Unbiasedness on rays of the tests of locations of homogeneous means in isotonic regression

Hu, Xiaomi

doi:10.1016/j.spl.2005.10.034

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…We notice that different forms of (5) can be used [2,8,13,31]. When N is large, N 1, and the computational problem arises, fast computation of (4) is commonly provided in DFT domain using FFT.…”

Section: Polynomial Signal Model and Problem Formulationmentioning

confidence: 99%

Computationally Efficient FIR Filtering of Polynomial Signals in DFT Domain

Castro-Tinttori

Ibarra-Manzano

Shmaliy

2012

Circuits Syst Signal Process

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Fast unbiased finite impulse response (UFIR) filtering of polynomial signals can be provided in the discrete Fourier transform (DFT) domain employing fast Fourier transform (FFT). We show that the computation time can further be reduced by utilizing properties of UFIR filters in the DFT domain. The transforms have been found and investigated in detail for low-degree FIRs most widely used in practice. As a special result, we address an explicit unbiasedness condition uniquely featured to UFIR filters in DFT domain. The noise power gain and estimation error bound have also been discussed. An application is given for state estimation in a crystal clock employing the Global Positioning System based measurement of time errors provided each second. Based upon it, it is shown that filtering in the time domain takes about 1 second, which is unacceptable for real-time applications. The Kalman-like algorithm reduces the computation time by the factor of about 8, the FFT-based algorithm by about 18, and FFT with the UFIR filter DFT properties by about 20.

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Section: Polynomial Signal Model and Problem Formulationmentioning

confidence: 99%

Computationally Efficient FIR Filtering of Polynomial Signals in DFT Domain

Castro-Tinttori

Ibarra-Manzano

Shmaliy

2012

Circuits Syst Signal Process

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On strong law of large numbers and growth rate for a class of random variables

Shen

Yang

2013

J Inequal Appl

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In this paper, we study the strong law of large numbers for a class of random variables satisfying the maximal moment inequality with exponent 2. Our results embrace the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for this class of random variables. In addition, strong growth rate for weighted sums of this class of random variables is presented. MSC: 60F15

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Unbiasedness on rays of the tests of locations of homogeneous means in isotonic regression

Cited by 2 publications

References 6 publications

Computationally Efficient FIR Filtering of Polynomial Signals in DFT Domain

Computationally Efficient FIR Filtering of Polynomial Signals in DFT Domain

On strong law of large numbers and growth rate for a class of random variables

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