INFORMATIONAL INDEX AND ITS APPLICATIONS IN HIGH DIMENSIONAL DATA

We introduce a new class of measures for testing independence between two random vectors, which uses expected difference of conditional and marginal characteristic functions. By choosing a particular weight function in the class, we propose a new index for measuring independence and study its property. Two empirical versions are developed, their properties, asymptotics, connection with existing measures and applications are discussed. Implementation and Monte Carlo results are also presented. We propose a two-stage sufficient variable selections method based on the new index to deal with large p small n data. The method does not require model specification and especially focuses on categorical response. Our approach always improves other typical screening approaches which only use marginal relation. Numerical studies are provided to demonstrate the advantages of the method. We introduce a novel approach to sufficient dimension reduction problems using the new measure. The proposed method requires very mild conditions on the predictors, estimates the central subspace effectively and is especially useful when response is categorical. It keeps the model-free advantage without estimating link function. Under regularity conditions, root-n consistency and asymptotic normality are established. The proposed method is very competitive and robust comparing to existing dimension reduction methods through simulations results

High-dimensional Variable Screening via Conditional Martingale Difference Divergence

Variable screening has been a useful research area that deals with ultrahigh-dimensional data. When there exist both marginally and jointly dependent predictors to the response, existing methods such as conditional screening or iterative screening often suffer from instability against the selection of the conditional set or the computational burden, respectively. In this article, we propose a new independence measure, named conditional martingale difference divergence (CMDH), that can be treated as either a conditional or a marginal independence measure. Under regularity conditions, we show that the sure screening property of CMDH holds for both marginally and jointly active variables. Based on this measure, we propose a kernel-based model-free variable screening method, which is efficient, flexible, and stable against high correlation among predictors and heterogeneity of the response. In addition, we provide a data-driven method to select the conditional set. In simulations and real data applications, we demonstrate the superior performance of the proposed method

Dimension reduction with expectation of conditional difference measure

In this article, we introduce a flexible model-free approach to sufficient dimension reduction analysis using the expectation of conditional difference measure. Without any strict conditions, such as linearity condition or constant covariance condition, the method estimates the central subspace exhaustively and efficiently under linear or nonlinear relationships between response and predictors. The method is especially meaningful when the response is categorical. We also studied the $\sqrt {n}$ -consistency and asymptotic normality of the estimate. The efficacy of our method is demonstrated through both simulations and a real data analysis

Dietary Counseling Aimed at Reducing Sugar Intake Yields the Greatest Improvement in Management of Weight and Metabolic Dysfunction in Children with Obesity

Pediatric obesity is a significant public health problem, the negative outcomes of which will challenge individual well-being and societal resources for decades to come. The objective of this study was to determine the effects of dietary counseling on weight management and metabolic abnormalities in children with obesity. One hundred and sixty-five patients aged 2–18 years old were studied over a two and a half year period. Data collected included demographic information, anthropometric assessment, laboratory measurements, and self-reported eating behaviors. Dietary counseling was provided at each visit. The data was analyzed from the first and last visits and the subjects were retrospectively divided into responders and non-responders based on a decrease in their BMI. After receiving dietary guidance, BMI decreased in 44% of the children, and these participants were classified as responders (BMI-R; n = 72). However, BMI did not improve in 56% of the participants, and these were classified as non-responders (BMI-NR; n = 93). At the initial visit, anthropometric measurements and dietary habits were similar between the groups. At the time of the last visit, mean change in BMI was −1.47 (SD 1.31) for BMI-R and +2.40 (SD 9.79) for BMI-NR. Analysis of food intake revealed that BMI-R significantly improved their dietary habits (p = 0.002) by reducing the intake of sugar-sweetened beverages (p = 0.019), processed foods (p = 0.002), sweets (p p = 0.009), as compared with BMI-NR. There was no change in the intake of second helpings, portion sizes, skipping meals, frequency of meals eaten at school, condiment use, intake of fruits and vegetables and consumption of whole grains between the groups. BMI-R also achieved an improvement in fasted glucose (p = 0.021), triglycerides (p p = 0.023), as compared to BMI-NR. In conclusion, children with obesity who were able to decrease their BMI implemented a significant reduction in consumption of foods with high sugar content. Focusing on reducing sugar intake may yield the biggest impact in terms of weight management and the improvement of metabolic abnormalities