Non-central limit theorems for random selections

Athreya K.: Bootstrap of the mean in the infinite variance case. Ann. Stat. 15, 724–731 (1987)

Aue A., Berkes I., Horváth L.: Selection from a stable box. Bernoulli 14, 125–139 (2008)

Berkes I., Philipp W.: Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7, 29–54 (1979)

Bergström, H.: The limit problem for sums of independent random variables which are not uniformly asymptotically negligible. Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes. Technical University of Prague, pp. 125–135. Academia, Prague (1971)

Bickel P., Freedman D.: Some asymptotic theory for the bootstrap. Ann. Stat. 9, 1196–1217 (1981)

Billingsley P.: Convergence of Probability Measures. Wiley, New York (1968)

Bingham N.H., Goldie C.M., Teugels J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)

Breiman L.: Probability. Addison-Wesley, Reading (1968)

Csörgő M., Csörgő S., Horváth L., Mason D.M.: Normal and stable convergence of integral functions of the empirical distribution function. Ann. Probab. 14, 86–118 (1986)

Csörgő S.: Rates of merge in generalized St. Petersburg games. Acta Sci. Math. (Szeged) 68, 815–847 (2002)

Feller W.: An Introduction to Probability Theory and its Applications, vol. 2. Wiley, New York (1966)

Gnedenko B.V., Kolmogorov A.N.: Limit Distributions of Sums of Independent Random Variables. Addison-Wesley, Reading (1968)

Hall P.: Asymptotic properties of the bootstrap for heavy-tailed distributions. Ann. Probab. 18, 1342–1360 (1990)

Le Cam L.: On the distribution of sums of independent random variables. In: Neyman, J., Le Cam, L. (eds) Bernoulli, Bayes, Laplace: Anniversary Volume, pp. 179–202. Springer, Heidelberg (1965)

Ledoux M., Talagrand M.: Probability in Banach Spaces. Springer, New York (1991)

LePage R., Woodroofe M., Zinn J.: Convergence to a stable distribution via order statistics. Ann. Probab. 9, 624–632 (1981)

Maller R., Resnick S.: Limiting behaviour of sums and the term of maximum modulus. Proc. Lond. Math. Soc. 49, 385–422 (1984)

Rosén B.: Limit theorems for sampling from finite populations. Ark. Mat. 5, 383–424 (1965)

Shorack G., Wellner J.: Empirical Processes with Applications to Statistics. Wiley, New York (1986)

Skorokhod A.V.: Limit theorems for stochastic processes. Theory Probab. Appl. 1, 261–290 (1956)