Skip to content

coskewness

May 31, 2012

Just discovered that the three-way ‘covariance’ I talked about here actually has a name: coskewness. It was hard to find a clear definition so I’m going to use,

coskew(x, y, z) = E((x - E(x))*(y - E(y))*(z - E(z)))

Also found this identity:

coskew(x, y, z) = E(xyz) - E(x)E(y)E(z) - E(x)cov(y,z) - E(y)cov(x,z) - E(z)cov(x,y)

Still not sure about Cauchy-Schwarz for this thing, but here’s a start. coskew and cov are related by,

coskew(x, y, z) = cov((x - E(x))*(y - E(y)), z)
coskew(x, y, z) = cov((y - E(y))*(z - E(z)), x)
coskew(x, y, z) = cov((z - E(z))*(x - E(x)), y)

Therefore, we can Cauchy-Schwarz all of these to get bounds on coskew. However, each of the three versions is not guaranteed to give the same bounds! So far I’ve taken the minimum of the three but I’ve got no proof that there aren’t lesser bounds to find.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: