Related papers: Two choice optimal stopping
Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
Given a countably infinite group $G$ acting on some space $X$, an increasing family of finite subsets $G_n$ and $x\in X$, a natural question to ask is what asymptotical distribution the sets $G_nx$ form. More formally, we define for a…
This paper studies a central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with an aggregation preference to incorporate all discount rates via an attitude…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
Consider the problem of a controller sampling sequentially from a finite number of $N \geq 2$ populations, specified by random variables $X^i_k$, $ i = 1,\ldots , N,$ and $k = 1, 2, \ldots$; where $X^i_k$ denotes the outcome from population…
Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…
This paper analyses a stochastic differential game of control and stopping in which one of the players modifies a diffusion process using impulse controls, an adversary then chooses a stopping time to end the game. The paper firstly…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
When dealing with the problem of simultaneously testing a large number of null hypotheses, a natural testing strategy is to first reduce the number of tested hypotheses by some selection (screening or filtering) process, and then to…
We study the finite temperature statistical mechanics of Hamiltonian paths between a set of N quenched randomly distributed points in a finite domain D. The energy of the path is a function of the distance between neighboring points on the…
In this work we are concerned with the design of efficient mechanisms while eliciting limited information from the agents. First, we study the performance of sampling approximations in facility location games. Our key result is to show that…
We consider a multi-hypothesis testing problem involving a K-armed bandit. Each arm's signal follows a distribution from a vector exponential family. The actual parameters of the arms are unknown to the decision maker. The decision maker…
Let $X_{1},X_{2},...$ be a sequence of independent random variables ($rv$)with common distribution function ($df$) $F$ such that $F(1)=0$ and for each $n\geq 1,$ let $X_{1,n}\leq X_{2,n}\leq ...\leq X_{n,n}$ denote the order statistics…
We address an optimal stopping problem over the set of Bermudan-type strategies $\Theta$ (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with non-linear operators (non-linear…
The following anticoncentration property is proved. The probability that the $k$-order statistic of an arbitrarily correlated jointly Gaussian random vector $X$ with unit variance components lies within an interval of length $\varepsilon$…
In the pivotal variable selection problem, we derive the exact non-asymptotic minimax selector over the class of all $s$-sparse vectors, which is also the Bayes selector with respect to the uniform prior. While this optimal selector is, in…
This paper considers two investors who perform mean-variance portfolio selection with asymmetric information: one knows the true stock dynamics, while the other has to infer the true dynamics from observed stock evolution. Their portfolio…
We consider a general problem of finding a strategy that minimizes the exponential moment of a given cost function, with an emphasis on its relation to the more common criterion of minimization the expectation of the first moment of the…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…