Approved for public release; distribution is unlimited / This study explores whether the attacker's daily casualty rate (DCR) changes according to the terrain. The data set is a part of a larger database, Division Level Engagement Database from the Dupuy Institute. There are data on 253 battles, 96 of which occurred in urban areas. All the engagements are selected from European Theater of Operation (ETO) in World War II. The available data set contains measurements about the battles like initial strengths, daily casualties, terrain, front width, linear density, attacker's and defender's country, and armor losses. Hypothesis tests are used to find if the DCR is different in urban operations. A linear regression model is constructed to predict outcomes of similar engagements and to see the effect of each variable. It is concluded that the attacker's daily casualty rate is, on average, lower in urban operations. Terrain and force ratio are the most effective drivers of the daily casualty rate. In addition, it is seen that allied forces (U.S., U.K. and Canada) had a different approach to Military Operations on Urban Terrain than Soviet and German forces. The Allies used extensive combat power in urban operations. / First Lieutenant, Turkish Army

is shown to follow an exponential distribution. These three models enable operators to explore the impact of various inputs prior to programming the vehicle, thus allowing them to choose the best combination of vehicle parameters that minimize the offset error between the reported and actual locations.

Approved for public release, distribution is unlimited / This thesis compares characteristics that influence intended stay/leave behavior of non prior service junior naval officers from two different time periods. Samples of officers, under the rank of lieutenant, with less then six years of active duty service from the 1992 and 1999 Department of Defense Surveys of Active Duty Personnel were used for this analysis. Metrics for important determinates of retention were constructed using similar questions from both surveys. Logistic regression was used to identify significant influences on retention intentions in both survey years. Two composite dimensions positively affected retention intentions in both survey years: satisfaction with Service Attributes and satisfaction with Present Employment Attributes. Being female negatively affected retention intentions in both surveys. The minority variable, Black, the number of PCS moves, and having debt greater than $7 ,500 positively affected retention intentions, while being stationed onboard a ship, probability of finding a civilian job, and the composite dimension, satisfaction with Future Employment Attributes, negatively affected retention intentions in 1992. Influence from a significant other and the number of hours worked positively affected retention in 1999. Monetary variables were highly significant for retention intentions in 1992 but not in 1999. It is likely that the force drawdown, base closures, and a weak economy in 1992 explain these differences. / Lieutenant, United States Navy

Spatial and temporal components play a critical role in explaining variability across geographic regions and time, and are necessary components to space-time epidemiological research. Until recent years, most spatial epidemiological studies have used simple space-time analyses, but the continuous advancements in statistical modeling software and geographic information systems have made more complex spatial analyses readily available. However, methods may be problematic and several ongoing statistical weaknesses have been documented, including failing to account for three significant correlative factors - spatial, temporal, and spatiotemporal autocorrelations. Using Eastern Equine Encephalitis (EEE) human incidence data, this Master's thesis aimed to answer the research question, is there a northeastern shift in human EEE incidence within the United States, by identifying a statistical model that adjusts for spatial, temporal, and spatiotemporal autocorrelations. This thesis introduced the spatial autoregressive distributed lag (SADL) model, a model that adjusts for spatial, temporal, and spatiotemporal autocorrelations. However, results demonstrated that EEE is too rare an event for the SADL model to be appropriate, and a non-autocorrelation model was used as the final model. Results showed that EEE incidence is significantly increasing over time for all infected regions of the United States, with a significant difference of 1.4 cases/10 million between 1964 and 2015. Results did not demonstrate a northeastern shift in EEE incidence as the northeastern US had the highest expected incidence across the entire study period (1964-1967: 2.9/10 million; 2012-2015: 6.8/10 million), but results did demonstrate that the northeastern US had the quickest increasing risk for EEE as compared to other infected regions of the US with an increase in expected incidence of 3.9/10 million between 1964 and 2015.

