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Last Updated: 07 March 2022

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On rates of convergence for sample average approximations in the almost sure sense and in mean

In the almost certain sense and as mean, we investigate the rates at which optimal estimators in the sample average approximation approach converge to their deterministic counterparts. We investigate the validity of these figures in a Banach space setting and first establish under fairly realistic assumptions that the approximating objective functions' convergence rates are expected to be transferred to the estimators for accurate measurements and solutions of the estimated problem, in order to determine these rates. In turn, this helps to measure optimal estimators' asymptotic bias as well as other conclusions on their mean squared error and estimations for the optimality gap. Without setting strict constraints on exponential times, we'll refer to the assumption of convergence in probability to derive probabilities in probability for the deviation of optimal estimators and error probabilities without imposing heavy constraints on exponential times.

Source link: https://doi.org/10.1007/s10107-019-01400-4


Measures of Opportunity to Learn Mathematics in PISA and TIMSS, Can We Be Sure that They Measure What They Are Supposed to Measure?

Both surveys found that assessments of content validity are based on the correlation between the OTL measurements and the frameworks that influenced the creation of the mathematics experiments. The content validity of the OTL report in TIMSS appears to be increasing, although the PISA survey shows a much greater connection with mathematics achievement.

Source link: https://doi.org/10.1007/978-3-030-38298-8_12-1

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions