In this thesis, an error analysis based method is proposed to calculate single shot hit probability (PSSH) values of a fire control system. The proposed method considers that a weapon and a threat are located in three dimensional space. They may or may not have relative motion in three dimensions with respect to each other. The method accounts for the changes in environmental conditions. It is applicable in modeling and simulation as well as in top down design of a fire control system to reduce the design cost. The proposed method is applied to a specific fire control system and it is observed that PSSH values highly depend on the distance between the weapon and the threat, hence they are time varying. Monte Carlo simulation is used to model various defense scenarios in order to evaluate a heuristic developed by G&uuml / lez (2007) for weapon-threat assignment and scheduling of weapons&rsquo / shots. The heuristic uses the proposed method for PSSH and time of flight computation. It is observed that the difference between the results of simulation and heuristic depends on the scenario used.

In this study, general geometric Levy market models are considered. Since these models are, in general, incomplete, that is, all contingent claims cannot be replicated by a self-financing portfolio consisting of investments in a risk-free bond and in the stock, it is suggested that the market should be enlarged by artificial assets based on the power-jump processes of the underlying Levy process. Then it is shown that the enlarged market is complete and the explicit hedging portfolios for claims whose payoff function depends on the prices of the stock and the artificial assets at maturity are derived. Furthermore, the portfolio optimization problem is considered in the enlarged market. The problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. It is shown that for particular choices of the equivalent martingale measure in the market, the optimal portfolio only consists of bonds and stocks. This corresponds to completing the market with additional assets in such a way that they are superfluous in the sense that the terminal expected utility is not improved by including these assets in the portfolio.

In quality control applications, Time-Between-Events (TBE) type observations may be monitored by using Exponentially Weighted Moving Average (EWMA) control charts. A widely accepted model for the TBE processes is the exponential distribution, and hence TBE EWMA charts are designed under this assumption. Nevertheless, practical applications do not always conform to the theory and it is common that the observations do not fit the exponential model. Therefore, control charts that are robust to departures from the assumed distribution are desirable in practice. In this thesis, robustness of the lower-sided TBE EWMA charts to the assumption of exponentially distributed observations has been investigated. Weibull and lognormal distributions are considered in order to represent the departures from the assumed exponential model and Markov Chain approach is utilized for evaluating the performance of the chart. By analyzing the performance results, design settings are suggested in order to achieve robust lower-sided TBE EWMA charts.

Let X and Y be two random variables such that Y depends on X=x. This is a very common situation in many real life applications. The problem is to estimate the location and scale parameters in the marginal distributions of X and Y and the conditional distribution of Y given X=x. We are also interested in estimating the regression coefficient and the correlation coefficient. We have a cost constraint for observing X=x, the larger x is the more expensive it becomes. The allowable sample size n is governed by a pre-determined total cost. This can lead to a situation where some of the largest X=x observations cannot be observed (Type II censoring). Two general methods of estimation are available, the method of least squares and the method of maximum likelihood. For most non-normal distributions, however, the latter is analytically and computationally problematic. Instead, we use the method of modified maximum likelihood estimation which is known to be essentially as efficient as the maximum likelihood estimation. The method has a distinct advantage: It yields estimators which are explicit functions of sample observations and are, therefore, analytically and computationally straightforward. In this thesis specifically, the problem is to evaluate the effect of the largest order statistics x(i) (i&gt / n-r) in a random sample of size n (i) on the mean E(X) and variance V(X) of X, (ii) on the cost of observing the x-observations, (iii) on the conditional mean E(Y|X=x) and variance V(Y|X=x) and (iv) on the regression coefficient. It is shown that unduly large x-observations have a detrimental effect on the allowable sample size and the estimators, both least squares and modified maximum likelihood. The advantage of not observing a few largest observations are evaluated. The distributions considered are Weibull, Generalized Logistic and the scaled Student&rsquo / s t.

