Nonparametric spectrum estimation for spatial data

Robinson, Peter

doi:10.1016/j.jspi.2006.06.021

Cited by 27 publications

(24 citation statements)

References 10 publications

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“…The biases are much smaller for d = 3, almost vanishing for larger n * and smaller τ . These features match those of the untapered and tapered periodogram based estimates in Robinson (2007), but there other features that differ from that paper. All biases there are negative, but we find that they are mostly positive.…”

Section: Monte Carlo Simulationssupporting

confidence: 65%

“…All biases there are negative, but we find that they are mostly positive. For d = 2 our biases sometimes dominate (in absolute value) those in Robinson (2007) but can become better than untapered estimates e.g. for n * = 9.…”

Section: Monte Carlo Simulationsmentioning

confidence: 85%

“…We experimented with more values of τ and n * than Robinson (2007), using the following specifications: d = 2 : τ = 0.05, 0.075, 0.10; n * = 5, 7, 9, 11 d = 3 : τ = 0.0075, 0.015, 0.03; n * = 3, 4, 5, 6, 7, 8.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

“…Yuan and Subba Rao (1993), Politis and Romano (1996), Robinson (2007) and Vidal Sanz (2009). Our autoregressive approach allows us to consider nonparametric estimates of the spectral density without the practitioner having to choose a taper or kernel.…”

Section: Introductionmentioning

confidence: 99%

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Autoregressive spatial spectral estimates

Gupta

2018

Journal of Econometrics

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Autoregressive spectral density estimation for stationary random fields on a regular spatial lattice has many advantages relative to kernel based methods. It provides a guaranteed positive-definite estimate even when suitable edge-effect correction is employed, is simple to compute using least squares and necessitates no choice of kernel. We truncate a true half-plane infinite autoregressive representation to estimate the spectral density. The truncation length is allowed to diverge in all dimensions in order to avoid the potential bias which would accrue due to truncation at a fixed lag-length. Consistency and strong consistency of the proposed estimator, both uniform in frequencies, are established. Under suitable conditions the asymptotic distribution of the estimate is shown to be zero-mean normal and independent at fixed distinct frequencies, mirroring the behaviour for time series. A small Monte Carlo experiment examines finite sample performance. We illustrate the technique by applying it to Los Angeles house price data and a novel analysis of voter turnout data in a US presidential election. Technically the key to the results is the covariance structure of stationary random fields defined on regularly spaced lattices. We study this in detail and show the covariance matrix to satisfy a generalization of the Toeplitz property familiar from time series analysis. JEL classifications : C14, C18, C21

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Section: Monte Carlo Simulationssupporting

confidence: 65%

Section: Monte Carlo Simulationsmentioning

confidence: 85%

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Autoregressive spatial spectral estimates

Gupta

2018

Journal of Econometrics

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“…where L = fs t : s 2 L; t 2 Lg ; c u = n 1 P (u) v t v t+u ; and (u) = ft : t 2 L; t + u 2 Lg ; where we assume that s i 2 r j=1 f1; :::; n j g = L for all i; where L is the smallest rectangular grid containing all s i : If h is either the modi…ed Bartlett window or the Parzen window, then 0 e 3 0 (see Robinson, 2007a), and hence e 3 is non-negative de…nite. We establish conditions for approximating…”

Section: Variance Estimationmentioning

confidence: 99%

Statistical inference on regression with spatial dependence

Robinson

Thawornkaiwong

2012

Journal of Econometrics

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Central limit theorems are developed for instrumental variables estimates of linear and semiparametric partly linear regression models for spatial data. General forms of spatial dependence and heterogeneity in explanatory variables and unobservable disturbances are permitted. We discuss estimation of the variance matrix, including estimates that are robust to disturbance heteroscedasticity and/or dependence. A Monte Carlo study of …nite-sample performance is included. In an empirical example, the estimates and robust and non-robust standard errors are computed from Indian regional data, following tests for spatial correlation in disturbances, and nonparametric regression …tting. Some …nal comments discuss modi…cations and extensions.JEL Classi…cations: C13; C14; C21

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Random Fields, Nonparametric Methods

Tjøstheim¹

2012

Encyclopedia of Environmetrics

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Nonparametric spectrum estimation for spatial data

Cited by 27 publications

References 10 publications

Autoregressive spatial spectral estimates

Autoregressive spatial spectral estimates

Statistical inference on regression with spatial dependence

Random Fields, Nonparametric Methods

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