In this paper we study random sets, with values in a separable Banach space. First we establish several useful properties of the set-valued conditional expectation and then prove some convergence ...

y <- (x-3)^3 + 3*x - .25*(x^2 * (x-3)) + rnorm(n=10000, mean=0, sd=3) dat <- data.frame(x = x, y = y) One of our most fundamental goals as data scientists is to produce predictions that are *good*. In ...

Abstract: This paper is concerned with the Tobit Kalman filtering for a class of discrete-time linear systems. A set of Bernoulli random variables is introduced to describe the randomly occurring ...

Abstract: Consider a pair of random vectors $(\mathrm{X}, \mathrm{Y})$ and the conditional expectation operator $\mathbb{E}[\mathrm{X} \mid \mathrm{Y}=\mathrm{y}]$. This work studies analytic ...