Klass, Michael J; University Of California Departments Of Mathematics And Statistics Berkeley, CA; Klass@stat.berkeley.edu, Nowicki, Krzysztof; Lund University Department Of Statistics Box 743 S-220 07 Lund, Sweden; Krzysztof.nowicki@stat.lu.se
Let X1, X2,... be independent and symmetric random variables such that Sn=X1+...+Xn converges to a finite valued random variable S a.s. and let S*=sup1 ≤ n
Pseudo-maximization and self-normalized processes (2007)
De La Peña, Victor H., Klass, Michael J., Lai, Tze Leung
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems,...
Pseudo-maximization and self-normalized processes ∗ (2007)
Michael J. Klass, Tze Leung Lai
Abstract: Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems,...
De La Pena, Victor H., Klass, Michael J., Lai, Tze Leung
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment...
De La Peña, Victor H., Klass, Michael J., Leung Lai, Tze
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment...
Klass, Michael J., Nowicki, Krzysztof
Let $\Phi$ be a symmetric function, nondecreasing on $[0,\infty)$ and satisfying a $\Delta_2$ growth condition, $(X_1, Y_1), (X_2, Y_2),\ldots,( X_n,Y_n)$ be independent random vectors such that (for...
An improvement of Hoffmann-Jørgensen’s inequality (2000)
Klass, Michael J., Nowicki, Krzysztof
Let $B$ be a Banach space and $\mathscr{F}$ any family of bounded linear functionals on $B$ of norm at most one. For $x\inB\set \|x\| = \sup_{\Lambda \in \mathscr{F}} \Lambda(x)(\|\cdot\|$ is at...
Hahn, Marjorie G., Klass, Michael J.
This paper quantifies the degree to which exponential bounds can be used to approximate tail probabilities of partial sums of arbitrary i.i.d. random variables. The introduction of a single...
Klass, Michael J., Nowicki, Krzysztof
Let $X_1, Y_1, Y_2, \dots, X_n, Y_n$ be independent nonnegative rv’s and let $\{b_{ij}\}_{1 \leq i, j \leq n}$ be an array of nonnegative constants. We present a method of obtaining the order of...
Choi, K. P., Klass, Michael J.
Let $\Phi (\cdot)$ be a nondecreasing convex function on $[0, \infty)$. We show that for any integer $n \geq 1$ and real $a$, $$E \Phi ((M_n - a)^+) \leq 2E \Phi ((S_n - a)^+) - \Phi (0)$$ and...
The Grossman and Zhou investment strategy is not always optimal
Klass, Michael J., Nowicki, Krzysztof
Grossman and Zhou [1993. Optimal investment strategies for controlling drawdowns. Math. Finance 3, 241-276] proposed a strategy to maximize the asymptotic long-run growth rate of one's fortune Ft...
Ratio prophet inequalities for convex functions of partial sums
Prophet inequalities expectations involving maxima of partial sums
A denormalized U-statistic which cannot be decoupled from some associated stopping times
Let X1,X2,... be i.i.d. mean zero random variables and Sn=X1+...+Xn. For any stopping time T w.r.t. {Xn} let denote a copy of T which is independent of {Xn}. We exhibit a family of distributions and...