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Appendix To Limits For Partial Maxima Of Gaussian Random Vectors
James Kuelbs, Joel Zinn
This appendix provides a short proof for sample path continuity of the Brownian motion induced by an arbitrary centered Gaussian measure on a separable Banach space, and also some…
Limits for Partial Maxima of Gaussian Random Vectors
James Kuelbs, Joel Zinn
We obtain almost sure limit theorems for partial maxima of norms of a sequence of Banach-valued Gaussian random variables.
Concerns with functional depth
James Kuelbs, Joel Zinn
We study some problems inherent with certain forms of functional depth, in particular, zero depth and lack of consistency.
Empirical Quantile CLTs For Some Self-Similar Processes
James Kuelbs, Joel Zinn
In a paper of Jason Swanson, a CLT for the sample median of independent Brownian motions with value 0 at 0 was proved. Here we extend this result in two ways. We prove such a resul…
A central limit theorem for projections of the cube
Grigoris Paouris, Peter Pivovarov, Joel Zinn
We prove a central limit theorem for the volume of projections of the N-cube onto a random subspace of dimension n, when n is fixed and N tends to infinity. Randomness in this case…
Empirical Quantile CLTs for Time Dependent Data
James Kuelbs, Joel Zinn
We establish empirical quantile process CLTs based on independent copies of a stochastic process that are uniform in and quantile levels ,…