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Sharpening Jensen’s inequality. (English) Zbl 07588155


MSC:

62-XX Statistics

References:

[1] Abramovich, S.; Persson, L.-E., “Some New Estimates of the Jensen Gap,, Journal of Inequalities and Applications, 2016, 39 (2016) · Zbl 1336.26019
[2] Abramovich, S.; Persson, L.-E.; Samko, N., “Some New Scales of Refined Jensen And Hardy Type Inequalities,, Mathematical Inequalities & Applications, 17, 1105-1114 (2014) · Zbl 1297.26039
[3] Becker, R. A., “The Variance Drain and Jensen”s Inequality,, Technical Report, CAEPR Working Paper No. 2012-004 (2012)
[4] Bennish, J., “A Proof of Jensen”s Inequality,, Missouri Journal of Mathematical Sciences, 15 (2003) · Zbl 1032.26013
[5] Casella, G.; Berger, R. L., Statistical Inference, 2 (2002), Pacific Grove: Pacific Grove, CA: Duxbury
[6] De Carvalho, M., “Mean, What Do You Mean?, The American Statistician, 70, 270-274 (2016) · Zbl 07665884
[7] Dempster, A. P.; Laird, N. M.; Rubin, D. B., “Maximum Likelihood from Incomplete Data via the EM Algorithm,, Journal of the Royal Statistical Society, Series B, 1-38 (1977) · Zbl 0364.62022
[8] Dragomir, S., “Jensen Integral Inequality for Power Series with Nonnegative Coefficients and Applications,, RGMIA Res. Rep. Collect, 17, 42 (2014)
[9] Horvath, L.; Khan, K. A.; Pecaric, J., “Refinement of Jensen”s Inequality for Operator Convex Functions,, Advances in inequalities and applications (2014)
[10] Jensen, J. L. W. V., “Sur les Fonctions Convexes et les Inégalités entre les Valeurs Moyennes,, Acta Mathematica, 30, 175-193 (1906) · JFM 37.0422.02
[11] Walker, S. G., “On a Lower Bound for the Jensen Inequality,, SIAM Journal on Mathematical Analysis, 46, 3151-3157 (2014) · Zbl 1312.26026
[12] Wasserman, L., All of Statistics: A Concise Course in Statistical Inference (2013), Springer Science & Business Media
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