Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Selected Works

Articles

2015

Articles 1 - 11 of 11

Full-Text Articles in Physical Sciences and Mathematics

An Omnibus Nonparametric Test Of Equality In Distribution For Unknown Functions, Alexander Luedtke, Marco Carone, Mark Van Der Laan Oct 2015

An Omnibus Nonparametric Test Of Equality In Distribution For Unknown Functions, Alexander Luedtke, Marco Carone, Mark Van Der Laan

Alex Luedtke

We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], using recent developments from the higher-order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed rather simply as U-statistics. We study the asymptotic behavior of the proposed tests under the null hypothesis and under both fixed and local alternatives. We provide examples to which our tests …

Go to article

Computerizing Efficient Estimation Of A Pathwise Differentiable Target Parameter, Mark J. Van Der Laan, Marco Carone, Alexander R. Luedtke Oct 2015

Computerizing Efficient Estimation Of A Pathwise Differentiable Target Parameter, Mark J. Van Der Laan, Marco Carone, Alexander R. Luedtke

Alex Luedtke

Frangakis et al. (2015) proposed a numerical method for computing the efficient influence function of a parameter in a nonparametric model at a specified distribution and observation (provided such an influence function exists). Their approach is based on the assumption that the efficient influence function is given by the directional derivative of the target parameter mapping in the direction of a perturbation of the data distribution defined as the convex line from the data distribution to a pointmass at the observation. In our discussion paper Luedtke et al. (2015) we propose a regularization of this procedure and establish the validity …

Go to article

Capacity Planning With Financial And Operational Hedging In Low‐Cost Countries, Lijian Chen, Shanling Li, Letian Wang Sep 2015

Capacity Planning With Financial And Operational Hedging In Low‐Cost Countries, Lijian Chen, Shanling Li, Letian Wang

Lance (Lijian) Chen

The authors of this paper outline a capacity planning problem in which a risk-averse firm reserves capacities with potential suppliers that are located in multiple low-cost countries. While demand is uncertain, the firm also faces multi-country foreign currency exposures. This study develops a mean-variance model that maximizes the firm’s optimal utility and derives optimal utility and optimal decisions in capacity and financial hedging size. The authors show that when demand and exchange rate risks are perfectly correlated, a risk- averse firm, by using financial hedging, will achieve the same optimal utility as a risk-neutral firm. In this paper as well, …

Go to article

A Simulation-Based Approach To Solve A Specific Type Of Chance Constrained Optimization, Lijian Chan Sep 2015

A Simulation-Based Approach To Solve A Specific Type Of Chance Constrained Optimization, Lijian Chan

Lance (Lijian) Chen

We solve the chance constrained optimization with convex feasible set through approximating the chance constraint by another convex smooth function. The approximation is based on the numerical properties of the Bernstein polynomial that is capable of effectively controlling the approximation error for both function value and gradient. Thus, we adopt a first-order algorithm to reach a satisfactory solution which is expected to be optimal. When the explicit expression of joint distribution is not available, we then use Monte Carlo approach to numerically evaluate the chance constraint to obtain an optimal solution by probability. Numerical results for known problem instances are …

Go to article

Re-Solving Stochastic Programming Models For Airline Revenue Management, Lijian Chen, Tito Homem-De-Mello Sep 2015

Re-Solving Stochastic Programming Models For Airline Revenue Management, Lijian Chen, Tito Homem-De-Mello

Lance (Lijian) Chen

We study some mathematical programming formulations for the origin-destination model in airline revenue management. In particular, we focus on the traditional probabilistic model proposed in the literature. The approach we study consists of solving a sequence of two-stage stochastic programs with simple recourse, which can be viewed as an approximation to a multi-stage stochastic programming formulation to the seat allocation problem. Our theoretical results show that the proposed approximation is robust, in the sense that solving more successive two-stage programs can never worsen the expected revenue obtained with the corresponding allocation policy. Although intuitive, such a property is known not …

Go to article

Ancillary Service Capacity Optimization For Both Electric Power Suppliers And Independent System Operator, Lijian Chen, Dengfeng Sun, Guang Li Sep 2015

Ancillary Service Capacity Optimization For Both Electric Power Suppliers And Independent System Operator, Lijian Chen, Dengfeng Sun, Guang Li

Lance (Lijian) Chen

Ancillary Services (AS) in electric power industry are critical to support the transmission of energy from generators to load demands while maintaining reliable operation of transmission systems in accordance with good utility practice. The ancillary services are procured by the independent system operator (ISO) through a process called the market clearing process which can be modeled by the partial equilibrium from the ends of ISO. There are two capacity optimization problems for both Market participants (MP) and Independent System Operator (ISO). For a market participant, the firm needs to determine the capacity allocation plan for various AS to pursue operating …

Go to article

Capacity-Driven Pricing Mechanism In Special Service Industries, Lijian Chen, Suraj M. Alexander Sep 2015

Capacity-Driven Pricing Mechanism In Special Service Industries, Lijian Chen, Suraj M. Alexander

Lance (Lijian) Chen

We propose a capacity driven pricing mechanism for several service industries in which the customer behavior, the price demand relationship, and the competition are significantly distinct from other industries. According our observation, we found that the price demand relationship in these industries cannot be modeled by fitted curves; the customers would neither plan in advance nor purchase the service strategically; and the competition would be largely local. We analyze both risk neutral and risk aversion pricing models and conclude the proposed capacity driven model would be the optimal solution under mild assumptions. The resulting pricing mechanism has been implemented at …

Go to article

Fast Super-Resolution With Affine Motion Using An Adaptive Wiener Filter And Its Application To Airborne Imaging, Russell C. Hardie, Kenneth J. Barnard, Raúl Ordóñez May 2015

Fast Super-Resolution With Affine Motion Using An Adaptive Wiener Filter And Its Application To Airborne Imaging, Russell C. Hardie, Kenneth J. Barnard, Raúl Ordóñez

Raúl Ordóñez

Fast nonuniform interpolation based super-resolution (SR) has traditionally been limited to applications with translational interframe motion. This is in part because such methods are based on an underlying assumption that the warping and blurring components in the observation model commute. For translational motion this is the case, but it is not true in general. This presents a problem for applications such as airborne imaging where translation may be insufficient. Here we present a new Fourier domain analysis to show that, for many image systems, an affine warping model with limited zoom and shear approximately commutes with the point spread function …

Go to article

Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee May 2015

Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee

Shannon O.S. Driskell

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …

Go to article

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti May 2015

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Shannon O.S. Driskell

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

Go to article

Trials Of The Urban Ecologist, Rebecca W. Dolan, Tim Carter, Travis J. Ryan, Carmen M. Salsbury, Thomas E. Dolan, Marjorie Hennessy Feb 2015

Trials Of The Urban Ecologist, Rebecca W. Dolan, Tim Carter, Travis J. Ryan, Carmen M. Salsbury, Thomas E. Dolan, Marjorie Hennessy

Travis J. Ryan

A group of scientists describe some of the obstacles encountered and insights gained while carrying out ecological research in and around the city of Indianapolis.

Go to article