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This paper considers Maximum Likelihood (ML) based estimation and inference procedures for linear dynamic panel data models with fixed effects. The paper first studies the asymptotic properties of MaCurdy's [MaCurdy, T., 1982. The use of time series processes to model the time structure of earnings in a longitudinal data analysis. Journal of Econometrics 18, 83-114] First Difference Maximum Likelihood (FDML) estimator for the covariance stationary panel AR(1)/unit root model with fixed effects, viz. [y.sub.i,t] = [rho][y.sub.i,t-1] + (1 - [rho])[[micro].sub.i] + [[epsilon].sub.i,t], under a variety of asymptotic plans. Subsequently, the paper shows through Monte Carlo simulations for panels of various dimensions the favourable finite sample properties of the FDMLE for [rho] as compared to those of a number of alternative fixed effects ML estimators for [rho] under covariance stationarity and normality of the data. The paper also discusses panel unit root test procedures that are based on the FDMLE. A Monte Carlo study conducted for one version of these tests reveals that it has very good size and power properties in comparison with alternative panel unit root tests. Keywords: Dynamic panel data models Maximum likelihood Multi-index asymptotics Efficiency bounds Unit root test

Efficient computation of extensions of banded, partially known covariance matrices is provided by the classical Levinson algorithm. One contribution of this paper is the introduction of a generalization of this algorithm that is applicable to a substantially broader class of extension problems. This generalized algorithm can compute unknown covariance elements in any order that satisfies certain graph-theoretic properties, which we describe. This flexibility, which is not provided by the classical Levinson algorithm, is then harnessed in a second contribution of this paper, the identification of a multiscale autoregressive (MAR) model for the maximum-entropy (ME) extension of a banded, partially known covariance matrix. The computational complexity of MAR model identification is an order of magnitude below that of explicitly computing a full covariance extension and is comparable to that required to build a standard autoregressive (AR) model using the classical Levinson algorithm. Index Terms--Chordal graphs, covariance completion, covariance extension, Levinson's algorithm, maximum entropy, multiscale autoregressive (MAR) models, reflection coefficients.

It is well known that there is a strong relation between class definition precision and classification accuracy in pattern classification applications. In hyperspectral data analysis, usually classes of interest contain one or more components and may not be well represented by a single Gaussian density function. In this paper, a model-based mixture classifier, which uses mixture models to characterize class densities, is discussed. However, a key outstanding problem of this approach is how to choose the number of components and determine their parameters for such models in practice, and to do so in the face of limited training sets where estimation error becomes a significant factor. The proposed classifier estimates the number of subclasses and class statistics simultaneously by choosing the best model. The structure of class covariances is also addressed through a model-based covariance estimation technique introduced in this paper. Index Terms--Covariance estimator, expectation-maximization, Gaussian mixtures.

In this paper, we show how a statistical model of facial shape can be embedded within a shape-from-shading algorithm. We describe how facial shape can be captured using a statistical model of variations in surface normal direction. To construct this model, we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to Cartesian points on a local tangent plane. The distribution of surface normal directions is captured using the covariance matrix for the projected point positions. The eigenvectors of the covariance matrix define the modes of shape-variation in the fields of transformed surface normals. We show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by Lambert's law. We demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details. We assess the accuracy of the technique on a variety of images with ground truth and real-world images. Index Terms--Shape-from-shading, albedo estimation, directional statistics, illumination, face modeling.

