On the Distribution of Some Statistical Estimates of Spectral Density

Bentkus, R.; Rudzkis, Rimantas

doi:10.1137/1127088

Cited by 17 publications

(17 citation statements)

References 2 publications

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“…Our results extend Bentkus and Rudzkis (1982) in that we do not assume boundedness of the spectral density at frequencies away from the origin. We give two lemmas about the bias of the estimate f (0) for V N .…”

Section: Distribution Of the Nonparametric Spectral Estimatesupporting

confidence: 77%

“…First, following Bentkus and Rudzkis (1982) we study the characteristic function of the spectral density estimate, which itself appears in the joint characteristic function. Define τ (t 2 ) = E [exp {it 2 u 2 }] = τ (t 2 ) exp {−it 2 E} , where…”

Section: First Step We Boundmentioning

confidence: 99%

“…In particular, this is the case in the work of Bentkus (1976), Bentkus and Rudzkis (1982) and Rudzkis (1985) on higher-order asymptotic theory for nonparametric spectral estimates, whose approach we in other respects follow. It is also the case in the econometric work referred to above on consistency of autocorrelation-consistent or long run variance estimates and on the first-order limiting distribution of studentized statistics, which resorts to summability conditions on mixing numbers.…”

Section: Introductionmentioning

confidence: 96%

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Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean

Velasco

Robinson²

2001

Econ. Theory

111

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We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the same mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our main focus is on stationary Gaussian series, though we discuss relaxation of the Gaussianity assumption. Only smoothness conditions on the spectral density that are local to the frequency of interest are imposed. We deduce empirical expansions from our Edgeworth expansions designed to improve on the normal approximation in practice, and also a feasible rule of bandwidth choice.

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Section: Distribution Of the Nonparametric Spectral Estimatesupporting

confidence: 77%

Section: First Step We Boundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean

Velasco

Robinson²

2001

Econ. Theory

111

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“…. , X n } from a p-variate Gaussian distribution with the Toeplitz covariance matrix Σ given as in (1). Now let us consider an"enlarged" experiment in which one observes an i.i.d.…”

Section: Minimax Lower Bound Under the Spectral Normmentioning

confidence: 99%

Optimal rates of convergence for estimating Toeplitz covariance matrices

Cai

Ren

Zhou

2012

Probab. Theory Relat. Fields

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Toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging, target detection, speech recognition, and communications systems. In this paper, we consider optimal estimation of large Toeplitz covariance matrices and establish the minimax rate of convergence for two commonly used parameter spaces under the spectral norm. The properties of the tapering and banding estimators are studied in detail and are used to obtain the minimax upper bound. The results also reveal a fundamental difference between the tapering and banding estimators over certain parameter spaces. The minimax lower bound is derived through a novel construction of a more informative experiment for which the minimax lower bound is obtained through an equivalent Gaussian scale model and through a careful selection of a finite collection of least favorable parameters. In addition, optimal rate of convergence for estimating the inverse of a Toeplitz covariance matrix is also established.

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“…We now mention additional works only. Bentkus and Rudzkis [8] and Janas [26] [14]. Taniguchi et al [37] developed the higher-order asymptotic theory of minimum contrast estimators based on f T (·).…”

Section: Introductionmentioning

confidence: 99%