Assume we have a cross-section of $N$ stocks. $Y_i$ is an sample variance estimate of stock returns for stock $i$. This sample variance is estimated using $T_i$ number of observations. All $T_i$ are not necessarily equal, i.e. the sample size for $Y$ estimation differ for i = 1,2,.., N.
Now I want to run a cross-sectional weighted least squares regression:
$Y_i = \beta X_i + \epsilon_i$
What is the best choice of weights here, such that the weights are based on $T_i$ for each $Y_i$. In other words, I want to assign a smaller weight to stock $i$ if $T_i$ is small.