On Stein's Identity and Near-Optimal Estimation in High-dimensional Index Models

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine learning and statistics. Our estimators leverage the score function based first and second-order Stein's identities and do not require the covariates to satisfy Gaussian or elliptical symmetry assumptions common in the literature. Moreover, to handle score functions and responses that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. We show that our estimator achieves near-optimal statistical rate of convergence in several settings. We supplement our theoretical results via simulation experiments that confirm the theory

Association between Personality Traits and Sleep Quality in Young Korean Women

<div><p>Personality is a trait that affects behavior and lifestyle, and sleep quality is an important component of a healthy life. We analyzed the association between personality traits and sleep quality in a cross-section of 1,406 young women (from 18 to 40 years of age) who were not reporting clinically meaningful depression symptoms. Surveys were carried out from December 2011 to February 2012, using the Revised NEO Personality Inventory and the Pittsburgh Sleep Quality Index (PSQI). All analyses were adjusted for demographic and behavioral variables. We considered beta weights, structure coefficients, unique effects, and common effects when evaluating the importance of sleep quality predictors in multiple linear regression models. Neuroticism was the most important contributor to PSQI global scores in the multiple regression models. By contrast, despite being strongly correlated with sleep quality, conscientiousness had a near-zero beta weight in linear regression models, because most variance was shared with other personality traits. However, conscientiousness was the most noteworthy predictor of poor sleep quality status (PSQI≥6) in logistic regression models and individuals high in conscientiousness were least likely to have poor sleep quality, which is consistent with an OR of 0.813, with conscientiousness being protective against poor sleep quality. Personality may be a factor in poor sleep quality and should be considered in sleep interventions targeting young women.</p></div

Hazard ratios^a (95% CI) of incident diabetes according to relative muscle mass category in clinically relevant subgroups.

<p>Hazard ratios<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0188650#t004fn002" target="_blank">^a</a> (95% CI) of incident diabetes according to relative muscle mass category in clinically relevant subgroups.</p

Discriminant function analysis (DFA) by the stepwise method for the separation between good sleepers and poor sleepers.

<p>N = 1,406</p><p>Discriminant function analysis (DFA) by the stepwise method for the separation between good sleepers and poor sleepers.</p

Logistic regression models predicting poor sleep quality based on personality characteristics.

<p>N = 1,406</p><p><i>Note</i>. CI: Wald Confidence Interval</p><p>^a Odds Ratios (ORs) per 10 <i>T</i>-score increase in a given personality trait, controlling for age, marital status, working status, education, caffeine intake, alcohol use, smoking status, and physical activity.</p><p>^b Model I: logistic regression model including a single domain or facet of personality as an independent variable.</p><p>^c Model II: multiple logistic regression model including all five domains of personality as independent variables. At a facet level, six facets of each domain were included in the model.</p><p>^d Logistic regression analyses of the facet level were performed in neuroticism and conscientiousness.</p><p>*<i>p</i><.05</p><p>**<i>p</i><.01</p><p>***<i>p</i><.001</p><p>Logistic regression models predicting poor sleep quality based on personality characteristics.</p

Linear regression analysis investigating the association between personality traits and sleep quality, as measured by PSQI global score.

<p>N = 1,406</p><p><i>Note</i>. All models were adjusted for age, marital status, smoking, and working status.</p><p>^a Model I: linear regression model including a single domain of personality as an independent variable (R2 = 0.043, 0.023, 0.020, 0.026, and 0.027; adjusted R² = 0.040, 0.020, 0.016, 0.022, and 0.023, <i>F</i> = 12.67, 6.70, 5.61, 7.45, and 7.68; <i>P</i><.001, <i><</i>.001, <0.001, <i><</i>.001, and <0.001 in N, E, O, A, and C, respectively).</p><p>^b Model II: multiple linear regression model including all five domains of personality as independent variables (R² = 0.0524, adjusted R² = 0.041, <i>F</i> = 4.80, <i>P</i><.001).</p><p>^c β: standardized coefficient in linear regression analyses.</p><p>^d Unique = proportion of criterion variance explained uniquely by the predictor.</p><p>^e Common = proportion of criterion variance explained by the predictor that is also explained by one or more other predictors. Unique + Common = <i>r</i>², <i>r</i> = zero-order correlation coefficient</p><p>*<i>p</i> <.05</p><p>**<i>p</i> <.01</p><p>***<i>p</i><.001</p><p>Linear regression analysis investigating the association between personality traits and sleep quality, as measured by PSQI global score.</p

Descriptive statistics for study participants.

<p><i>Note</i>. PSQI: Pittsburgh Sleep Quality Index; SD: Standard Deviation</p><p>^a Quantitative variable. Mean (standard deviation) and p-value from t-test are shown.</p><p>^b Nominal scale. Frequency (percentage) and p-value from χ² test are shown.</p><p>Descriptive statistics for study participants.</p

Baseline characteristics: Relative muscle mass of male participants.

<p>Baseline characteristics: Relative muscle mass of male participants.</p

Correlation coefficients for sleep quality, covariates, and personality traits.

<p>N = 1,406</p><p>^a Pearson’s correlation coefficients</p><p>^b Spearman correlation coefficients</p><p>*<i>p</i><.05</p><p>**<i>p</i><.01</p><p>***<i>p</i><.001</p><p>Correlation coefficients for sleep quality, covariates, and personality traits.</p

Development of type 2 diabetes by relative muscle mass.

<p>Development of type 2 diabetes by relative muscle mass.</p