Vector Covariance Research Articles

Owner-Occupied Housing and the Composition of the Household Portfolio

For most homeowners, the house is the single most important consumption good appearing as an argument of the utility function, and, at the same time, the dominant asset in the portfolio. This paper uses a mean-variance efficiency framework to examine the household’s optimal portfolio problem when owner-occupied housing is included in the list of available assets. Housing differs from stocks and bonds in a crucial way: since the household’s ownership of residential real estate determines the level of its consumption of housing services, the household’s demand for real estate is “overdetermined” in the sense that the level of real estate ownership which is optimal from the point of view of the consumption of housing services may differ from the optimal level of housing assets from a portfolio point of view. With rental markets for housing, a household can, in principle, divorce the size of its holdings of real estate assets from the level of housing services it consumes. However, rental housing is by no means a perfect substitute for owner-occupied housing. We assume, instead, that the preferential tax treatment of owner-occupied housing and the transactions costs and agency costs involved in the rental market for housing create frictions large enough to effectively constrain the household to include in its asset portfolio the level of housing consistent with its consumption of housing services. The paper focuses on the impact of the portfolio constraint imposed by the consumption demand for housing on the household’s optimal holdings of financial assets. Section II of the paper is similar in spirit to a recent paper by Jan K. Brueckner (1997), which analyzes the interaction between the consumption demand and the investment demand for housing in a mean-variance portfolio model. Brueckner considers a general covariance matrix and mean vector of returns and a general utility function, and derives analytical results. In contrast, our implementation of the meanvariance framework is quantitative. That is, we estimate the covariance matrix and vector of expected returns for housing and financial assets and solve for the efficient frontiers and optimal portfolios numerically. The risk characteristics of housing are estimated using two distinct sources: data from the Panel Study of Income Dynamics (PSID) and data from Karl E. Case and Robert J. Shiller (1989) based on repeat sales transactions prices for four U.S. cities. Both data sources indicate that housing prices have a large idiosyncratic component; the standard deviation of the return to housing, at the level of the individual house, is about 0.14. In addition to housing, the portfolio can include nonnegative amounts of Treasury bills, Treasury bonds, and stocks. The household can borrow only in the form of a mortgage, which is limited to 100 percent of the value of the house. Using the estimated vector of expected returns and covariance matrix of asset returns, we plot the constrained meanvariance efficient frontiers for various values of the household’s ratio of house value to wealth, h (the “housing constraint”). The housing constraint has an enormous effect on the risk and return trade-off available to the household. Young households, which typically have large holdings of real estate relative to their net worth, are highly leveraged and therefore forced into a situation of high risk (and return). As a result, these young households have a strong incentive to reduce the risk of their portfolio by using their net worth to either pay down their * Flavin: Department of Economics, University of California, San Diego, CA 92093, and National Bureau of Economic Research (e-mail: mflavin@ucsd.edu); Yamashita: Department of Economics, University of Nevada, Las Vegas, NV 89154 (e-mail: tyamashi@ccmail.nevada.edu). We thank Elena Bisagni, Jan Brueckner, Wouter den Haan, James Hamilton, Bruce Lehmann, Greg Mankiw, and the referees for comments, and Robert Shiller for providing the house price transactions data. 1 The implications of the dual role of housing (as both a consumption good and an investment good) for tenure decisions of households were first analyzed by J. Vernon Henderson and Yannis M. Ioannides (1983).

Supercompact multiwavelets for flow field simulation

A supercompact multiwavelet scheme for computational fluid dynamics is presented. Beam and Warming's supercompact wavelet method is an appropriate wavelet for fluid simulation data in the sense that it can provide compact support. The compactness of the wavelets avoids unnecessary interaction with remotely located data (e.g. across a shock discontinuity or vortex) and significantly reduces computational data processing time. Thresholding for data compression with the supercompact wavelets is applied based on a covariance vector structure of multiwavelets. The extension of this scheme to three dimensions is analyzed. Numerical tests demonstrate that the analytic advantages actually result in large data compression ratios.

