Some properties of canonical correlations and variates in infinite dimensions

AbstractIn this paper the notion of functional canonical correlation as a maximum of correlations of linear functionals is explored. It is shown that the population functional canonical correlation is in general well defined, but that it is a supremum rather than a maximum, so that a pair of canonical variates may not exist in the spaces considered. Also the relation with the maximum eigenvalue of an associated pair of operators and the corresponding eigenvectors is not in general valid. When the inverses of the operators involved are regularized, however, all of the above properties are restored. Relations between the actual population quantities and their regularized versions are also established. The sample functional canonical correlations can be regularized in a similar way, and consistency is shown at a fixed level of the regularization parameter

“Don’t Be Stupid, Stupid!” Cognitive-Behavioral Techniques to Reduce Irrational Beliefs and Enhance Focus in a Youth Tennis Player

This case reports the intervention approach the first author adopted while working with a youth tennis player. The athlete held irrational beliefs and was struggling to maintain emotional control. The neophyte sport psychology practitioner adopted a cognitive-behavioral approach to practice. The intervention focused on (a) using rational emotive behavior therapy (REBT) to replace unhelpful beliefs about unforced errors with a new rational philosophy and (b) using a distraction-control plan to restructure the player’s thoughts and beliefs in relation to opponents’ perceived gamesmanship. Intervention effectiveness was evaluated through qualitative data from the athlete and his parents and the reflections of the practitioner. Feedback suggests that REBT and distraction-control plans can be effective in helping youth athletes manage their thought patterns and improve emotional control during competition. This case also demonstrates the importance of practitioners’ having a flexible and adaptable approach to practice—one that meets individual client needs

Thinking Aloud: Stress and Coping in Junior Cricket Batsmen during Challenge and Threat States

The present study examined stress and coping of cricket batsmen during challenge and threat states using the Think-Aloud method. Ten male elite-level junior cricket batsmen took part in the study. A repeated measures design was implemented, with participants verbalizing while both in (a) a threat state and (b) a challenge state. Participants were required to score 36 runs in 30 balls during the threat and challenge conditions. Verbalizations were subsequently transcribed verbatim and analyzed for stressors, coping strategies, and any other reoccurring themes. A paired-samples t-test was conducted to examine differences in the number of verbalizations made for each theme between conditions. Ten secondary themes were grouped into four primary themes; these included (a) stressors, (b) problem-focused coping, (c) emotion-focused coping, and (d) gathering information. There were significant differences( p≤0.05) between stressor verbalizations, with significantly more verbalizations made by participants during a threat state. No significant differences were found between any other themes. Thus, during a threat state, participants reported significantly more stressor verbalizations compared to a challenge state, while there were no significant differences in coping strategies reported (p>0.05). This finding offers a potential explanation for why athletic performance diminishes when in a threat state, as athletes then experience a greater number of stressors but do not report engaging in more coping strategies

Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction

We consider the problem of bandwidth selection by cross-validation from a sequential point of view in a nonparametric regression model. Having in mind that in applications one often aims at estimation, prediction and change detection simultaneously, we investigate that approach for sequential kernel smoothers in order to base these tasks on a single statistic. We provide uniform weak laws of large numbers and weak consistency results for the cross-validated bandwidth. Extensions to weakly dependent error terms are discussed as well. The errors may be {\alpha}-mixing or L2-near epoch dependent, which guarantees that the uniform convergence of the cross validation sum and the consistency of the cross-validated bandwidth hold true for a large class of time series. The method is illustrated by analyzing photovoltaic data.Comment: 26 page

Thinking Aloud: Stress and coping in junior cricket batsman during challenge and threat states

The present study examined stress and coping of cricket batsmen during challenge and threat states using the Think-Aloud method. Ten male elite-level junior cricket batsmen took part in the study. A repeated measures design was implemented, with participants verbalizing while both in (a) a threat state and (b) a challenge state. Participants were required to score 36 runs in 30 balls during the threat condition and 15 runs in 30 balls during the challenge condition. Verbalizations were subsequently transcribed verbatim and analyzed for stressors, coping strategies, and any other reoccurring themes. A paired-samples t-test was conducted to examine differences in the number of verbalizations made for each theme between conditions. Ten secondary themes were grouped into four primary themes; these included (a) stressors, (b) problem-focused coping, (c) emotion-focused coping, and (d) gathering information. There were significant differences( p≤0.05) between stressor verbalizations, with significantly more verbalizations made by participants during a threat state. No significant differences were found between any other themes. Thus, during a threat state, participants reported significantly more stressor verbalizations compared to a challenge state, while there were no significant differences in coping strategies reported (p>0.05). This finding offers a potential explanation for why athletic performance diminishes when in a threat state, as athletes then experience a greater number of stressors but do not report engaging in more coping strategies

Sport psychology consulting in professional rugby union in the United Kingdom

This article describes my experiences of working within professional rugby union in South Wales, United Kingdom. Initially, I locate the context of professional rugby union in the country alongside how my various subcultural understandings of the sport were obtained. After outlining my consulting philosophy developed for working in a professional rugby union context, subsequent cultural challenges for practitioners working in the sport are then explored, together with example strategies used to account for such cultural considerations. I conclude by reflecting upon the importance of practitioners possessing and developing contextual intelligence and cultural competency to work effectively in high performance environments