Non-Local Means (NLM) and its variants have proven to be effective and robust in many image denoising tasks. In this letter, we study approaches to selecting center pixel weights (CPW) in NLM. Our ...key contributions are 1) we give a novel formulation of the CPW problem from a statistical shrinkage perspective; 2) we construct the James-Stein shrinkage estimator in the CPW context; and 3) we propose a new local James-Stein type CPW (LJSCPW) that is locally tuned for each image pixel. Our experimental results showed that compared to existing CPW solutions, the LJSCPW is more robust and effective under various noise levels. In particular, the NLM with the LJSCPW attains higher means with smaller variances in terms of the peak signal and noise ratio (PSNR) and structural similarity (SSIM), implying it improves the NLM denoising performance and makes the denoising less sensitive to parameter changes.
On homogeneous James–Stein type estimators Boukehil, Djamila; Fourdrinier, Dominique; Mezoued, Fatiha ...
Statistics & probability letters,
December 2022, 2022-12-00, Letnik:
191
Journal Article
Recenzirano
Odprti dostop
The shrinkage factor of the James–Stein estimators of a multivariate normal involves the power of the squared norm of X. We show powers of the norm greater than 2 also give improvement, while lesser ...powers do not.
•Multivariate control chart is a useful tool in quality control.•We use the James–Stein estimator to construct better control charts.•JS-type control charts are proposed.
In this study, we focus on ...improving parameter estimation in Phase I study to construct more accurate Phase II control limits for monitoring multivariate quality characteristics. For a multivariate normal distribution with unknown mean vector, the usual mean estimator is known to be inadmissible under the squared error loss function when the dimension of the variables is greater than 2. Shrinkage estimators, such as the James–Stein estimators, are shown to have better performance than the conventional estimators in the literature. We utilize the James–Stein estimators to improve the Phase I parameter estimation. Multivariate control limits for the Phase II monitoring based on the improved estimators are proposed in this study. The resulting control charts, JS-type charts, are shown to have substantial performance improvement over the existing ones.
Demonstrating bioequivalence of several pharmacokinetic (PK) parameters, such as AUC and Cmax, that are calculated from the same biological sample measurements is in fact a multivariate problem, even ...though this is neglected by most practitioners and regulatory bodies, who typically settle for separate univariate analyses. We believe, however, that a truly multivariate evaluation of all PK measures simultaneously is clearly more adequate. In this paper, we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation. Some of them work well for idealised scenarios but break down when faced with real‐data challenges such as unknown variance and correlation among the PK parameters. We study the shapes of the confidence regions resulting from different methods, discuss how marginal simultaneous confidence intervals for the individual PK measures can be derived, and illustrate the application to data from a trial on ticlopidine hydrochloride. An R package is available.
The Poisson regression model (PRM) aims to model a counting variable y, which is usually estimated by using maximum likelihood estimation (MLE) method. The performance of MLE is not satisfactory in ...the presence of multicollinearity. Therefore, we propose a Poisson James-Stein estimator (PJSE) as a solution to the problems of inflated variance and standard error of MLE with multicollinear explanatory variables. For assessing the superiority of proposed estimator, we present a theoretical comparison based on the matrix mean squared error (MMSE) and scalar mean squared error (MSE) criterions. A Monte Carlo simulation study is performed under different conditions in order to investigate the performance of the proposed estimator where MSE is considered as an evaluation criterion. In addition, an aircraft damage data is also considered to assess the superiority of proposed estimator. Based on the results of simulation and real data application, it is shown that the PJSE outperforms the classical MLE and other biased estimation methods in a sense of minimum MSE criterion.
This article proposes some new estimators, namely Stein’s estimators for ridge regression and Kibria and Lukman estimator and compares their performance with some existing estimators, namely maximum ...likelihood estimator (MLE), ridge regression estimator, Liu estimator, almost unbiased ridge and Liu estimators, adjusted Liu estimator, James stein’s estimator, Kibria and Lukman estimator, Dorugade estimator, and modified ridge estimator for the logistic regression model to solve the multicollinearity problem. The bias, covariance matrix, and mean square error matrix for each of the estimators are provided. A Monte Carlo simulation has been conducted to compare the performance of different estimators. We consider the smaller mean squared error value as a performance criterion. From the simulation study, it is evident that all proposed estimators performed better than the MLE. Finally, a real-life data is analyzed to illustrate the findings of the article. Some promising estimators are recommended for the practitioners.
A non-local means (NLM) filter is a weighted average of a large number of non-local pixels with various image intensity values. The NLM filters have been shown to have powerful denoising performance, ...excellent detail preservation by averaging many noisy pixels, and using appropriate values for the weights, respectively. The NLM weights between two different pixels are determined based on the similarities between two patches that surround these pixels and a smoothing parameter. Another important factor that influences the denoising performance is the self-weight values for the same pixel. The recently introduced local James-Stein type center pixel weight estimation method (LJS) outperforms other existing methods when determining the contribution of the center pixels in the NLM filter. However, the LJS method may result in excessively large self-weight estimates since no upper bound is assumed, and the method uses a relatively large local area for estimating the self-weights, which may lead to a strong bias. In this paper, we investigated these issues in the LJS method, and then propose a novel local self-weight estimation methods using direct bounds (LMM-DB) and reparametrization (LMM-RP) based on the Baranchik's minimax estimator. Both the LMM-DB and LMM-RP methods were evaluated using a wide range of natural images and a clinical MRI image together with the various levels of additive Gaussian noise. Our proposed parameter selection methods yielded an improved bias-variance trade-off, a higher peak signal-to-noise (PSNR) ratio, and fewer visual artifacts when compared with the results of the classical NLM and LJS methods. Our proposed methods also provide a heuristic way to select a suitable global smoothing parameters that can yield PSNR values that are close to the optimal values.
We consider the problem of efficient estimation of the drift of Riemann-Liouville fractional Brownian motion
with Hurst parameter H less than
We also construct superefficient James-Stein type ...estimators which dominate under the usual quadratic risk, the natural maximum likelihood estimator.
In this paper, we consider the problem of efficient estimation for the drift parameter
θ
∈
R
d
in the linear model
Z
t
:
=
θ
t
+
σ
1
B
H
1
(
t
)
+
σ
2
B
H
2
(
t
)
,
t
∈
0
,
T
.
Where
B
H
1
and
B
H
...2
are two independent d-dimensional fractional Brownian motions with Hurst indices H
1
and H
2
such that
1
2
≤
H
1
<
H
2
<
1
.
The main goal is firstly to define the maximum likelihood estimator (MLE) of the drift θ, and secondly to provide a sufficient condition for the James-Stein type estimators which dominate, under the usual quadratic risk, the usual estimator (MLE).
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