Non-Asymptotic Bounds

Abstract

Most asymptotic errors in statistical inference are based on error estimates when the sample size n and the dimension p of observations are large. More precisely, such statistical statements are evaluated when n and/or p tend to infinity. On the other hand, “non-asymptotic” results are derived under the condition that n, p, and the parameters involved are fixed. In this chapter, we explain non-asymptotic error bounds, while giving the Edgeworth expansion, Berry–Essen bounds, and high-dimensional approximations for the linear discriminant function.