Making a Non-Parametric Density Estimator More Attractive, and More Accurate, by Data Perturbation

Doosti, Hassan; Hall, Peter

doi:10.1111/rssb.12120

Cited by 9 publications

(5 citation statements)

References 37 publications

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“…Using a tilting approach to estimate

in a GAM setting leads to improvement of the performance of the nonparametric regression estimator. Hall and Presnell [ 32 ], Hall and Huang [ 33 ], Carroll [ 34 ], Doosti and Hall [ 35 ], and Doosti et al. [ 36 ] used setup-specific Distance Measure approaches for estimating the tilting parameters.…”

Section: Discussionmentioning

confidence: 99%

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An Analysis of the Areas Occupied by Vessels in the Ocular Surface of Diabetic Patients: An Application of a Nonparametric Tilted Additive Model

Boroumand

Shakeri

Banaee

et al. 2021

IJERPH

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(1) Background: As diabetes melllitus (DM) can affect the microvasculature, this study evaluates different clinical parameters and the vascular density of ocular surface microvasculature in diabetic patients. (2) Methods: In this cross‑sectional study, red‑free conjunctival photographs of diabetic individuals aged 30–60 were taken under defined conditions and analyzed using a Radon transform‑based algorithm for vascular segmentation. The Areas Occupied by Vessels (AOV) images of different diameters were calculated. To establish the sum of AOV of different sized vessels. We adopt a novel approach to investigate the association between clinical characteristics as the predictors and AOV as the outcome, that is Tilted Additive Model (TAM). We use a tilted nonparametric regression estimator to estimate the nonlinear effect of predictors on the outcome in the additive setting for the first time. (3) Results: The results show Age (p-value = 0.019) and Mean Arterial Pressure (MAP) have a significant linear effect on AOV (p-value = 0.034). We also find a nonlinear association between Body Mass Index (BMI), daily Urinary Protein Excretion (UPE), Hemoglobin A1C, and Blood Urea Nitrogen (BUN) with AOV. (4) Conclusions: As many predictors do not have a linear relationship with the outcome, we conclude that the TAM will help better elucidate the effect of the different predictors. The highest level of AOV can be seen at Hemoglobin A1C of 9% and AOV increases when the daily UPE exceeds 600 mg. These effects need to be considered in future studies of ocular surface vessels of diabetic patients.

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“…Using a tilting approach to estimate

Section: Discussionmentioning

confidence: 99%

“…A tilting method used in [ 34 ] led to curve estimators under some constraints. Doosti and Hall [ 35 ] introduced a new higher order nonparametric density estimator, using a tilting method, where they used

-metric between the proposed estimator and a consistent ’Sinc’ kernel-based estimator. Doosti et al.…”

Section: Discussionmentioning

confidence: 99%

An Analysis of the Areas Occupied by Vessels in the Ocular Surface of Diabetic Patients: An Application of a Nonparametric Tilted Additive Model

Boroumand

Shakeri

Banaee

et al. 2021

IJERPH

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“…The new estimate is

\overset{f}{true} (x) = \frac{1}{n \det (h)} \sum_{i = 1}^{n} w_{j (i)} ϕ_{d} ((), h^{- 1} (x - z_{i})),

where w j ( i ) is the weight of the cell to which z i belongs. The type of perturbation of estimator is denoted “tilting” by Doosti and Hall ().…”

Section: Non‐parametric Local Smoothingmentioning

confidence: 99%

“…where w j(i) is the weight of the cell to which z i belongs. The type of perturbation of estimator (2) is denoted 'tilting' by Doosti & Hall (2016).…”

Section: Non-parametric Local Smoothingmentioning

confidence: 99%

Combining local and global smoothing in multivariate density estimation

Azzalini

2016

Stat

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“…Choi et al (2000) presents a simple, but effective, method of sharpening data to reduce bias in nonparametric regression. Doosti and Hall (2016) demonstrate the benefits to be accrued when sharpening and tilting are applied in combination yielding improved "perturbed" density estimates, both qualitatively and in terms of accuracy; theoretical results supplied there show that uniform consistency is attained for a large class of densities.…”

Section: Introductionmentioning

confidence: 99%

Data Sharpening Guided by Global Constraint in Local Regression

Braun¹,

Hu²,

Kang³

2018

STAT SINICA

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Data sharpening for kernel regression and density estimation was introduced by the late Peter Hall. We review briefly his enormous contribution to the literature in this area and then propose a data sharpening procedure arising from imposition of a soft global functional constraint in local regression analysis. Instead of enforcing the constraint everywhere, the procedure guides the data in directions which enable satisfaction or near-satisfaction of the given property globally through the use of a penalty. It results in a modified local regression estimator which possesses a closed functional form and which includes a conventional local regression estimator as a special case. The approach can accommodate various constraints, most of which in practice are motivated by expert prior knowledge. We demonstrate theoretically and numerically that the proposed estimator is an improved variant of the corresponding local regression estimator. It achieves a reduction in variance while maintaining the bias at the same level. Although the focus in the paper is on local polynomial regression, the technique can be applied, in principle, to any linear nonparametric estimator, including regression splines, smoothing and penalized splines and other recently proposed kernel estimators. We exhibit usefulness of the proposed approach with an analysis of a collection of temperatures at the airport of Vancouver. The analysis reveals a possible monotonic trend underlying the conventional supposition of a periodic (seasonal) temporal structure.

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Making a Non-Parametric Density Estimator More Attractive, and More Accurate, by Data Perturbation

Cited by 9 publications

References 37 publications

An Analysis of the Areas Occupied by Vessels in the Ocular Surface of Diabetic Patients: An Application of a Nonparametric Tilted Additive Model

An Analysis of the Areas Occupied by Vessels in the Ocular Surface of Diabetic Patients: An Application of a Nonparametric Tilted Additive Model

Combining local and global smoothing in multivariate density estimation

Data Sharpening Guided by Global Constraint in Local Regression

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