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1 vote

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 $\displaystyle \sum_{t = 1}^{T_i}$, ...
statmerkur's user avatar
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0 votes

What is the variance decomposition method?

Not sure what your book is referring to, but it would seem to me that if you estimated variance at fixed $i$: $$ Var\left[x_{ij}|i=const\right]=Var\left[z_{ij}|i=const\right]\approx\sigma_z^2,\,\mbox{...
Cryo's user avatar
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2 votes

Confidence interval on ratio of estimates for exponential random variables

Note: The CI is an interval for a population parameter not a sample estimate. The estimates will crop up in the endpoints of your interval The (ordinary) F distribution for the ratio of estimates ...
Glen_b's user avatar
  • 278k
1 vote

Maximum Likelihood Estimation for a Unique Probability Density Function

As said in the comments, you cannot ignore the indicator functions. Note that, for $\theta \in \mathbb R_{> 0}, n \in \mathbb N_{\geq 1}$, we have $$ \begin{align} \prod_{i=1}^n \left[\frac{3\theta^...
statmerkur's user avatar
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0 votes

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 ...
Preston Botter's user avatar
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 ...
mlofton's user avatar
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3 votes

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 ...
Ben's user avatar
  • 118k
4 votes

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(\...
Julian Singh's user avatar
5 votes

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 ...
kjetil b halvorsen's user avatar

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