Partial Consistency with Sparse Incidental Parameters

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this penalization principle to a linear regression model with a finite-dimensional vector of structural parameters and a high-dimensional vector of sparse incidental parameters. For the estimators of the structural parameters, we derive their consistency and asymptotic normality, which reveals an oracle property. However, the penalized estimators for the incidental parameters possess only partial selection consistency but not consistency. This is an interesting partial consistency phenomenon: the structural parameters are consistently estimated while the incidental ones cannot. For the structural parameters, also considered is an alternative two-step penalized estimator, which has fewer possible asymptotic distributions and thus is more suitable for statistical inferences. We further extend the methods and results to the case where the dimension of the structural parameter vector diverges with but slower than the sample size. A data-driven approach for selecting a penalty regularization parameter is provided. The finite-sample performance of the penalized estimators for the structural parameters is evaluated by simulations and a real data set is analyzed

Risks of Large Portfolios

Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the volatility matrix. However, the accuracy of such a risk estimator for large portfolios is largely unknown, and a simple inequality in the previous literature gives an infeasible upper bound for the estimation error. In addition, numerical studies illustrate that this upper bound is very crude. In this paper, we propose factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the accuracy of the risk estimation. The H-CLUB is constructed based on three different estimates of the volatility matrix: sample covariance, approximate factor model with known factors, and unknown factors (POET, Fan, Liao and Mincheva, 2013). For the first time in the literature, we derive the limiting distribution of the estimated risks in high dimensionality. Our numerical results demonstrate that the proposed upper bounds significantly outperform the traditional crude bounds, and provide insightful assessment of the estimation of the portfolio risks. In addition, our simulated results quantify the relative error in the risk estimation, which is usually negligible using 3-month daily data. Finally, the proposed methods are applied to an empirical study

Automatic registration of multi-modal airborne imagery

This dissertation presents a novel technique based on Maximization of Mutual Information (MMI) and multi-resolution to design an algorithm for automatic registration of multi-sensor images captured by various airborne cameras. In contrast to conventional methods that extract and employ feature points, MMI-based algorithms utilize the mutual information found between two given images to compute the registration parameters. These, in turn, are then utilized to perform multi-sensor registration for remote sensing images. The results indicate that the proposed algorithms are very effective in registering infrared images taken at three different wavelengths with a high resolution visual image of a given scene. The MMI technique has proven to be very robust with images acquired with the Wild Airborne Sensor Program (WASP) multi-sensor instrument. This dissertation also shows how wavelet based techniques can be used in a multi-resolution analysis framework to significantly increase computational efficiency for images captured at different resolutions. The fundamental result of this thesis is the technique of using features in the images to enhance the robustness, accuracy and speed of MMI registration. This is done by using features to focus MMI on places that are rich in information. The new algorithm smoothly integrates with MMI and avoids any need for feature-matching, and then the applications of such extensions are studied. The first extension is the registration of cartographic maps and image datum, which is very important for map updating and change detection. This is a difficult problem because map features such as roads and buildings may be mis-located and features extracted from images may not correspond to map features. Nonetheless, it is possible to obtain a general global registration of maps and images by applying statistical techniques to map and image features. To solve the map-to-image registration problem this research extends the MMI technique through a focus-of-attention mechanism that forces MMI to utilize correspondences that have a high probability of being information rich. The gradient-based parameter search and exhaustive parameter search methods are also compared. Both qualitative and quantitative analysis are used to assess the registration accuracy. Another difficult application is the fusion of the LIDAR elevation or intensity data with imagery. Such applications are even more challenging when automated registrations algorithms are needed. To improve the registration robustness, a salient area extraction algorithm is developed to overcome the distortion in the airborne and satellite images from different sensors. This extension combines the SIFT and Harris feature detection algorithms with MMI and the Harris corner label map to address difficult multi-modal registration problems through a combination of selection and focus-of-attention mechanisms together with mutual information. This two-step approach overcomes the above problems and provides a good initialization for the final step of the registration process. Experimental results are provided that demonstrate a variety of mapping applications including multi-modal IR imagery, map and image registration and image and LIDAR registration

Quantum corrected full-band semiclassical Monte Carlo simulation research of charge transport in Si, stressed-Si, and SiGe MOSFETs

This Ph.D. research is centered around a full-band Monte Carlo device simulator (“Monte Carlo at the University of Texas”, MCUT) with quantum corrections (based on one-dimensional Schrödinger equation solver). The code itself was based on a solid infrastructure of a Monte Carlo simulator, “MoCa” from the University of Illinois at Urbana-Champaign. To that there were added new methods and features during my Ph.D. program, including strained band structures, alternative (to conventional 100 ) surface orientations, full-band scattering mechanisms, and valley-dependent quantum correction. These features enable “MCUT” to be used to model various strained and/or alloyed silicon MOSFETs, as well as the MOSFETs composed of alternative materials such as Ge, in sub-100 nm regime. Monte Carlo simulation, itself, handles short channel effects and hot carriers in ultra small device well; full-band structure replaces the inaccurate and unknown (for new/strained materials) analytical formulae; and the quantum corrections approximate quantum-confinement effects on device performance. The goal is to understand and predict the device behavior of the so called “non-classical” CMOS ― beyond bulk Si based CMOS ― in the sub-100 nm regime.Electrical and Computer Engineerin

Local martingale difference approach for service selection with dynamic QoS

AbstractUsers in Service-oriented architecture (SOA) seek the best Quality of service (QoS) by service selection from the candidates responding in succession. In case the QoS changes dynamically, choosing one service and stop the searching is problematic for a service user who makes the choice online. Lack of accurate knowledge of service distribution, the user is unable to make a good decision. The Local Martingale Difference (LMD) approach is developed in this paper to help users to achieve optimal results, in the sense of probability. The stopping time is proved to be bounded to ensure the existence of an optimal solution first. Then, a global estimation over the time horizon is transformed to a local determination based on current martingale difference to make the algorithm feasible. Independent of any predetermined threshold or manual intervention, LMD enables users to stop around the optimal time, based on the information collected during the stochastic process. Verified to be efficient by comparison with three traditional methods, LMD is adaptable in vast applications with dynamic QoS

l-connectivity, l-edge-connectivity and spectral radius of graphs

Let G be a connected graph. The toughness of G is defined as t(G)=min{\frac{|S|}{c(G-S)}}, in which the minimum is taken over all proper subsets S\subset V(G) such that c(G-S)\geq 2 where c(G-S) denotes the number of components of G-S. Confirming a conjecture of Brouwer, Gu [SIAM J. Discrete Math. 35 (2021) 948--952] proved a tight lower bound on toughness of regular graphs in terms of the second largest absolute eigenvalue. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] then studied the toughness of simple graphs from the spectral radius perspective. While the toughness is an important concept in graph theory, it is also very interesting to study |S| for which c(G-S)\geq l for a given integer l\geq 2. This leads to the concept of the l-connectivity, which is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. Gu [European J. Combin. 92 (2021) 103255] discovered a lower bound on the l-connectivity of regular graphs via the second largest absolute eigenvalue. As a counterpart, we discover the connection between the l-connectivity of simple graphs and the spectral radius. We also study similar problems for digraphs and an edge version