Nonparametric density estimation of streaming data using orthogonal series

Caudle, Kyle; Wegman, Edward J.

doi:10.1016/j.csda.2009.06.014

Cited by 17 publications

(7 citation statements)

References 6 publications

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“…For the density estimation of streaming data of a nonstationary process in [Caudle & Wegman, 2009], the simple idea introduced by Cencov [1962] was used to find the coefficients of the orthogonal series from expectations of basis functions. We have also used this simple idea to determine the unknown coefficients a i s of the estimated PDF in terms of the nonorthogonal B-splines as: multiplying both sides of Eq.…”

Section: One-dimensional (1d) Density Estimation Using B-splinesmentioning

confidence: 99%

Estimating Probability Density Functions and Entropies of Chua's Circuit Using B-Spline Functions

Savacı

Güngör

2012

Int. J. Bifurcation Chaos

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Section: One-dimensional (1d) Density Estimation Using B-splinesmentioning

confidence: 99%

Estimating Probability Density Functions and Entropies of Chua's Circuit Using B-Spline Functions

Savacı

Güngör

2012

Int. J. Bifurcation Chaos

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“…The main downfall of these bases is their infinite support, demanding a large number of terms in the series expansion to accurately approximate complex densities containing multiple modes and abrupt variations. With the advent and growing use of wavelets, we are now seeing more uses of OSE [15,30,7,5]. In fact, Peter and Rangarajan [28] show wavelet density estimators (WDE) often outperform many other nonparametric density estimators.…”

Section: Relevant Workmentioning

confidence: 99%

Multiwavelet density estimation

Locke¹,

Peter²

2013

Applied Mathematics and Computation

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Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel density estimators have been the predominant tools of choice, primarily due to their ease of use and mathematical simplicity. More recently, the use of wavelets for density estimation has gained in popularity due to their ability to approximate a large class of functions, including those with localized, abrupt variations. However, a well-known attribute of wavelet bases is that they can not be simultaneously symmetric, orthogonal, and compactly supported. Multiwavelets-a more general, vector-valued, construction of wavelets-overcome this disadvantage, making them natural choices for estimating density functions, many of which exhibit local symmetries around features such as a mode. We extend the methodology of wavelet density estimation to use multiwavelet bases and illustrate several empirical results where multiwavelet estimators outperform their wavelet counterparts at coarser resolution levels.

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“…If data arrive in batches, where there is no particular ordering within a batch, it may be advantageous to weight each data element within a batch equally, but exponentially weight the batches themselves. Extending the above methodology to k batches of size p (with kp = n ) results in the following updating algorithm2 For example, consider a data stream of 1000 observations that has been obtained in four batches of 250 observations. Further assume that within each batch there is no specific ordering.…”

Section: Discounting Old Datamentioning

confidence: 99%

Discounting older data

Caudle

Fowler

Jager

et al. 2010

WIREs Computational Stats

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This article describes two general methods for discounting older data in the realtime analysis of a data stream. In the first method, the distribution of a data stream is estimated by a series of orthogonal basis functions, and the coefficients of this estimate are updated as new data arrive by combining windowing and exponential smoothing techniques. The second method involves sequential hypothesis testing. When new data arrive, test significance level is adjusted by alpha-investing, which raises or reduces the significance level of subsequent hypothesis tests on the basis of whether the previous hypothesis test rejects or fails to reject the null hypothesis. Both these methods are nonparametric in nature. 

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Nonparametric density estimation of streaming data using orthogonal series

Cited by 17 publications

References 6 publications

Estimating Probability Density Functions and Entropies of Chua's Circuit Using B-Spline Functions

Estimating Probability Density Functions and Entropies of Chua's Circuit Using B-Spline Functions

Multiwavelet density estimation

Discounting older data

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