Likelihood Analysis of Power Spectra and Generalized Moment Problems

We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In the present paper we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure

Digital Signal Processing

Contains research objectives and reports on sixteen research projects.U.S. Navy - Office of Naval Research (Contract N00014-75-C-0852)National Science Foundation FellowshipNational Science Foundation (Grant ENG76-24117)U.S. Navy - Office of Naval Research (Contract N00014-77-C-0257)U.S. Air Force (Contract F19628-80-C-0002)U.S. Navy - Office of Naval Research (Contract N00014-75-C-0951)Schlumberger-Doll Research Center FellowshipHertz Foundation FellowshipGovernment of Pakistan ScholarshipU.S. Navy - Office of Naval Research (Contract N00014-77-C-0196

An econometric approach to macroeconomic risk. A cross country study

A contribution to the study of volatility and country risk is made in order to achieve a successful crosscountry comparison. We present a methodology for the evaluation of country risk that include endogenous detection of multiple structural breaks (also identifying its different kinds), determination of persistence of shocks through their structural-break free fractional integration order and determination of the adjusted volatility which best characterizes the economy. This methodology is applied to developed and emerging countries' GDPs (taking 9 countries from each group). Although the former have fewer structural breaks than the latter, these breaks are extremely relevant in 14 of the 18 countries. This affects the calculation of the series persistence and volatility. Comparing a traditional risk indicator to our suggested one we find that the cluster of reference of 60% of the countries changes. Most countries present fractional integration (long memory) being the distribution between both groups heterogeneous. Country volatility varies strongly if we isolate structural breaks that present a probabilistic distribution different from intrinsic GDP volatility. Clusters arrangement is different with some risk country evaluation methodologies.Risk, Volatility, Persistence, Structural breaks, Forescastability, Macroeconomic variables, Cross country analysis

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target Identification in Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood (ML) estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar (SAR) data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations (exponentials frequencies) are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as (1) stationary noise, (2) autoregressive (AR) noise and (3) autoregressive moving-average (ARMA) noise and in two dimensions as (1) stationary noise, and (2) white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood (IQML) methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation (MODE) techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target in Identification Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood ML estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar SAR data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations exponentials frequencies are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as 1 stationary noise, 2 autoregressive AR noise and 3 autoregressive moving-average ARMA noise and in two dimensions as 1 stationary noise, and 2 white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood IQML methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation MODE techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Digital Signal Processing

Contains introduction and reports on seventeen research projects.U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)U.S. Navy - Office of Naval Research (Contract N00014-77-C-0266)National Science Foundation (Grant ECS80-07102)Bell Laboratories FellowshipAmoco Foundation FellowshipSchlumberger-Doll Research Center FellowshipSanders Associates, Inc.Toshiba Company FellowshipM.I.T. Vinton Hayes FellowshipHertz Foundation Fellowshi

Assessment of spontaneous cardiovascular oscillations in Parkinson's disease

Parkinson's disease (PD) has been reported to involve postganglionic sympathetic failure and a wide spectrum of autonomic dysfunctions including cardiovascular, sexual, bladder, gastrointestinal and sudo-motor abnormalities. While these symptoms may have a significant impact on daily activities, as well as quality of life, the evaluation of autonomic nervous system (ANS) dysfunctions relies on a large and expensive battery of autonomic tests only accessible in highly specialized laboratories. In this paper we aim to devise a comprehensive computational assessment of disease-related heartbeat dynamics based on instantaneous, time-varying estimates of spontaneous (resting state) cardiovascular oscillations in PD. To this end, we combine standard ANS-related heart rate variability (HRV) metrics with measures of instantaneous complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra). Such measures are computed over 600-s recordings acquired at rest in 29 healthy subjects and 30 PD patients. The only significant group-wise differences were found in the variability of the dominant Lyapunov exponent. Also, the best PD vs. healthy controls classification performance (balanced accuracy: 73.47%) was achieved only when retaining the time-varying, non-stationary structure of the dynamical features, whereas classification performance dropped significantly (balanced accuracy: 61.91%) when excluding variability-related features. Additionally, both linear and nonlinear model features correlated with both clinical and neuropsychological assessments of the considered patient population. Our results demonstrate the added value and potential of instantaneous measures of heartbeat dynamics and its variability in characterizing PD-related disabilities in motor and cognitive domains