The large number of bands in hyperspectral images leads to a large number of parameters to estimate. It has been argued in the literature that class-conditional distributions of hyperspectral images are non-Gaussian; thus, multiple components might be needed to describe the classes accurately. In this paper, we propose to represent the Gaussian components in the classifier with a smaller number of parameters by allowing some or all component distributions to share eigenstructure by decomposing the covariance matrix [[summation].sub.k] of each of the k components into a product of three parameters, namely: 1) scalar [[lambda].sub.k] measuring volume; 2) diagonal matrix [A.sub.k] of normalized eigenvalues measuring shape; and 3) matrix of eigenvectors [D.sub.k] measuring orientation. Any combination of these parameters can be common for any subset of the covariance matrices, allowing a flexible set of possible configurations that can be used to approximate the true covariance using fewer parameters. A simple bottom-up algorithm for searching for possible parameter-sharing models is developed. Experiments on three data sets were performed: one concerned with woodland classification and two on urban mapping. Results from these experiments indicate that the method outperforms conventional classifiers and performs comparably with state-of-the-art classifiers such as support vector machines. Index Terms--Covariance approximation, eigendecomposition, hyperspectral data analysis, image classification, mixture classifier.

This paper presents a framework for weighted fusion of several Active Shape and Active Appearance Models. The approach is based on the eigenspace fusion method proposed by Hall et al., which has been extended to fuse more than two weighted eigenspaces using unbiased mean and covariance matrix estimates. To evaluate the performance of fusion, a comparative assessment on segmentation precision as well as facial verification tests are performed using the AR, EQUINOX, and XM2VTS databases. Based on the results, it is concluded that the fusion is useful when the model needs to be updated online or when the original observations are absent. Index Terms--AAM, ASM, model fusion, statistical model, segmentation.

In this paper, covariance behavior of several features (signature identifiers) that are determined from the voltage waveform within a time window for power-quality (PQ) event detection and classification is analyzed. A feature vector using selected signature identifiers such as local wavelet transform extrema at various decomposition levels, spectral harmonic ratios, and local extrema of higher order statistical parameters, is constructed. It is observed that the feature vectors corresponding to power quality event instances can be efficiently classified according to the event type using a covariance based classifier known as the common vector classifier. Arcing fault (high impedance fault) type events are successfully classified and distinguished from motor startup events under various load conditions. It is also observed that the proposed approach is even able to discriminate the loading conditions within the same class of events at a success rate of 70%. In addition, the common vector approach provides a redundancy and usefulness information about the feature vector elements. Implication of this information is experimentally justified with the fact that some of the signature identifiers are more important than others for the discrimination of PQ event types. Index Terms--Covariance analysis, event classification, higher order statistics, power-quality (PQ) analysis.

Fitting multidimensional parametric models in frequency domain using nonparametric noise models is considered in this paper. A nonparametric estimate of the noise statistics is obtained from a finite number of independent data sets. The estimated noise model is then substituted for the the true noise covariance matrix in the maximum likelihood loss function to obtain suboptimal parameter estimates. The goal here is to present an analysis of the resulting estimates. Sufficient conditions for consistency are derived, and an asymptotic accuracy analysis is carried out. The first- and second-order statistics of the cost function at the global minimum point are also explored, which can be used for model validation. The analytical findings are validated using numerical simulation results. Index Terms--Consistency, frequency domain, nonparametric noise models, multivariable models, multiple-input-multiple-output (MIMO) systems, statistical analysis, system identification.

The paper describes a method for determining homologous classes of compounds in a multicomponent complex chromatogram obtained under programming elution conditions. The method is based on the computation of the autocovariance function of the experimental chromatogram (EACVF). The EACVF plot, if properly interpreted, can be regarded as a 'class chromatogram' i.e., a virtual chromatogram formed by peaks whose positions and heights allow identification and quantification of the different homologous series, even if they are embedded in a random complex chromatogram. Theoretical models were developed to describe complex chromatograms displaying random retention pattern, ordered sequences or a combination of them. On the basis of theoretical autocovariance function, the properties of the chromatogram can be experimentally evaluated, under well-defined conditions: in particular, the two components of the chromatogram, ordered and random, can be identified. Moreover, the total number of single components (SCs) and the separated number of the SCs belonging to the random and ordered components can be determined, when the two components display the same concentration. If the mixture contains several homologous series with common frequency and different phase values, the number and identity of the different homologous series as well as the number of SCs belonging to each of them can be evaluated. Moreover, the power of the EACVF method can be magnified by applying it to the single ion monitoring (SIM) signals to selectively detect specific compound classes in order to identify the different homologous series. By this way, a full 'decoding' of the complex multicomponent chromatogram is achieved. The method was validated on synthetic mixtures containing known amount of SCs belonging to homologous series of hydrocarbon, alcohols, ketones, and aromatic compounds in addition to other not structurally related SCs. The method was applied to both the total ion monitoring (TIC) and the SIM signals, to describe step by step the essence of the procedure. Moreover, the systematic use of both SIM and TIC can simplify the decoding procedure of complex chromatograms by singling out only specific compound classes or by confirming the identification of the different homologous series. The method was further applied to a sample containing unknown number of compounds and homologous series (a petroleum benzin, bp 140-160[degrees]C): the results obtained were meaningful in terms of both the identified number of components and identified homologous series.