Assessing Image Features for Vision-Based Robot Positioning

The development of any robotics application relying on visual information always raises the key question of what image features would be most informative about the motion to be performed. In this paper, we address this question in the context of visual robot positioning, where a neural network is used to learn the mapping between image features and robot movements, and global image descriptors are preferred to local geometric features. Using a statistical measure of variable interdependence called Mutual Information, subsets of image features most relevant for determining pose variations along each of the six degrees of freedom (dof's) of camera motion are selected. Four families of global features are considered: geometric moments, eigenfeatures, Local Feature Analysis vectors, and a novel feature called Pose-Image Covariance vectors. The experimental results described show the quantitative and qualitative benefits of performing this feature selection prior to training the neural network: Less network inputs are needed, thus considerably shortening training times; the dof's that would yield larger errors can be determined beforehand, so that more informative features can be sought; the order of the features selected for each dof often accepts an intuitive explanation, which in turn helps to provide insights for devising features tailored to each dof.

Parametric identification of noisy closed-loop linear systems

The problem of identification of closed-loop linear systems via the direct approach is studied in a general setting. The process noise acting on the plant, the input measurement noise and the output measurement noise may be coloured and they may be arbitrarily correlated with each other. A parameter estimation method is proposed by using the bias correction principle. The kernel of this method is that the noise covariance vector, which determines the noise-induced bias in the standard least-squares estimator, is obtained in an efficient manner. It is shown that the strength of the proposed direct identification method is that it can derive accurate parameter estimates from noisy closed-loop data irrespective of noise dynamics.

Shaping filters and the upward continuation problem

An attempt is made to bridge the gap between closed-form harmonic upward continuation (HUC) of analytic covariance functions of the disturbing potential of the anomalous local gravity field and the numerical shaping filter construction when the local gravity vector is modelled in the framework of Kalman filtering. Some fundamental concepts of the local gravity field, interpreted as a stochastic process that is stationary in the plane and harmonic in the upper half space, are reviewed. The shaping-filter modelling technique for the local gravity vector is introduced. To determine the relation between the disturbing potential covariance function and the gravity vector covariance matrix, the role of the so-called admissible pair is established. It is shown that rescaling an admissible pair leads to an analogue rescaling of the shaping filter matrices derived hereof; no cumbersome numerical recalculations are necessary. The class of covariance functions whose corresponding shaping filters possess a closed-form HUC are identified as models whose HUC can be interpreted as a rescaling.

Modeling of two-dimensional random fields

This paper presents a method of conditional stochastic modeling of two-dimensional fields which can be used to predict values at certain field points at a given time, based on field values at other locations at the same time and on data about second order field moments at given points. For computer simulations, the Gaussian truncated distributions are used. The aim of this work is also to present a derivation of a formula for the probability density of an n-dimensional random variable with the Gaussian conditional truncated distribution. As a numerical example, a soil contamination field described by correlation functions corresponding to the white noise field, the Shinozuka field and the Markov field is analyzed. The acceptance-rejection method is applied to generate covariance matrices and vectors of field values. Then, conditional expected field values for adequate correlation functions are calculated.

Convergence of matrix LMS algorithms with applications to LMS/Newton

Necessary and sufficient conditions for convergence of a general matrix LMS algorithm are derived in the case where the adaptation matrix and the input correlation matrix commute. It is shown that the LMS/Newton algorithm is an important special case of the introduced algorithm. From this fact we deduce that the bounds on adaptation gain commonly quoted in the literature for LMS/Newton and sequential regression algorithms are not strict enough and must be reduced to provide convergence of the weight vector covariance matrix. The steady-state performance of the algorithm as well as its performance in a nonstationary environment are also discussed. Previous results in this area are extended while using fewer assumptions. Finally, a class of nonlinear processes is introduced. Performance on an example process is given to show that our algorithm performs well in this environment which naturally has large eigenvalue spreads.

