Asheber Abebe

Associations Between Timing in the Baseball Pitch and Shoulder Kinetics, Elbow Kinetics, and Ball Speed

Background: A baseball pitcher’s ability to maximize ball speed while avoiding shoulder and elbow injuries is an important determinant of a successful career. Pitching injuries are attributed to microtrauma brought about by the repetitive stress of high-magnitude shoulder and elbow kinetics. Hypothesis: Over a number of pitches, variations in timing peak angular velocities of trunk segment rotations will be significantly associated with ball speed and upper extremity kinetic parameters. Study Design: Descriptive laboratory study. Methods: Kinematic and kinetic data were derived from 9 to 15 fastball pitches performed by 16 active, healthy collegiate (n = 8) and professional (n = 8) pitchers via 3-dimensional motion capture (240 Hz). Each pitch was decomposed into 4 phases corresponding to the time between peak angular velocities of sequential body segment rotations. Four mixed models were used to evaluate which phases varied significantly in relation to ball speed, peak shoulder proximal force, peak shoulder internal rotation torque, and peak elbow varus torque. Mixed-model parameter coefficient estimates were used to quantify the influence of these variations in timing on ball speed and upper extremity kinetics. Results: All 4 mixed models were significant (P < .05). The time from stride-foot contact to peak pelvis angular velocity varied significantly in relation to all upper extremity kinetic parameters and ball speed. Increased time in this phase correlated with decreases in all parameters. Decreased ball speed also correlated with increased time between peak upper torso and elbow extension angular velocities. Decreased shoulder proximal force also correlated with increased time between peak pelvis and upper torso angular velocities. Conclusion: There are specific phases that vary in relation to ball speed and upper extremity kinetic parameters, reinforcing the importance of effectively and consistently timing segmental interactions. For the specific interactions that varied significantly, increased phase times were associated with decreased kinetics and ball speed. Clinical Relevance: Although increased time within specific phases correlates with decreases in the magnitude of upper extremity kinetics linked to overuse injuries, it also correlates with decreased ball speed. Based on these findings, it may appear that minimizing the risk of injury (ie, decreased kinetics) and maximizing performance quality (ie, increased ball speed) are incompatible with one another. However, there may be an optimal balance in timing that is effective for satisfying both outcomes.

Rank estimation of regression coefficients using iterated reweighted least squares

This paper is concerned with the rank estimator for the parameter vector β in a linear model which is obtained by the minimization of a rank dispersion function. The rank estimator has many advantages over the regular least squares estimator, but the inaccessibility of software to carry out its computation has limited its use. An iterated reweighted least squares algorithm is presented for the computation of the rank estimator. The method is simple in concept and can be carried out readily with a wide variety of statistical software. Details of the method are discussed along with some results on its asymptotic distribution and numerical stability. Some examples are presented to show advantages of the rank method.

A Note on Multiplication and Composition Operators in Lorentz Spaces

we revisit the Lorentz spaces 𝐿(𝑝,𝑞) for 𝑝>1,𝑞>0 defined by G. G. Lorentz in the nineteen fifties and we show how the atomic decomposition of the spaces 𝐿(𝑝,1) obtained by De Souza in 2010 can be used to characterize the multiplication and composition operators on these spaces. These characterizations, though obtained from a completely different perspective, confirm the various results obtained by S. C. Arora, G. Datt and S. Verma in different variants of the Lorentz Spaces.

Classification Based on Depth Transvariations

Suppose y, a d-dimensional (d ≥ 1) vector, is drawn from a mixture of k (k ≥ 2) populations, given by ∏1, ∏2,…,∏k. We wish to identify the population that is the most likely source of the point y. To solve this classification problem many classification rules have been proposed in the literature. In this study, a new nonparametric classifier based on the transvariation probabilities of data depth is proposed. We compare the performance of the newly proposed nonparametric classifier with classical and maximum depth classifiers using some benchmark and simulated data sets.

Semi-parametric rank regression with missing responses

We consider a semi-parametric regression model with responses missing at random and study the rank estimator of the regression coefficient. Consistency and asymptotic normality of the proposed estimator are established. Monte Carlo simulation experiments show that the proposed estimator is more efficient than the least squares estimator whenever the error distribution is heavy tailed or contaminated. When the errors follow a normal distribution, these simulation experiments show that the rank estimator can be more efficient than its least squares counterpart for cases with large proportion of missing responses.

