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Convergence generally means that a sequence of a certain sample quantity approaches a constant as the sample size tends to infinity. Convergence is also a property of an iterative algorithm to stabilize on some aim value.

5 votes
1 answer
7k views

Show that the sample covariance converges in probability to the $Cov(X,Y)$

Suppose we are given $[(Y_i,X_i)]^{n}_{i=1}$ which is a random sample from the joint distribution of $(Y,X). Show that the sample covariance converges in probability to the $Cov(X,Y)$ My thought pr …
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48 votes
7 answers
18k views

Intuitive explanation of convergence in distribution and convergence in probability

What is the intuitive difference between a random variable converging in probability versus a random variable converging in distribution? I've read numerous definitions and mathematical equations, bu …
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