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45
HAC estimation in a spatial framework
 J. Econom
, 2007
"... We suggest a nonparametric heteroscedasticity and autocorrelation consistent (HAC) estimator of the variancecovariance (VC) matrix for a vector of sample moments within a spatial context. We demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial model ..."
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Cited by 46 (7 self)
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We suggest a nonparametric heteroscedasticity and autocorrelation consistent (HAC) estimator of the variancecovariance (VC) matrix for a vector of sample moments within a spatial context. We demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models. We allow for more than one measure of distance, each of which may be measured with error. Monte Carlo results suggest that our estimator is reasonable in finite samples. We then consider a spatial model containing various complexities and demonstrate that our HAC estimator can be applied in the context of that model.
Secondorder statistics of complex signals
 IEEE Trans. Signal Processing
, 1997
"... Abstract — The secondorder statistical properties of complex signals are usually characterized by the covariance function. However, this is not sufficient for a complete secondorder description, and it is necessary to introduce another moment called the relation function. Its properties, and espec ..."
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Cited by 41 (0 self)
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Abstract — The secondorder statistical properties of complex signals are usually characterized by the covariance function. However, this is not sufficient for a complete secondorder description, and it is necessary to introduce another moment called the relation function. Its properties, and especially the conditions that it must satisfy, are analyzed both for stationary and nonstationary signals. This leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise. Finally, this is applied to complex autoregressive signals, and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration. I.
Generalized Stochastic Subdivision
 ACM Transactions on Graphics
, 1987
"... This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functi ..."
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Cited by 39 (2 self)
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This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct highquality random functions, including those with nonfractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism <F11.
2003): “Testing for neglected nonlinearity in regression models based on the theory of random fields
 Journal of Econometrics
"... Within a flexible regression model (Hamilton, 2001) we offer a battery of new Lagrange multiplier statistics that circumvent the problem of unidentified nuisance parameters under the null hypothesis of linearity and that are robust to the specification of the covariance function that defines the ra ..."
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Cited by 24 (4 self)
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Within a flexible regression model (Hamilton, 2001) we offer a battery of new Lagrange multiplier statistics that circumvent the problem of unidentified nuisance parameters under the null hypothesis of linearity and that are robust to the specification of the covariance function that defines the random field. These advantages are the result of (i) switching from the L2 to the L1 norm; and (ii) assuming that the random field is sufficiently smooth for its covariance function to be locally approximated by a high order Taylor expansion. A Monte Carlo simulation suggests that our statistics have superior power performance on detecting bilinear, neural network, and smooth transition autoregressive specifications. We also provide an application to the Industrial Production Index of sixteen OECD countries.
The fading number of singleinput multipleoutput fading channels with memory
 IEEE Transactions on Information Theory
, 2006
"... We derive the fading number of stationary and ergodic (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channels with memory. This is the second term, after the double logarithmic term, of the high signaltonoise ratio (SNR) expansion of channel capacity. The transmitter and rec ..."
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Cited by 16 (6 self)
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We derive the fading number of stationary and ergodic (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channels with memory. This is the second term, after the double logarithmic term, of the high signaltonoise ratio (SNR) expansion of channel capacity. The transmitter and receiver are assumed to be cognizant of the probability law governing the fading but not of its realization. It is demonstrated that the fading number is achieved by IID circularly symmetric inputs of squaredmagnitude whose logarithm is uniformly distributed over an SNR dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sublogarithmically in the SNR. The converse relies inter alia on a new observation regarding input distributions that escape to infinity. Lower and upper bounds on the fading number for Gaussian fading are also presented. These are related to the mean squarederrors of the onestep predictor and the onegap interpolator of the fading process respectively. The bounds are computed explicitly for stationary mth order autoregressive AR(m) Gaussian fading processes.
The fading number of SIMO fading channels with memory
 In Proc. IEEE Int. Symp. on Inf. Theory and its Appl. (ISITA
, 2004
"... We derive the fading number of a general (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channel with memory, where the transmitter and receiver—while fully cognizant of the probability law governing the fading process—have no access to the fading realization. It is demonstrate ..."
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Cited by 6 (3 self)
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We derive the fading number of a general (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channel with memory, where the transmitter and receiver—while fully cognizant of the probability law governing the fading process—have no access to the fading realization. It is demonstrated that the fading number is achieved by IID circularlysymmetric inputs of log squaredmagnitude that is uniformly distributed over a signaltonoise (SNR) dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sublogarithmically in the SNR. Among the new ingredients in the proof is a new theorem regarding input distributions that escape to infinity. Upper and lower bounds on the fading number for SIMO Gaussian fading are also presented. Those are computed explicitly for stationary mth order autoregressive AR(m) Gaussian fading processes.
Optimal prediction for the KuramotoSivashinsky equation
, 2003
"... Abstract. We examine the problem of predicting the evolution of solutions of the KuramotoSivashinsky equation when initial data are missing. We use the optimal prediction method to construct equations for the reduced system. The resulting equations for the resolved components of the solution are ra ..."
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Cited by 5 (2 self)
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Abstract. We examine the problem of predicting the evolution of solutions of the KuramotoSivashinsky equation when initial data are missing. We use the optimal prediction method to construct equations for the reduced system. The resulting equations for the resolved components of the solution are random integrodifferential equations. The accuracy of the predictions depends on the type of projection used in the integral term of the optimal prediction equations and on the choice of resolved components. The novel features of our work include the first application of the optimal prediction formalism to a nonlinear, nonHamiltonian equation and the use of a noninvariant measure constructed through inference from empirical data.
Modeling and Generation of SpaceTime Correlated Signals for Sensor Network Fields
 In Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM
, 2011
"... Abstract—In the past few years, a large number of networking protocols for data gathering through aggregation, compression and recovery in Wireless Sensor Networks (WSNs) have utilized the spatiotemporal statistics of real world signals in order to achieve good performance in terms of energy saving ..."
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Cited by 3 (3 self)
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Abstract—In the past few years, a large number of networking protocols for data gathering through aggregation, compression and recovery in Wireless Sensor Networks (WSNs) have utilized the spatiotemporal statistics of real world signals in order to achieve good performance in terms of energy savings and improved signal reconstruction accuracy. However, very little has been said in terms of suitable spatiotemporal models of the signals of interest. These models are very useful to prove the effectiveness of the proposed data gathering solutions as they can be used in the design of accurate simulation tools for WSNs. In addition, they can also be considered as reference models to prove theoretical results for data gathering algorithms. In this paper, we address this gap by devising a mathematical model for real world signals that are correlated in space and time. We thus describe a method to reproduce synthetic signals with tunable correlation
A new procedure for stochastic realization of spectral density matrices
 SIAM J. Control Optim
, 1984
"... Abstract. In this paper we consider the problem of obtaining a state space realization of a zero mean gaussian vector process. A new algorithm is presented for the case in which the process is given in terms of its spectral density function. Contrary to the usual procedure followed, which requires a ..."
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Cited by 2 (0 self)
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Abstract. In this paper we consider the problem of obtaining a state space realization of a zero mean gaussian vector process. A new algorithm is presented for the case in which the process is given in terms of its spectral density function. Contrary to the usual procedure followed, which requires a partial fraction expansion, the algorithm presented starts with a (deterministic) realization of the spectral density function itself.