Generalization Of The Radix Method Of Finding The Median To Weighted Median, Order Statistic And Weighted Order Statistic Filters

1988 ◽  
Author(s):  
Olli Yli-Harja ◽  
Jaakko Astola ◽  
Yrjo Nuevo
Keyword(s):  
Order Statistic ◽  
Median Order ◽  
Weighted Median

PERFORMANCE BOUNDARIES OF OPTIMAL WEIGHTED MEDIAN FILTERS

2004 ◽  
Vol 04 (02) ◽  
pp. 157-182 ◽  
Author(s):  
RASTISLAV LUKAC
Keyword(s):  
Order Statistic ◽  
Impulse Noise ◽  
Nonlinear Filter ◽  
Edge Preservation ◽  
Sign Function ◽  
Median Filters ◽  
Weighted Median ◽  
Statistic Theory ◽  
Weighted Median Filters ◽  
Optimization Schemes

This paper focuses on image filtering using weighted median (WM) filters, a nonlinear filter class taking advantages of the robust order-statistic theory and capability to adapt a filter behavior for a variety of statistics related to the desired signals and the noise distributions. The main contribution of the paper is the analysis of the four WM optimization schemes, namely genetic WM optimization, non-adaptive WM optimization algorithm and adaptive WM filtering utilizing the linear and the sigmoidal approximation of the sign function. The analysis is done by extensive simulations, in which several features such as noise reduction, edge preservation, error estimation and dependence of error criteria on the degree of the impulse noise corruption, are examined.

Life Course Adiposity and Alzheimer’s Disease: A Mendelian Randomization Study

2021 ◽  
pp. 1-10
Author(s):  
Xian Li ◽  
Yan Tian ◽  
Yu-Xiang Yang ◽  
Ya-Hui Ma ◽  
Xue-Ning Shen ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Life Course ◽  
Mendelian Randomization ◽  
Association Studies ◽  
Meta Analysis ◽  
Genome Wide Association Studies ◽  
Fat Percentage ◽  
Regression Methods ◽  
Weighted Median

Background: Several studies showed that life course adiposity was associated with Alzheimer’s disease (AD). However, the underlying causality remains unclear. Objective: We aimed to examine the causal relationship between life course adiposity and AD using Mendelian randomization (MR) analysis. Methods: Instrumental variants were obtained from large genome-wide association studies (GWAS) for life course adiposity, including birth weight (BW), childhood body mass index (BMI), adult BMI, waist circumference (WC), waist-to-hip ratio (WHR), and body fat percentage (BFP). A meta-analysis of GWAS for AD including 71,880 cases and 383,378 controls was used in this study. MR analyses were performed using inverse variance weighted (IVW), weighted median, and MR-Egger regression methods. We calculated odds ratios (ORs) per genetically predicted standard deviation (1-SD) unit increase in each trait for AD. Results: Genetically predicted 1-SD increase in adult BMI was significantly associated with higher risk of AD (IVW: OR = 1.03, 95% confidence interval [CI] = 1.01–1.05, p = 2.7×10–3) after Bonferroni correction. The weighted median method indicated a significant association between BW and AD (OR = 0.94, 95% CI = 0.90–0.98, p = 1.8×10–3). We also found suggestive associations of AD with WC (IVW: OR = 1.03, 95% CI = 1.00–1.07, p = 0.048) and WHR (weighted median: OR = 1.04, 95% CI = 1.00–1.07, p = 0.029). No association was detected of AD with childhood BMI and BFP. Conclusion: Our study demonstrated that lower BW and higher adult BMI had causal effects on increased AD risk.

A Note on the Accuracy of Normal Approximation of Random Quantities

2021 ◽  
Vol 73 (1) ◽  
pp. 62-67
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Sample Size ◽  
Order Statistic ◽  
Normal Approximation ◽  
Order Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Limiting Distribution ◽  
Exact Order ◽  
Fixed Sample ◽  
Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

scholarly journals A Mendelian randomization analysis of the relationship between cardioembolic risk factors and ischemic stroke

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Danyang Tian ◽  
Linjing Zhang ◽  
Zhenhuang Zhuang ◽  
Tao Huang ◽  
Dongsheng Fan
Keyword(s):  
Risk Factors ◽  
Ischemic Stroke ◽  
Mendelian Randomization ◽  
P Wave ◽  
Cardioembolic Stroke ◽  
Large Artery ◽  
Weighted Analysis ◽  
Inverse Variance ◽  
Weighted Median ◽  
Genetically Determined

AbstractObservational studies have shown that several risk factors are associated with cardioembolic stroke. However, whether such associations reflect causality remains unknown. We aimed to determine whether established and provisional cardioembolic risk factors are causally associated with cardioembolic stroke. Genetic instruments for atrial fibrillation (AF), myocardial infarction (MI), electrocardiogram (ECG) indices and N-terminal pro-brain natriuretic peptide (NT-pro BNP) were obtained from large genetic consortiums. Summarized data of ischemic stroke and its subtypes were extracted from the MEGASTROKE consortium. Causal estimates were calculated by applying inverse-variance weighted analysis, weighted median analysis, simple median analysis and Mendelian randomization (MR)-Egger regression. Genetically predicted AF was significantly associated with higher odds of ischemic stroke (odds ratio (OR): 1.20, 95% confidence intervals (CI): 1.16–1.24, P = 6.53 × 10–30) and cardioembolic stroke (OR: 1.95, 95% CI: 1.85–2.06, P = 8.81 × 10–125). Suggestive associations were found between genetically determined resting heart rate and higher odds of ischemic stroke (OR: 1.01, 95% CI: 1.00–1.02, P = 0.005), large-artery atherosclerotic stroke (OR: 1.02, 95% CI: 1.00–1.04, P = 0.026) and cardioembolic stroke (OR: 1.02, 95% CI: 1.00–1.04, P = 0.028). There was no causal association of P‐wave terminal force in the precordial lead V1 (PTFVI), P-wave duration (PWD), NT-pro BNP or PR interval with ischemic stroke or any subtype.

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