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Full-Text Articles in Statistics and Probability
An Omnibus Nonparametric Test Of Equality In Distribution For Unknown Functions, Alexander Luedtke, Marco Carone, Mark Van Der Laan
An Omnibus Nonparametric Test Of Equality In Distribution For Unknown Functions, Alexander Luedtke, Marco Carone, Mark Van Der Laan
Alex Luedtke
We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], using recent developments from the higher-order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed rather simply as U-statistics. We study the asymptotic behavior of the proposed tests under the null hypothesis and under both fixed and local alternatives. We provide examples to which our tests …
Computerizing Efficient Estimation Of A Pathwise Differentiable Target Parameter, Mark J. Van Der Laan, Marco Carone, Alexander R. Luedtke
Computerizing Efficient Estimation Of A Pathwise Differentiable Target Parameter, Mark J. Van Der Laan, Marco Carone, Alexander R. Luedtke
Alex Luedtke
Frangakis et al. (2015) proposed a numerical method for computing the efficient influence function of a parameter in a nonparametric model at a specified distribution and observation (provided such an influence function exists). Their approach is based on the assumption that the efficient influence function is given by the directional derivative of the target parameter mapping in the direction of a perturbation of the data distribution defined as the convex line from the data distribution to a pointmass at the observation. In our discussion paper Luedtke et al. (2015) we propose a regularization of this procedure and establish the validity …
Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee
Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee
Shannon O.S. Driskell
This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …
Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti
Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti
Shannon O.S. Driskell
This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.
Modern Spectral Climate Patterns In Rhythmically Deposited Argillites Of The Gowganda Formation (Early Proterozoic), Southern Ontario, Canada, Gary B. Hughes, Robert Giegengack, Haralambos N. Kritikos
Modern Spectral Climate Patterns In Rhythmically Deposited Argillites Of The Gowganda Formation (Early Proterozoic), Southern Ontario, Canada, Gary B. Hughes, Robert Giegengack, Haralambos N. Kritikos
Gary B. Hughes
Rhythmically deposited argillites of the Gowganda Formation (ca. 2.0–2.5 Ga) probably formed in a glacial setting. Drop stones and layered sedimentary couplets in the rock presumably indicate formation in a lacustrine environment with repeating freeze–thaw cycles. It is plausible that temporal variations in the thickness of sedimentary layers are related to interannual climatic variability, e.g. average seasonal temperature could have influenced melting and the amount of sediment source material carried to the lake. A sequence of layer couplet thickness measurements was made from high-resolution digitized photographs taken at an outcrop in southern Ontario, Canada. The frequency spectrum of thickness measurements …