On Wavelet Methods for Estimating Smooth Functions

Hall, Peter A.; Patil, Prakash

doi:10.2307/3318680

Cited by 44 publications

(28 citation statements)

References 11 publications

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“…Jadi koefisien wavelet empiris k j d , memuat sejumlah noise dan hanya relatif sedikit yang memuat sinyal signifikan sehingga dapat direkonstruksi estimator wavelet dengan menggunakan sejumlah koefisien terbesar. Oleh karena itu Hall&Patil [4] dan Ogden [7] memberikan metode yang menekankan rekonstruksi wavelet dengan menggunakan sejumlah koefisien wavelet terbesar, yakni hanya koefisien yang lebih besar dari suatu nilai tertentu yang diambil, sedangkan koefisien selebihnya diabaikan, karena dianggap 0. Nilai tertentu tersebut dinamakan nilai threshold (nilai ambang) dan estimatornya menghasilkan…”

Section: Estimator Wavelet Shrinkageunclassified

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Suparti¹,

Tarno²,

Haryono³

2012

Medstat

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If X is predictor variable and Y is response variable of following model Y = f (X) +e with function f is regression which not yet been known and e is independent random variable with mean 0 and variant 2 σ , hence function of f can estimate with parametric and nonparametric approach.At this paper estimate f with nonparametric approach. Nonparametric approach that used is wavelet shrinkage or wavelet thresholding method. At function estimation with method of wavelet thresholding, what most dominant determine level of smoothing estimator is value of threshold. The small threshold give function estimation very no smoothly, while the big value of threshold give function estimation very smoothly. Therefore require to be selected value of optimal threshold to determine optimal function estimation.One of the method to determine the value of optimal threshold is with procedure of False Discovery Rate ( FDR). In procedure of FDR, the optimal threshold determined by selection of level of significance. Smaller mount used significance progressively smoothly its .

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Section: Estimator Wavelet Shrinkageunclassified

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Suparti¹,

Tarno²,

Haryono³

2012

Medstat

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“…Otherwise, the resulting estimation may not be reasonably smooth and useful. In order to achieve an estimation with the desirable degree of smoothness, several methods are proposed in the literature (Kerkyacharian and Picard, 1992;Hall and Patil, 1993;Pinheiro and Vidakovic, 1995). The simplest is to express the estimation as wavelet analysis to some extent, it is a more natural way to m work with data on the interval [O, 11.…”

Section: Wavelet-based Density Estimatorsmentioning

confidence: 99%

Wavelet‐based density estimation and application to process monitoring

1997

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“…Shrinkage is basic in statistical work with wavelets, Donoho and Johnstone [19], Kerkyacharian and Picard [32], Donoho [8] and Hall and Patil [24].…”

Section: Shrinkage Estimatesmentioning

confidence: 99%

“…These will be used later in the paper. A parameter like U was introduced by Hall and Patil [24] to facilate the study of large sample properties of wavelet estimates. General references to wavelet analysis are Daubechies [14], Walter [47][48][49], Meyer [36], Strichartz [44], Benedetto and Frazier [4].…”

Section: Cumulantsmentioning

confidence: 99%

<title>Uses of cumulants in wavelet analysis</title>

Brillinger

1994

Advanced Signal Processing: Algorithms, Architectures, and Implementations V

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Cumulants are useful in studying nonlinear phenomena and in developing (approximate) statistical properties of quantities computed from random process data. Wavelet analysis is a powerful tool for the approximation and estimation of curves and surfaces. This work considers both wavelets and cumulants, developing some sampling properties of linear wavelet fits to a signal in the presence of additive stationary noise via the calculus of cumulants. Of some concern is the construction of approximate confidence bounds around a fit. Some extensions to spatial processes, irregularly observed processes and long memory processes are indicated.

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On Wavelet Methods for Estimating Smooth Functions

Cited by 44 publications

References 11 publications

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Wavelet‐based density estimation and application to process monitoring

<title>Uses of cumulants in wavelet analysis</title>

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