There are a number of statistical tests for stochastic dominance and I'm having a hard time choosing which one to use. I would appreciate any suggestions on the topic.

My brother came up with a fun problem:1) Solve x^x^x^x^... = 22) Solve x^x^x^x^... = 4Resolve the paradox.

1000-(2+4+8+16+32+64+128+256+512)/9=886.444...

<r>After running OLS regressions of hedge funds' excess returns with respect to its benchmark excess return, I found that t-statistics of alpha can be unreasonably high (around 60) which could be due to short track record and noise. I would like to improve estimates of alpha and t-statistic of alpha...

QuoteOriginally posted by: ehI would have thought that a maximum likelihood estimation (MLE) would work.I would be happy to use MLE but the question is how to implement it for alpha-stable case. I haven't seen that anywhere.

I am trying to estimate parameters of ARMA(1,1)-GARCH(1,1) model when residuals have alpha-stable distribution. I would appreciate if someone could point me in the right direction.

<t>QuoteOriginally posted by: AlanQuoteYour formula should work. If A = Q'*Diag(lambda1, ..., lambdan)*Q, where Q is an orthogonal matrix, then I-A = Q'*I*Q-Q'*diag(lambda1, ..., lambdan)*Q=Q'*diag(1-lambda1, ..., 1-lambdan)*Q -> inv(I-A)=Q'*diag(1/(lambda1-1), ..., 1/(lambdan-1))*Q. What about rho ...

<t>QuoteOriginally posted by: AlanQuoteOriginally posted by: maratikusAlan, thanks for your suggestion. I am familiar with that decomposition. However, just as you said, it converges only if all eigenvalues are below 1. What if rho>0 and some eigenvalues are above 1?It's possible the last formula I ...

Alan, thanks for your suggestion. I am familiar with that decomposition. However, just as you said, it converges only if all eigenvalues are below 1. What if rho>0 and some eigenvalues are above 1?

C is a correlation matrix, rho is average correlation (average of all non-diagonal elements), D(rho) is a matrix with 1 on the diagonal and rho everywhere else, alpha is a scalar between 0 and 1. I'm looking for a formula for the inverse matrix of alpha*C+(1-alpha)*D(rho).

<t>Let's say I go long US equity futures (for example, S&P 500) and short European equity futures (for example, Eurostoxx or Dax) so that dollar value of notional exposure is equal (for example, if I buy 100 E-mini S&P 500 futures that represents 100*$50*1,195=$5,975,000 and I need to calcul...

I agree with chocolatemoney. Prices of A and B should be equal. Their price will adjust to match aggregate demand and aggregate supply.

Quoteone gets the minimum is 1+(N-1)*alpha when -1/(N-1)<=alpha<=0, and 1-alpha when 0<=alpha<=1.That's correct!

What's the smallest eigenvalue of correlation matrix with all non-diagonal elements equal to alpha, where alpha: -1<alpha<1?

<t>QuoteOriginally posted by: wileyswhow about this:the problem essentially asks for 90!/10^21 (mod 100), where 21 comes from counting the power of 5 as already pointed out.since 100=25*4 with 25 and 4 are coprime, and 90!/10^21 apparently is divisible by 4, so we just need to find 90!/10^21 (mod 25...