Titlebook: Normal Approximation by Stein’s Method; Louis H.Y. Chen,Larry Goldstein,Qi-Man Shao Textbook 2011 Springer-Verlag GmbH Berlin Heidelberg 2

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陳腐思想

Kaleidoscope

Jubilation

Non-normal Approximation,statistical physics, at the critical inverse temperature, by a distribution with density proportional to exp?(?../12). Bounds for approximation by the exponential distribution are also derived, and applied to the spectrum of the Bernoulli Laplace Markov chain, and first passage times for Markov chains.

heirloom

來自于

,Berry–Esseen Bounds for Independent Random Variables,st by concentration inequalities, then by induction. This chapter concludes with a lower bound for the Berry–Esseen inequality. As seen in the chapter dependency diagram that follows, Chaps. 2 and 3 form much of the basis of this book.

Armory

,, by Bounded Couplings,n . and ., a small bound being a reflection of a small distance. The chapter concludes with the use of smoothing inequalities to obtain distances between . and the normal over general function classes, one special case being the derivation of Kolmogorov distance bounds when bounded size bias couplings exist.

音樂等

情感脆弱

,, Bounds,and applied to the approximation of the distribution of the volume covered by randomly placed spheres in the Euclidean torus. Results are then given for sums of locally dependent random variables, with applications including the number of local maxima on a graph. The chapter concludes with a conside

Thyroid-Gland