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Results tagged with consistency
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user 313581
Refers generally to a property of a statistical procedure to go to the "right" place as the sample size tends to infinity, primarily referring to estimators converging to the true parameter value as the sample sizes diverges. Use also for Fisher consistency, the property that an estimator when applied to the complete population gives the right answer.
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Proving estimator consistency
I have the following estimator: $\hat{\sigma}^2_N = \frac{1}{h^2}\sum\limits_{i=1}^{N}x^2_i$, where $x_i \sim i.i.d. \; \mathcal{N}(\mu\frac{h}{N}, \sigma^2\frac{h}{N})$.
We can show that $E[\hat{\sig …
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Accepted
Proving estimator consistency
To prove consistency it is sufficient to show that $E[(\hat{\sigma}^2_N - \sigma^2)^2]$ goes to $0$ as $N \to \infty$. …
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Asymptotic normality implies consistency
I'm trying without success to solve the following exercise in my econometric textbook:
Show that $\sqrt{N}\left(\widehat{\beta_1} - \beta_1 \right) \xrightarrow{d} \mathcal{N}(0,a^2)$, where $a^2$ is …