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### Mathematical Step for consistency

In what follows I assume that you use $\displaystyle \sum_{i \in N}$ and $\displaystyle \sum_{t \in T_i}$ and as notation for $\displaystyle \sum_{i=1}^N$ and $\displaystyle \sum_{t = 1}^{T_i}$, ...

### ML vs WLSMV: which is better for categorical data and why?

Your question does not specifically reference factor analysis (FA) or structural equation modeling (SEM), though I will assume you are broadly interested in differences between estimators for ...
1 vote

### Unable to estimate AR(p) coefficients and $\sigma^2$

The trick is to re-label the time units so that the unit of time equals 2. Then things become easier. Let `$X^{*}_{t} = X_{2t}$ and $W^{*}_t = W_{2t} ~\forall~t = 0,1,2,3, \ldots \infty$, Then, you ...

### How to prove $s^2$ is a consistent estimator of $\sigma^2$?

Vanishing variance (and resulting convergence in mean square) occurs if the underlying distribution has finite kurtosis The other answer here considers the case of a sample variance of IID normally ...