Limiting behaviour of moving average processes under ρ\rho-mixing assumption

Let \{Y_i, -\infty<i<\infty\} be a doubly infinite sequence of identically distributed $\rho$-mixing random variables, \{a_i,-\infty<i< \infty\} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes $\{\sum\limits^\infty_{i=-\infty}a_i Y_{i+n},n\geq1\}$

The Sex-Specific Detrimental Effect of Diabetes and Gender-Related Factors on Pre-admission Medication Adherence Among Patients Hospitalized for Ischemic Heart Disease: Insights From EVA Study

Background: Sex and gender-related factors have been under-investigated as relevant determinants of health outcomes across non-communicable chronic diseases. Poor medication adherence results in adverse clinical outcomes and sex differences have been reported among patients at high cardiovascular risk, such as diabetics. The effect of diabetes and gender-related factors on medication adherence among women and men at high risk for ischemic heart disease (IHD) has not yet been fully investigated.Aim: To explore the role of sex, gender-related factors, and diabetes in pre-admission medication adherence among patients hospitalized for IHD.Materials and Methods: Data were obtained from the Endocrine Vascular disease Approach (EVA) (ClinicalTrials.gov Identifier: NCT02737982), a prospective cohort of patients admitted for IHD. We selected patients with baseline information regarding the presence of diabetes, cardiovascular risk factors, and gender-related variables (i.e., gender identity, gender role, gender relations, institutionalized gender). Our primary outcome was the proportion of pre-admission medication adherence defined through a self-reported questionnaire. We performed a sex-stratified analysis of clinical and gender-related factors associated with pre-admission medication adherence.Results: Two-hundred eighty patients admitted for IHD (35% women, mean age 70), were included. Around one-fourth of the patients were low-adherent to therapy before hospitalization, regardless of sex. Low-adherent patients were more likely diabetic (40%) and employed (40%). Sex-stratified analysis showed that low-adherent men were more likely to be employed (58 vs. 33%) and not primary earners (73 vs. 54%), with more masculine traits of personality, as compared with medium-high adherent men. Interestingly, women reporting medication low-adherence were similar for clinical and gender-related factors to those with medium-high adherence, except for diabetes (42 vs. 20%, p = 0.004). In a multivariate adjusted model only employed status was associated with poor medication adherence (OR 0.55, 95%CI 0.31–0.97). However, in the sex-stratified analysis, diabetes was independently associated with medication adherence only in women (OR 0.36; 95%CI 0.13–0.96), whereas a higher masculine BSRI was the only factor associated with medication adherence in men (OR 0.59, 95%CI 0.35–0.99).Conclusion: Pre-admission medication adherence is common in patients hospitalized for IHD, regardless of sex. However, patient-related factors such as diabetes, employment, and personality traits are associated with adherence in a sex-specific manner

On weighted densities

summary:The continuity of densities given by the weight functions $n^{\alpha }$, $\alpha \in [-1,\infty [$, with respect to the parameter $\alpha$ is investigated

On the concentration phenomenon for [phi]-subgaussian random elements

We study the deviation probability P{[short parallel]X[short parallel]-E[short parallel]X[short parallel]>t} where X is a [phi]-subgaussian random element taking values in the Hilbert space l2 and [phi](x) is an N-function. It is shown that the order of this deviation is exp{-[phi]*(Ct)}, where C depends on the sum of [phi]-subgaussian standard of the coordinates of the random element X and [phi]*(x) is the Young-Fenchel transform of [phi](x). An application to the classically subgaussian random variables ([phi](x)=x2/2) is given.Concentration of measure phenomenon [phi]-Subgaussian random variables N-function Young-Fenchel transform Exponential inequalities