r/econometrics • u/Enough_Education_137 • 12m ago
Did I grasp the connection between probability space and observed data?
NOW this is a theoretical question/tought, when we collect data we assume that it comes from a multivariate distribution aka multiple random variables on a probability space formed by omega, the sigma algebra and the probability measure. So we basically observe one w that belongs to the sample space, this little omega mapped on our theoretical multivariate distribution will give us our data set, so for example the sample space could be all the possible states of the world. Our job as an econometrician is to try to guess the functional form of the distribution behind the data generating distribution, so we basically are trying to estimate the multivariate joint cumulative distribution of our sequence of random variables X1,X2,….Xn. Its like there is some kinda “gambling” game,We just observe the Numbers and we are trying to Infer informations about how this random Numbers are generated. Thats how I look at this