Entropy-like functionals on operator algebras have been studied since the pioneering work of von Neumann, Umegaki, Lindblad, and Lieb. The best known are the von Neumann entropy I([rho]) := -trace([rho] log [rho]) and a generalization of the Kullback-Leibler distance S(p [parellel] [sigma]) := trace([rho] log [rho] - [rho] log [sigma]), refered to as quantum relative entropy and used to quantify distance between states of a quantum system. The purpose of this paper is to explore I and S as regularizing functionals in seeking solutions to multivariable and multidimensional moment problems. It will be shown that extrema can be effectively constructed via a suitable homotopy. The homotopy approach leads naturally to a further generalization and a description of all the solutions to such moment problems. This is accomplished by a renormalization of a Riemannian metric induced by entropy functionals. As an application, we discuss the inverse problem of describing power spectra which are consistent with second-order statistics, which has been the main motivation behind the present work. Index Terms--Covariance realization, moment problem, multivariable, multidimensional, quantum entropy, spectral analysis.

We consider optimization of the capacity of a multi-input single-output wideband cellular "downlink," in which the base station has estimates of the statistics of the spatial channel. Our main focus is on orthogonal frequency-division multiplexed (OFDM) systems, although some of our results apply to single-carrier systems, as well. Prior work has shown that estimates of the channel spatial covariance can be obtained without overhead for both frequency-division duplex (FDD) and time-division duplex (TDD) systems by suitably averaging uplink measurements. In this paper, we investigate the benefits of supplementing this "free" covariance feedback with mean feedback, where the latter refers to estimates of the spatial channel realization in each subcarrier. Mean feedback can be obtained using reciprocity for TDD systems, and requires explicit feedback for FDD systems. We first devise strategies for using both covariance and mean feedback, mainly restricting attention to beamforming, which is optimal or near-optimal for many outdoor channels with narrow spatial spread. Second, since mean feedback degrades rapidly with feedback delay for mobile channels, we develop quantitative rules of thumb regarding the accuracy required for the mean feedback to be a useful supplement to the already available, and robust, covariance feedback. Our results validate the following intuition: the accuracy requirements for mean feedback to be useful are more relaxed for channels with larger spatial spread, or for a larger number of transmit elements. Index Terms--Fading channels, information rates, multiple-input multiple-output (MIMO) systems.

This paper examines a nonparametric test for Granger-causality for a vector covariance stationary linear process under, possibly, the presence of long-range dependence. We show that the test converges to a nondistribution free multivariate Gaussian process, say vec([??]([mu])) indexed by [mu] [member of] [0, 1]. Because, contrary to the scalar situation, it is not possible, except in very specific cases, to find a time transformation g([micro]) such that vec([??](g([mu]))) is a vector with independent Brownian motion components, it implies that inferences based on vec([??]([mu])) will be difficult to implement. To circumvent this problem, we propose to bootstrapping the test by two alternative, although similar, algorithms showing their validity and consistency. JEL classification. C22 Keywords. Causality tests; Long-range; Bootstrap tests

Abstract A covariance analysis of constructs related to the process of mathematical discovery is presented. The constructs are derived from Polya's ideas on problem solving and include sophistication, traits that [...]