14 when w n n 12 n converges in probability to c we

Info icon This preview shows pages 14–22. Sign up to view the full content.

View Full Document Right Arrow Icon
14
Image of page 14

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
When W n : n 1,2,..., n converges in probability to c we also say that c is the probability limit of W n . Sometimes we get sloppy and refer to W n , but convergence in probability is about sequences of random variables. More notation. We write plim n W n c (and often drop “ n ”) or W n p c 15
Image of page 15
There is an important notation for the special case W n p 0. As we will see later, to facilitate the alebra of asymptotic theory, it is handy to write W n o p 1 (read “little oh pee one”) when W n p 0. We will see in Section 4 where the “1” in parentheses comes from. The definition extends immediately to the idea of convergence in probability to a random variable rather than a constant (although it comes up less often). We require, for all 0, P | W n W | 0 as n . 16
Image of page 16

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon