Robust Adaptive Lasso method for parameter’s estimation and variable selection in high-dimensional sparse models

<div><p>High dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. To address this issue different penalized regression procedures have been introduced in the litrature, but these methods cannot cope with the problem of outliers and leverage points in the heavy tailed high dimensional data. For this purppose, a new Robust Adaptive Lasso (RAL) method is proposed which is based on pearson residuals weighting scheme. The weight function determines the compatibility of each observations and downweight it if they are inconsistent with the assumed model. It is observed that RAL estimator can correctly select the covariates with non-zero coefficients and can estimate parameters, simultaneously, not only in the presence of influential observations, but also in the presence of high multicolliearity. We also discuss the model selection oracle property and the asymptotic normality of the RAL. Simulations findings and real data examples also demonstrate the better performance of the proposed penalized regression approach.</p></div

The Q-Q plot and boxplot of the response variable “lcavol”.

<p>The Q-Q plot and boxplot of the response variable “lcavol”.</p

(a) Histogram and (b) Boxplot for production rate in riboflavin.

<p>(a) Histogram and (b) Boxplot for production rate in riboflavin.</p

Simulation results are based on 1000 replications and <i>δ</i> is the level of contamination in the model (1 − <i>δ</i>)<i>exp</i>(1) + <i>δexp</i>(0.2).

<p>Simulation results are based on 1000 replications and <i>δ</i> is the level of contamination in the model (1 − <i>δ</i>)<i>exp</i>(1) + <i>δexp</i>(0.2).</p

Estimated coefficients and model error results, for various regularization procedures applied to the prostate data.

<p>The dashed entries correspond to predictors that are estimated “0”.</p

Simulation results for the location level of contamination in the model(1 − <i>δ</i>)<i>N</i>(0, 1) + <i>δN</i>(−10, 1) in high-dimensional data set.

<p>Simulation results for the location level of contamination in the model(1 − <i>δ</i>)<i>N</i>(0, 1) + <i>δN</i>(−10, 1) in high-dimensional data set.</p

Simulation results for the location level of contamination in the model(1 − <i>δ</i>)<i>N</i>(0, 1) + <i>δN</i>(−10, 1).

<p>Simulation results for the location level of contamination in the model(1 − <i>δ</i>)<i>N</i>(0, 1) + <i>δN</i>(−10, 1).</p

Simulation results for the scale level of contamination in the model(1 − <i>δ</i>)<i>N</i>(0, 1) + <i>δN</i>(0, 25).

<p>Simulation results for the scale level of contamination in the model(1 − <i>δ</i>)<i>N</i>(0, 1) + <i>δN</i>(0, 25).</p

Comparison of percentage test error.

<p>Comparison of percentage test error.</p

Data_Sheet_1_Sex differences in the association between blood pressure and atrial fibrillation: A case-control study.DOCX

BackgroundTo examine the association of hypertension (HBP) and its control with atrial fibrillation (AF) and how patient sex affects this association.Materials and methodsA case control study of patients admitted to our hospital from 2015 to 2019 was conducted. Patients were divided into subgroups according to their blood pressure (BP) levels and control status, in which odd ratios (OR) by sex for AF was estimated using a logistic regression model and restrictive cubic splines before and after propensity score matching.ResultsA total of 3,212 patients with AF and 8,307 without AF were investigated. Compared to patients with normal BP, patients with HBP had more AF [OR = 1.75 (1.52–2.02), OR = 2.66 (2.24–3.15), and OR = 4.30 (3.40–5.44) in patients with grade 1, 2, and 3 HBP, respectively]. In HBP patients with grade 3, the OR of AF was much higher in women than in men (OR = 7.15, 95% CI: 4.43–11.50 vs. OR = 2.48, 95% CI: 1.66–3.72). BP over 133.1/79.9 mmHg in men or 127.1/75.1 mmHg in women was positively associated with AF. In patients with HBP, uncontrolled BP was more associated with AF (OR = 3.00, 95% CI: 2.53–3.56), especially in women (OR = 3.09, 95% CI: 2.27–4.19). BP and prevalence of AF correlated with each other positively in patients admitted to a cardiology ward. Lowering BP to 145.1/85.8 mmHg in men or 140.5/82.5 mmHg in women led to less AF.ConclusionThere is more significant relationship between HBP and AF in female patients. A lower and individualized BP target may be formulated to prevent AF in women.</p