Due to its complex and multidisciplinary nature, the conceptual design phase of helicopters becomes critical in meeting customer satisfaction. Statistical (probabilistic) design methods can be employed to understand the design better and target a design with lower variability. In this thesis, a conceptual design and helicopter sizing methodology is developed and shown on a helicopter design for Turkey.

In this thesis, Bayesian semiparametric models for the missing data mechanisms of nonignorably missing covariates in logistic regression are developed. In the missing data literature, fully parametric approach is used to model the nonignorable missing data mechanisms. In that approach, a probit or a logit link of the conditional probability of the covariate being missing is modeled as a linear combination of all variables including the missing covariate itself. However, nonignorably missing covariates may not be linearly related with the probit (or logit) of this conditional probability. In our study, the relationship between the probit of the probability of the covariate being missing and the missing covariate itself is modeled by using a penalized spline regression based semiparametric approach. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm to estimate the parameters is established. A WinBUGS code is constructed to sample from the full conditional posterior distributions of the parameters by using Gibbs sampling. Monte Carlo simulation experiments under different true missing data mechanisms are applied to compare the bias and efficiency properties of the resulting estimators with the ones from the fully parametric approach. These simulations show that estimators for logistic regression using semiparametric missing data models maintain better bias and efficiency properties than the ones using fully parametric missing data models when the true relationship between the missingness and the missing covariate has a nonlinear form. They are comparable when this relationship has a linear form.

The scope of this study is to estimate the zero-coupon yield curve of tomorrow by using Vasicek yield curve model with the zero-coupon bond yield data of today. The raw data of this study is the yearly simple spot rates of the Turkish zero-coupon bonds with different maturities of each day from July 1, 1999 to March 17, 2004. We completed the missing data by using Nelson-Siegel yield curve model and we estimated tomorrow yield cuve with the discretized Vasicek yield curve model.

This thesis presents a comprehensive example framework on how current multiple model state estimation algorithms for jump Markov linear systems can be improved. The possible improvements are categorized as: -Design of multiple model state estimation algorithms using new criteria. -Improvements obtained using existing multiple model state estimation algorithms. In the first category, risk-sensitive estimation is proposed for jump Markov linear systems. Two types of cost functions namely, the instantaneous and cumulative cost functions related with risk-sensitive estimation are examined and for each one, the corresponding multiple model estate estimation algorithm is derived. For the cumulative cost function, the derivation involves the reference probability method where one defines and uses a new probability measure under which the involved processes has independence properties. The performance of the proposed risk-sensitive filters are illustrated and compared with conventional algorithms using simulations. The thesis addresses the second category of improvements by proposing -Two new online transition probability estimation schemes for jump Markov linear systems. -A mixed multiple model state estimation scheme which combines desirable properties of two different multiple model state estimation methods. The two online transition probability estimators proposed use the recursive Kullback-Leibler (RKL) procedure and the maximum likelihood (ML) criteria to derive the corresponding identification schemes. When used in state estimation, these methods result in an average error decrease in the root mean square (RMS) state estimation errors, which is proved using simulation studies. The mixed multiple model estimation procedure which utilizes the analysis of the single Gaussian approximation of Gaussian mixtures in Bayesian filtering, combines IMM (Interacting Multiple Model) filter and GPB2 (2nd Order Generalized Pseudo Bayesian) filter efficiently. The resulting algorithm reaches the performance of GPB2 with less Kalman filters.

Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.

The ordinary least squares (OLS) is one of the most widely used methods for modelling the functional relationship between variables. However, this estimation procedure counts on some assumptions and the violation of these assumptions may lead to nonrobust estimates. In this study, the simple linear regression model is investigated for conditions in which the distribution of the error terms is Generalised Logistic. Some robust and nonparametric methods such as modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares, least trimmed squares (LTS), Theil and weighted Theil are compared via computer simulation. In order to evaluate the estimator performance, mean, variance, bias, mean square error (MSE) and relative mean square error (RMSE) are computed.