In this discussion paper, we argue that the literature on tree algorithms is very fragmented. We identify possible causes and discuss good and bad sides of this situation. Among the latter is the lack of free open-source implementations for many algorithms. We argue that if the community adopts a standard of creating and sharing free open-source implementations for their developed algorithms and creates easy access to these programs the bad sides of the fragmentation will be actively combated and will benefit the whole scientific community. (authors' abstract)

Quantile Regression, as introduced by Koenker, R. and Bassett, G. (1978), provides a complete picture of the relationship between the response variable and covariates by estimating a family of conditional quantile functions. Also, it offers a natural solution to challenges such as; homoscedasticity and sometimes unrealistic normality assumption in the usual conditional mean regression. Most of the results for quantile regression are based on simple random sampling (SRS). In this thesis, we study the quantile regression with rank-based sampling methods. Rank-based sampling methods have a wide range of applications in medical, ecological and environmental research, and have been shown to perform better than SRS in estimating several population parameters. We propose a new objective function which takes into account the ranking information to estimate the unknown model parameters based on the maxima or minima nomination sampling designs. We compare the mean squared error of the proposed quantile regression estimates using maxima (or minima) nomination sampling design and observe that it provides higher relative e ciency when compared with its counterparts under SRS design for analyzing the upper (or lower) tails of the distribution of the response variable. We also evaluate the performance of our proposed methods when ranking is done with error. / February 2017

No description available.

Master of Science / Department of Statistics / Weixing Song / There has been a continuing interest among statisticians in the problem of regression models wherein the independent variables are measured with error and there is considerable literature on the subject. In the following report, we discuss the errors-in-variables regression model: yi = β0 + β1xi + β2zi + ϵi,Xi = xi + ui,Zi = zi + vi with i.i.d. errors (ϵi, ui, vi), for i = 1, 2, ..., n and find the least square estimators for the parameters of interest. Both weak and strong consistency for the least square estimators βˆ0, βˆ1, and βˆ2 of the unknown parameters β0, β1, and β2 are obtained. Moreover, under regularity conditions, the asymptotic normalities of the estimators are reported.

Master of Science / Department of Statistics / Weixing Song / In the classical Tobit regression model, the regression error term is often assumed to have a zero mean normal distribution with unknown variance, and the regression function is assumed to be linear. If the normality assumption is violated, then the commonly used maximum likelihood estimate becomes inconsistent. Moreover, the likelihood function will be very complicated if the regression function is nonlinear even the error density is normal, which makes the maximum likelihood estimation procedure hard to implement. In the full nonparametric setup when both the regression function and the distribution of the error term [epsilon] are unknown, some nonparametric estimators for the regression function has been proposed. Although the assumption of knowing the distribution is strict, it is a widely adopted assumption in Tobit regression literature, and is also confirmed by many empirical studies conducted in the econometric research. In fact, a majority of the relevant research assumes that [epsilon] possesses a normal distribution with mean 0 and unknown standard deviation. In this report, we will try to develop a semi-parametric estimation procedure for the regression function by assuming that the error term follows a distribution from a class of 0-mean symmetric location and scale family. A minimum distance estimation procedure for estimating the parameters in the regression function when it has a specified parametric form is also constructed. Compare with the existing semiparametric and nonparametric methods in the literature, our method would be more efficient in that more information, in particular the knowledge of the distribution of [epsilon], is used. Moreover, the computation is relative inexpensive. Given lots of application does assume that [epsilon] has normal or other known distribution, the current work no doubt provides some more practical tools for statistical inference in Tobit regression model.

Master of Science / Department of Computing and Information Sciences / William H. Hsu / Logistic regression is a model for function estimation that measures the relationship between independent variables and a categorical dependent variable, and by approximating a conditional probabilistic density function using a logistic function, also known as a sigmoidal function. Multinomial logistic regression is used to predict categorical variables where there can be more than two categories or classes. The most common type of algorithm for optimizing the cost function for this model is gradient descent. In this project, I implemented logistic regression using conjugate gradient descent (CGD). I used the 20 Newsgroups data set collected by Ken Lang. I compared the results with those for existing implementations of gradient descent. The conjugate gradient optimization methodology outperforms existing implementations.