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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 $\displaystyle \sum_{t = 1}^{T_i}$, ...
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• 5,340

### 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 ...
• 1,332
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 ...
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### 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 ...
• 118k

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

I have found a much simpler proof using the weak law of large numbers (This requires finite second moment): \$\begin{aligned} \frac{1}{n-1}\sum\left(x_i-\bar{x}_n\right)^2 & =\frac{1}{n-1}\left(\...
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### Is the sample mean an unbiased estimator of population mean in the presence of autocorrelation?

Yes, autocorrelation (or spatial correlation or ...) do not destroy the unbiasedness of the sample mean as an estimator of population mean. Expectation is a linear operator, so when you calculate the ...
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