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The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.
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Finding $\hat{\theta}$ using the moment method, given $X \sim \mathrm{UNIF}(-\theta, \theta)$
Let $x_1, \cdots, x_n \sim f(x;\theta) = \frac{1}{2\theta}, -\theta < x < \theta$ and $\theta > 0$. I'm tasked with finding $\hat{\theta}$ using the moment method.
It's clear that $f(x;\theta) \sim \m …
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$\mathrm{Var}\left(\frac{1}{n}\sum_{i=1}^{n}{(\ln(x)-\mu)^2}\right)$ where $x \sim \mathrm{L...
I apologize for asking so many questions. My last question, I am stuck with evaluating $\mathrm{Var}\left(\frac{1}{n}\sum_{i=1}^{n}{(\ln(x)-\mu)^2}\right)$, where $x \sim \mathrm{LogNorm}(\mu, \sigma …
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Is the pursuit of asymptotic variance for a novel estimator always required even if the esti...
I am working on an academic paper proposing a new estimator for a population mean. It works quite well in simulations across various superpopulation models (linear, quadratic, and strictly nonlinear). …
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ANOVA formulas not matching with correct answer
I'm trying to compare the results of a by hand, one-way between-groups ANOVA with those given from R. Weirdly, I get completely different results.
I used formulas given by my professor:
\begin{align} …
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2
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Finding $\mathbb{E}\left[\hat{\sigma}^2\right] = \frac{\sum_{i=1}^{n}{\left(\ln(x)-\mu\right...
I'm tasked with finding $\mathbb{E}\left(\hat{\sigma}^2\right)$ where $\hat{\sigma}^2 = \frac{\sum_{i=1}^{n}{\left(\ln(x)-\mu\right)^2}}{n}$, $x \sim \mathrm{Lognorm}(\mu, \sigma^{2}$) . So far I get, …
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Expectation of the sum of ln(x) squared
I am trying to derive the bias and variance of $\hat{\mu}_{MLE} = \frac{-\sum_{i=1}^{n}{\ln(x)}}{2\sigma^2n}$, where $x \sim \mathrm{LogNorm}(\mu, \sigma^2)$. So far I have $$
\mathrm{Bias} = \mu\lef …