In the June/July 2013 issue of the Institute of Mathematical Statistics (IMS) Bulletin, Contributing Editor Anirban DasGupta (Department of Statistics, Purdue University) contributed an installment of his column, Anirban's Angle, entitled Top Inequalities for a PhD Student.
- Cauchy-Schwarz
- Jensen
- Hölder and triangular
- Fatou
- Bessel
- Hausdorff-Young
- Basic Sobolev inequality in three dimensions only
- Frobenius
SylvestreSylvester's rank inequality- Determinant bounds, e.g. Hadamard
- Kantorovich
- Courant-Fischer
- Boole's inequality, from both directions
- Chebyshev and Markov
- Bernstein
- Hoeffding in the Rademacher case, 1963
- Bounds on Mills ratio from both directions
- Upper tail of Binomial and Poisson
- Slepian's lemma, 1962
- Anderson's inequality on probabilities of symmetric convex sets, 1955
- Rosenthal, 1970
- Kolmogorov's basic maximal inequality
- Basic Barry-Esseen in one dimension
- Le Cam's bound on Poisson approximations (Le Cam, 1960)
- DKW with a mention of Massart's constant (Massart, 1990)
- Bounds on expectation of normal maximum from both directions
- Comparison lemma on multinormal CDFs (Leadbetter, Lindgren, and Rootzén, 1983)
- Talagrand (as in 1995, Springer)
- Inequality between Hellinger and Kullback-Leibler distance
- Cramér-Rao
- Rao-Blackwell (which is an inequality)
- Wald's SPRT (Sequential Probability Ratio Test) inequalities