Fully polarimetric classification of the Black Forest MAESTRO 1 AIRSAR data

Abstract In this paper we present a study on the application of polarimetric supervised classification techniques to the case of a forested area where the influence of topography is important. For the experimental part of the study, we use the polarimetric AIRSAR data at C, Land P band, acquired over the Black Forest near Freiburg “Germany” during the 1989 MAESTRO I Campaign. Two classification schemes are considered: one is of the classical Bayes type, while the other is based on the concept of maximum contrast. We show practical results of the use of both classifiers in a classification context based on tree age classes. Also the dependency of the classification accuracy on a number of parameters, such as calibration, feature vector dimensions and covariance matrix representation, is discussed. Finally, we focus on the influence of topography on classification and indicate how we can improve the classification results using a priori knowledge of the terrain slope.

The principle of speckle filtering in polarimetric SAR imagery

The principle of speckle reduction in polarimetry is reconsidered. It is shown that polarimetric data can be speckle reduced if and only if all the elements of the Mueller matrix are filtered, which is equivalent to filtering the scattering vector covariance matrix. Assuming that speckle is multiplicative and stationary, the algorithms proposed by S.L.Lee et al. (1991) and S.Goze et al. (1993) are extended to filter the covariance matrix of reciprocal and nonreciprocal targets on one-look and multilook images. The problem of estimation of the first- and second-order statistics of the four-channel speckle vector is discussed, and a solution is proposed for one-look and multilook images. >

Generating random numbers on a simplex

Algorithms for three types of random compositional vectors are provided in this article. The first is intuitive. Random basis (“open”) vectors are transformed into compositional vectors by dividing each vector's components by the sum of its components. The second algorithm uses a coordinate transformation to map uniform random vectors in a d-dimensional hypertetrahedron into uniformly distributed compositional variables on the d + 1 dimensional simplex. The third algorithm operates upon a logratio population covariance matrix and vector of means to produce random compositional vectors drawn from the same distribution. The statistical attributes of the crude compositional data also are honored by this method.

Preconditioning of real-time optical Wiener filters for array processing

In adaptive array processors, a performance measure, such as mean square error or signal to noise ration, coverages to the optimum Wiener solution starting from an initial setting. The choice of adaptive algorithms to solve the Wiener filtering problem is mainly guided by the desired processing time. In an optical realization for direct calculation of the optimum weights the covariance matrix and vector for a Wiener filter are computed at a high speed on acousto-optic processors. The resulting linear system of equations can be solved on an iterative optical processor. The matrix and vector data should be recomputed in every iteration for better tracking and adaptation. This introduces variations in their values due to the time-varying jamming and interference noise and the optical errors and noise. Time variant steepest descent algorithm is a simple method that converges to the common solution. In this paper, we describe a real-time preconditioning technique for such nonstationary iterative methods. Preconditioning will progressively lower the condition number of each matrix in the sequence, thereby improving the convergence speed and accuracy of the solution. This preconditioning process involves matrix-matrix multiplications that can be performed at high speed on parallel optical processors. Results of simulations illustrate the superlinear convergence obtained from preconditioning.

Statistical analysis of initialization methods for RLS adaptive filters

Theoretical analysis is used to evaluate the mean and second-moment properties of recursive least squares algorithms incorporating the fast exact initialization and soft constrained initialization methods during the initialization period. It is shown that the weight vector mean and covariance produced by fast exact initialization are undefined for this period. Theoretical results are derived for soft constrained initialization that show that the weight vector mean and covariance are finite, and expressions are given for these quantities. Simulations for various cases are presented to support the accuracy of these theoretical results. >

Robustness of the best linear unbiased estimator and predictor in linear regression models

If is shown that in linear regression models we do not make a great mistake if we substitute some sufficiently precise approximations for the unknown covariance matrix and covariance vector in the expressions for computation of the best linear unbiased estimator and predictor.