A nonparametric allocation scheme for classification based on transvariation probabilities

In this paper, a nonparametric discriminant analysis procedure that is less sensitive than traditional procedures to deviations from the usual assumptions is proposed. The procedure uses the projection pursuit methodology where the projection index is the two-group transvariation probability. Montanari [A. Montanari, Linear discriminant analysis and transvariation, J. Classification 21 (2004), pp. 71–88] proposed and used this projection index to measure group separation but allocated the new observation using distances. Our procedure employs a method of allocation based on group–group transvariation probability to classify the new observation. A simulation study shows that the procedure proposed in this paper provides lower misclassification error rates than classical procedures like linear discriminant analysis and quadratic discriminant analysis and recent procedures like maximum depth and Montanaris transvariation-based classifiers, when the underlying distributions are skewed and/or the prior probabilities are unequal.

Iterated reweighted rank-based estimates for GEE models

Repeated measurement designs occur in many areas of statistical research. In 1986, Liang and Zeger offered an elegant analysis of these problems based on a set of generalized estimating equations (GEEs) for regression parameters, that specify only the relationship between the marginal mean of the response variable and covariates. Their solution is based on iterated reweighted least squares fitting. In this paper, we propose a rank-based fitting procedure that only involves substituting a norm based on a score function for the Euclidean norm used by Liang and Zeger. Our subsequent fitting, while also an iterated reweighted least squares solution to GEEs, is robust to outliers in response space and the weights can easily be adapted for robustness in factor space. As with the fitting of Liang and Zeger, our rank-based fitting utilizes a working covariance matrix. We prove that our estimators of the regression coefficients are asymptotically normal. The results of a simulation study show that the our proposed estimators are empirically efficient and valid. We illustrate our analysis on a real data set drawn from a hierarchical (three-way nested) design.

Characterization of lacunary functions in weighted Bergman–Besov–Lipschitz spaces

We consider the weighted Bergman–Besov–Lipschitz space B ρ of analytic functions F in the unit disc 𝔻 = {z ∈ ℂ, |z| ≤ 1} for which and we show that a lacunary function belongs to B ρ if and only if the sequence a n satisfies , where I n are diadic intervals defined by I n  = {k ∈ ℕ : 2 n−1 ≤ k < 2 n }, ρ belongs to a certain class of weights and K(n, ρ) > 0 is a function of n and ρ.

Robust Signed-Rank Variable Selection in Linear Regression

The growing need for dealing with big data has made it necessary to find computationally efficient methods for identifying important factors to be considered in statistical modeling. In the linear model, the Lasso is an effective way of selecting variables using penalized regression. It has spawned substantial research in the area of variable selection for models that depend on a linear combination of predictors. However, work addressing the lack of optimality of variable selection when the model errors are not Gaussian and/or when the data contain gross outliers is scarce. We propose the weighted signed-rank Lasso as a robust and efficient alternative to least absolute deviations and least squares Lasso. The approach is appealing for use with big data since one can use data augmentation to perform the estimation as a single weighted L1 optimization problem. Selection and estimation consistency are theoretically established and evaluated via simulation studies. The results confirm the optimality of the rank-based approach for data with heavy-tailed and contaminated errors or data containing high-leverage points.

Testing the reproductive and somatic trade‐off in female Columbian ground squirrels

Abstract Energetic trade‐offs in resource allocation form the basis of life‐history theory, which predicts that reproductive allocation in a given season should negatively affect future reproduction or individual survival. We examined how allocation of resources differed between successful and unsuccessful breeding female Columbian ground squirrels to discern any effects of resource allocation on reproductive and somatic efforts. We compared the survival rates, subsequent reprodction, and mass gain of successful breeders (females that successfully weaned young) and unsuccessful breeders (females that failed to give birth or wean young) and investigated “carryover” effects to the next year. Starting capital was an important factor influencing whether successful reproduction was initiated or not, as females with the lowest spring emergence masses did not give birth to a litter in that year. Females that were successful and unsuccessful at breeding in one year, however, were equally likely to be successful breeders in the next year and at very similar litter sizes. Although successful and unsuccessful breeding females showed no difference in over winter survival, females that failed to wean a litter gained additional mass during the season when they failed. The next year, those females had increased energy “capital” in the spring, leading to larger litter sizes. Columbian ground squirrels appear to act as income breeders that also rely on stored capital to increase their propensity for future reproduction. Failed breeders in one year “prepare” for future reproduction by accumulating additional mass, which is “carried over” to the subsequent reproductive season.