882 research outputs found

    Some properties of canonical correlations and variates in infinite dimensions

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    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

    Optimal Grouping, Spacing, Stratification, and Piecewise Constant Approximation

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

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    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

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    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

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    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

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    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

    On the Computational Complexity of Measuring Global Stability of Banking Networks

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    Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic
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