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Walker’s self-improvement inequality revisited

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  • Lupu, Cezar
  • Tanase, Roxana

Abstract

In this paper, we revisit a self-improvement inequality of the celebrated Cauchy–Schwarz’s inequality given by Walker (2017). In fact, we show that his inequality follows from the classical variance–covariance inequality. Moreover, we generalize his result by using a more general version of the variance–covariance inequality. In the supplementary material, we provide some applications by revisiting the standard normal and the Cramer–Rao inequality and by deriving a lower bound on the mean squared error in the case of biased estimators.

Suggested Citation

  • Lupu, Cezar & Tanase, Roxana, 2026. "Walker’s self-improvement inequality revisited," Statistics & Probability Letters, Elsevier, vol. 234(C).
    • Handle: RePEc:eee:stapro:v:234:y:2026:i:c:s0167715226000593
    DOI: 10.1016/j.spl.2026.110695
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