On the probability density function of the LMS adaptive filter weights

The joint probability density function of the weight vector in least-mean-square (LMS) adaptation is studied for Gaussian data models. An exact expression is derived for the characteristic function of the weight vector at time n+1, conditioned on the weight vector at time n. The conditional characteristic function is expanded in a Taylor series and averaged over the unknown weight density to yield a first-order partial differential-difference equation in the unconditioned characteristic function of the weight vector. The equation is approximately solved for small values of the adaption parameter and the weights are shown to be jointly Gaussian with time-varying mean vector and covariance matrix given as the solution to well-known difference equations for the weight vector mean and covariance matrix. The theoretical results are applied to analyzing the use of the weights in detection and time delay estimation. Simulations that support the theoretical results are also presented. >

Some Results on the Existence, Uniqueness, and Computation of the M-Estimates of Multivariate Location and Scatter

The M-estimates of multivariate location and scatter are a class of robust alternatives to the sample mean vector and sample covariance matrix. They also have applications to bounded influence regression. There are a number of problems, though, which need to be resolved before they can become widely applicable. This paper addresses the problems of existence, uniqueness and computation of the M-estimates for finite sample sizes.The main contribution of this paper is the introduction of a new algorithm for calculating the scatter component. This algorithm is essentially a fixed point algorithm with a scale adjustment made at each iteration. The algorithm is shown to converge “monotonically” and under less restrictive conditions than those demanded by previous algorithms. The existence and uniqueness of the M-estimates are also established under less restrictive conditions than those previously known. These relaxed conditions are most important for the more robust M-estimates and also when using more conserv...

New recursive parameter estimation algorithms with varying but bounded gain matrix

The main disadvantage of the standard recursive weighted least-squares algorithm is the unbounded increase in its gain matrix when the covariance vector is not sufficiently rich. We propose a general method for updating the gain matrix. This allows us to derive many new specific algorithms in which the boundedness of the gain matrix is ensured automatically.

Convergence rate determination for gradient-based adaptive estimators

A convergence rate estimate is derived for the homogeneous gradient-based adaptive linear estimator algorithm. This estimate involves the eigenvalues of the regression vector covariance matrix, yielding a useful measure for the choice of input signals for adaptive parameter estimation. The connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas.

On some properties of Gaussian channels with strongly equivalent noises

The complicated additive Gaussian channels can be constructed in the following way. For the sake of simplicity, we consider both the input spaces and the output spaces to be a real separable Hilbert space H. Suppose that the noise source pLN is a Gaussian measure on H with mean vector mN and covariance operator R, and the input source px is a probability measure on H with mean vector m, and covariance operator R,. Let pXN be a joint probability measure such that

Convergence Rate Determination for Gradient-Based Adaptive Estimators

A convergence rate estimate is derived for the homogeneous gradient-based adaptive linear estimator algorithm. This estimate involves the eigenvalues of the regression vector covariance matrix, yielding a useful measure for the choice of input signals for adaptive parameter estimation. The connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas.

On an application of game theory to a problem of testing statistical hypothesis

Consider an-dimensional random vector with known covariance matrix. The expectation values of its single components may take arbitrary values subject to the restriction that their sum is a prescribed positive constant. Now choose a linear combination of these components, take its expectation value and divide this by the square root of its variance. This quotient, which is of importance in some problems of test theory serves as the pay-off function of a two-person zero-sum game. Player I wants to maximize the quotient by forming suitable linear combinations and player II wants to minimize it by choosing appropriate expectation values of the single components of the random vector subject to the restriction stated above. It is shown that the game possesses an essentially unique equilibrium point. In the more complicated case, when the strategies of the second player are confined to non-negative expectation values of the random vector's components, there is also an essentially unique equilibrium point of the game. It coincides with that one of the unconstrained case if and only if the row sums of the random vector's covariance matrix are all nonnegative.