Nonlinear models with measurement errors subject to single-indexed distortion

AbstractWe study nonlinear regression models whose both response and predictors are measured with errors and distorted as single-index models of some observable confounding variables, and propose a multicovariate-adjusted procedure. We first examine the relationship between the observed primary variables (observed response and observed predictors) and the confounding variables by appropriately estimating the single index. We then develop a semiparametric profile nonlinear least square estimation procedure for the parameters of interest after we calibrate the error-prone response and predictors. Asymptotic properties of the proposed estimators are established. To avoid estimating the asymptotic covariance matrix that contains the infinite-dimensional nuisance distorting functions and the single index, and to improve the accuracy of the proposed estimation, we also propose an empirical likelihood-based statistic, which is shown to be asymptotically chi-squared. A simulation study is conducted to evaluate the performance of the proposed methods and a real dataset is analyzed as an illustration

Monopoly quality degradation and regulation in cable television

Using an empirical framework based on the Mussa-Rosen model of monopoly quality choice, we calculate the degree of quality degradation in cable television markets and the impact of regulation on those choices. We find lower bounds of quality degradation ranging from 11 to 45 percent of offered service qualities. Furthermore, cable operators in markets with local regulatory oversight offer significantly higher quality, less degradation, and greater quality per dollar, despite higher prices

Intersubject Regularity in the Intrinsic Shape of Human V1

Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results

Graded quantization for multiple description coding of compressive measurements

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics

A Stochastic Model for the Luminosity Fluctuations of Accreting Black Holes

In this work we have developed a new stochastic model for the fluctuations in lightcurves of accreting black holes. The model is based on a linear combination of stochastic processes and is also the solution to the linear diffusion equation perturbed by a spatially correlated noise field. This allows flexible modeling of the power spectral density (PSD), and we derive the likelihood function for the process, enabling one to estimate the parameters of the process, including break frequencies in the PSD. Our statistical technique is computationally efficient, unbiased by aliasing and red noise leak, and fully accounts for irregular sampling and measurement errors. We show that our stochastic model provides a good approximation to the X-ray lightcurves of galactic black holes, and the optical and X-ray lightcurves of AGN. We use the estimated time scales of our stochastic model to recover the correlation between characteristic time scale of the high frequency X-ray fluctuations and black hole mass for AGN, including two new `detections' of the time scale for Fairall 9 and NGC 5548. We find a tight anti-correlation between the black hole mass and the amplitude of the driving noise field, which is proportional to the amplitude of the high frequency X-ray PSD, and we estimate that this parameter gives black hole mass estimates to within ~ 0.2 dex precision, potentially the most accurate method for AGN yet. We also find evidence that ~ 13% of AGN optical PSDs fall off flatter than 1 / f^2, and, similar to previous work, find that the optical fluctuations are more suppressed on short time scales compared to the X-rays, but are larger on long time scales, suggesting the optical fluctuations are not solely due to reprocessing of X-rays.Comment: 22 pages, 10 figures, resubmitted to match accepted version, in press at Ap

Coupling Vanishing Point Tracking with Inertial Navigation to Estimate Attitude in a Structured Environment

This research aims to obtain accurate and stable estimates of a vehicle\u27s attitude by coupling consumer-grade inertial and optical sensors. This goal is pursued by first modeling both inertial and optical sensors and then developing a technique for identifying vanishing points in perspective images of a structured environment. The inertial and optical processes are then coupled to enable each one to aid the other. The vanishing point measurements are combined with the inertial data in an extended Kalman filter to produce overall attitude estimates. This technique is experimentally demonstrated in an indoor corridor setting using a motion profile designed to simulate flight. Through comparison with a tactical-grade inertial sensor, the combined consumer-grade inertial and optical data are shown to produce a stable attitude solution accurate to within 1.5 degrees. A measurement bias is manifested which degrades the accuracy by up to another 2.5 degrees

Enhanced Image-Aided Navigation Algorithm with Automatic Calibration and Affine Distortion Prediction

This research aims at improving two key steps within the image aided navigation process: camera calibration and landmark tracking. The camera calibration step is improved by automating the point correspondence calculation within the standard camera calibration algorithm, thereby reducing the required time for calibration while maintaining the output model accuracy. The feature landmark tracking step is improved by digitally simulating affine distortions on input images in order to calculate more accurate feature descriptors for improved feature matching in high relative viewpoint change. These techniques are experimentally demonstrated in an outdoor environment with a consumer-grade inertial sensor and three imaging sensors, one of which is orthogonal to the rest. Using a tactical-grade inertial sensor coupled with GPS position data for comparison, the improved image aided navigation algorithm is shown to reduce navigation errors by 24% in position, 16% in velocity and 35% in attitude when compared to the standard image-aided navigation algorithm

Nonparametric covariate-adjusted regression

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general scenarios. We show that, although our nonparametric estimators are constructed from predictors of the unobserved undistorted data, they have the same first order asymptotic properties as the standard estimators that could be computed if the undistorted data were available. We illustrate the good numerical performance of our methods on both simulated and real datasets.Comment: 32 pages, 4 figure