Miscellanea. Data sharpening as a prelude to density estimation

Choi, Edwin; Hall, Peter

doi:10.1093/biomet/86.4.941

Cited by 67 publications

(41 citation statements)

References 16 publications

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“…Recent unimodal density estimation research has been focussed on utilizing data sharpening techniques, introduced by Choi and Hall (1999) and Choi et al (2000), to implement unimodal constraints on standard nonparametric density estimators. Data sharpening involves shifting data points in a controlled manner before executing estimation techniques.…”

Section: Unimodal Density Estimationmentioning

confidence: 99%

Unimodal density estimation using Bernstein polynomials

Turnbull

Ghosh

2014

Computational Statistics & Data Analysis

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The estimation of probability density functions is one of the fundamental aspects of any statistical inference. Many data analyses are based on an assumed family of parametric models, which are known to be unimodal (e.g., exponential family, etc.). Often a histogram suggests the unimodality of the underlying density function. Parametric assumptions, however, may not be adequate for many inferential problems. This paper presents a flexible class of mixture of Beta densities that are constrained to be unimodal. We show that the estimation of the mixing weights, and the number of mixing components, can be accomplished using a weighted least squares criteria subject to a set of linear inequality constraints. We efficiently compute the number of mixing components and associated mixing weights of the beta mixture using quadratic programming techniques. Three criterion for selecting the number of mixing weights are presented and compared in a small simulation study. More extensive simulation studies are conducted to demonstrate the performance of the density estimates in terms of popular functional norms (e.g., L p norms). The true underlying densities are allowed to be unimodal symmetric and skewed, with finite, infinite or semi-finite supports. Code for an R function is provided which allows the user to input a data set and returns the estimated density, distribution, quantile, and random sample generating functions.

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Section: Unimodal Density Estimationmentioning

confidence: 99%

Unimodal density estimation using Bernstein polynomials

Turnbull

Ghosh

2014

Computational Statistics & Data Analysis

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“…For example, we expect that MMD with the combined transformation might not work well for heavy-tailed data and/or data containing outliers. In these cases, data sharpening techniques (e.g., Choi and Hall, 1999;Wang et al 2007) may be used. For example, the eGG and eLNN models proposed by Lo and Gottardo (2007) relaxed the assumption of a constant coefficient of variation across genes required by the GG and LNN models, by imposing a prior distribution to the rate parameter of GG model and the variance of LNN model.…”

Section: Discussionmentioning

confidence: 99%

A Marginal Mixture Model for Selecting Differentially Expressed Genes across Two Types of Tissue Samples

Qiu

Wang

et al. 2008

The International Journal of Biostatistics

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Bayesian hierarchical models that characterize the distributions of (transformed) gene profiles have been proven very useful and flexible in selecting differentially expressed genes across different types of tissue samples (e.g. Lo and Gottardo, 2007). However, the marginal mean and variance of these models are assumed to be the same for different gene clusters and for different tissue types. Moreover, it is not easy to determine which of the many competing Bayesian hierarchical models provides the best fit for a specific microarray data set. To address these two issues, we propose a marginal mixture model that directly models the marginal distribution of transformed gene profiles. Specifically, we approximate the marginal distributions of transformed gene profiles via a mixture of three-component multivariate Normal distributions, each component of which has the same structures of marginal mean vector and covariance matrix as those for Bayesian hierarchical models, but the values can differ. Based on the proposed model, a method is derived to select genes differentially expressed across two types of tissue samples. The derived gene selection method performs well on a real microarray data set and consistently has the best performance (based on class agreement indices) compared with several other gene selection methods on simulated microarray data sets generated from three different mixture models.

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“…Alternatively, in higher dimensions away from peaks and valleys, one can annihilate pointwise bias by balancing directions of positive curvature against directions of negative curvature; see Terrell and Scott (1992). An even more intriguing idea literally adjusts the raw data points towards peaks and away from valleys to reduce bias; see Choi and Hall (1999).…”

Section: No Unbiased Density Estimatorsmentioning

confidence: 99%

Multivariate Density Estimation and Visualization

Scott

2011

Handbook of Computational Statistics

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Miscellanea. Data sharpening as a prelude to density estimation

Cited by 67 publications

References 16 publications

Unimodal density estimation using Bernstein polynomials

Unimodal density estimation using Bernstein polynomials

A Marginal Mixture Model for Selecting Differentially Expressed Genes across Two Types of Tissue Samples

Multivariate Density Estimation and Visualization

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