Background Tourette syndrome (TS) is a childhood-onset neuropsychiatric disorder that is characterized by both motor and phonic tics. One half to two thirds of children with TS experience a reduction or complete resolution of tic symptoms during adolescence. At least one third of adults with TS have comorbid obsessive-compulsive disorder (OCD). Objectives To clarify the clinical course of tic and OCD symptoms in children with TS and determine if baseline clinical measurements in childhood are associated with future symptom severity in late adolescence and early adulthood. Design Prospective cohort study. Setting Yale Child Study Center tic and OCD outpatient specialty clinic. Participants Forty-six children with TS who received a structured clinical evaluation prior to age 14 years. Main Outcome Measures Expert-rated tic and OCD symptom severity at follow-up interview an average of 7.6 years later (range, 3.8-12.8 years). Results Eighty-five percent of subjects reported a reduction in tic symptoms during adolescence. Only increased tic severity in childhood was associated with increased tic severity at follow-up. The average age at worst-ever tic severity was 10.6 years. Forty-one percent of patients with TS reported at one time experiencing at least moderate OCD symptoms. Worst-ever OCD symptoms occurred approximately 2 years later than worst-ever tic symptoms. Increased childhood IQ was strongly associated with increased OCD severity at follow-up. Conclusion Obsessive-compulsive disorder symptoms in children with TS became more severe at a later age and were more likely to persist than tic symptoms.

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this article, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness in a way that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are -consistent and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower noncausal selection rate. Furthermore, we reanalyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.

Significance: Best-subset selection is a benchmark optimization problem in statistics and machine learning. Although many optimization strategies and algorithms have been proposed to solve this problem, our splicing algorithm, under reasonable conditions, enjoys the following properties simultaneously with high probability: 1) its computational complexity is polynomial; 2) it can recover the true subset; and 3) its solution is globally optimal.

Precise classification of tumors is critically important for cancer diagnosis and treatment. It is also a scientifically challenging task. Recently, efforts have been made to use gene expression profiles to improve the precision of classification, with limited success. Using a published data set for purposes of comparison, we introduce a methodology based on classification trees and demonstrate that it is significantly more accurate for discriminating among distinct colon cancer tissues than other statistical approaches used heretofore. In addition, competing classification trees are displayed, which suggest that different genes may coregulate colon cancers.