Statistical Inequalities

Overview


Many theoretical results in statistics and machine learning use statistical inequalities to place bounds on a given process or measure. The following is a list of some of the inequalities commonly used.

Inequalities


  • Tchebychev's Inequality
    {% P(|X-m_X| \geq \epsilon) \leq \frac{\sigma_X^2}{\epsilon^2} %}
  • Markov's Inequality
    {% P(X \geq \alpha) \leq \frac{\mathbb{E}[X]}{\alpha} %}
    given that {% X \geq 0 %} and {% \alpha \geq 0 %}
  • Jensen's Inequality
    {% \mathbb{E}[f(X)] \geq f(\mathbb{E}[X]) %}
    for a convex function {% f(x) %}.

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