Search

We present a novel regression framework centered on a coherent and averse measure of risk, the superquantile risk (also called conditional value-at-risk), which yields more conservatively fitted curves than classical least squares and quantile regressions. In contracts to other generalized regression techniques that approximate conditional superquantiles by various combinations of conditional quantiles, we directly and inperfect analog to classical regressional obtain superquantile regression functions as optimal solutions of certain error minimization problems. We show the existence and possible uniqueness of regression functions, discuss the stability of regression functions under perturbations and approximation of the underlying data, and propose an extension of the coefficient of determination R-squared and Cook’s distance for assessing the goodness of fit for both quantile and superquantile regression models. We present two classes of computational methods for solving the superquantile regression problem, compare both methods’ complexity, and illustrate the methodology in eight numerical examples in the areas of military applications, concerning mission employment of U.S. Navy helicopter pilots and Portuguese Navy submarines, reliability engineering, uncertainty quantification, and financial risk management.

This thesis deals with a type of stochastic optimization problem where the decision maker does not have complete information concerning the objective function. Specifically, we consider a discrete time-and-space search optimization problem where we seek to find a moving target in an area of operations. There are two sources of uncertainty: the target location and the sensor performance. We formulate the objective function for this problem in terms of a risk measure of a parameterized random variable and consider three cases involving various degrees of knowledge about the sensor performance. In all cases, we consider both the expectation and superquantile risk measures. While the expectation results in an objective function representing the probability of missing the target, the superquantile gives rise to more conservative search plans that perform reasonably well even under exceptional circumstances. In the case of incomplete in-formation about the distribution of the sensor performance, we approximate the random variable using a nonstandard regression that minimizes the error induced in some sense. We examine the cases in a series of numerical examples., http://archive.org/details/searchplanningun109455479, Approved for public release; distribution is unlimited.

This thesis deals with a type of stochastic optimization problem where the decision maker does not have complete information concerning the objective function. Specifically, we consider a discrete time-and-space search optimization problem where we seek to nd a moving target in an area of operations. There are two sources of uncertainty: the target location and the sensor performance. We formulate the objective function for this problem in terms of a risk measure of a parameterized random variable and consider three cases involving various degrees of knowledge about the sensor performance. In all cases, we consider both the expectation and superquantile risk measures. While the expectation results in an objective function representing the probability of missing the target, the superquantile gives rise to more conservative search plans that perform reasonably well even under exceptional circumstances. In the case of incomplete in- formation about the distribution of the sensor performance, we approximate the random variable using a nonstandard regression that minimizes the error induced in some sense. We examine the cases in a series of numerical examples., The original document contains color images.

This thesis deals with a type of stochastic optimization problem where the decision maker does not have complete information concerning the objective function. Specifically, we consider a discrete time-and-space search optimization problem where we seek to find a moving target in an area of operations. There are two sources of uncertainty: the target location and the sensor performance. We formulate the objective function for this problem in terms of a risk measure of a parameterized random variable and consider three cases involving various degrees of knowledge about the sensor performance. In all cases, we consider both the expectation and superquantile risk measures. While the expectation results in an objective function representing the probability of missing the target, the superquantile gives rise to more conservative search plans that perform reasonably well even under exceptional circumstances. In the case of incomplete in-formation about the distribution of the sensor performance, we approximate the random variable using a nonstandard regression that minimizes the error induced in some sense. We examine the cases in a series of numerical examples.

We present a novel regression framework centered on a coherent and averse measure of risk, the superquantile risk (also called conditional value-at-risk), which yields more conservatively fitted curves than classical least squares and quantile regressions. In contracts to other generalized regression techniques that approximate conditional superquantiles by various combinations of conditional quantiles, we directly and inperfect analog to classical regressional obtain superquantile regression functions as optimal solutions of certain error minimization problems. We show the existence and possible uniqueness of regression functions, discuss the stability of regression functions under perturbations and approximation of the underlying data, and propose an extension of the coefficient of determination R-squared and Cook’s distance for assessing the goodness of fit for both quantile and superquantile regression models. We present two classes of computational methods for solving the superquantile regression problem, compare both methods’ complexity, and illustrate the methodology in eight numerical examples in the areas of military applications, concerning mission employment of U.S. Navy helicopter pilots and Portuguese Navy submarines, reliability engineering, uncertainty quantification, and financial risk management., http://archive.org/details/superquantilereg1094544618, Lieutenant, Portuguese Navy, Approved for public release; distribution is unlimited.