume the risk factor X as a non-stochastic variable. In most situations, however, X is stochastic. In this study, we discuss the case when X is stochastic in nature, which is more realistic from a practical point of view than X being non-stochastic. We show that our solutions are much more precise than those obtained by treating X as non-stochastic when, in fact, it is stochastic.

A robust alternative to the ratio estimator under non-normality

Oral, E. and Oral, E.
Statistics and Probability Letters, 2011

In sampling theory, the traditional ratio estimator is the most common estimator of the
population mean when the correlation between study and auxiliary variables is positively
high. We introduce a new ratio-type estimator based on the order statistics of a simple
random sample. We show that this new estimator is considerably more efficient than the
traditional ratio estimator under non-normality, and remarkably robust to data anomalies
such as presence of outliers in data sets.

Sensitivity and specificity of frequently used electrocardiographic criteria for left ventricular hypertrophy in patients with anterior wall myocardial infarction