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STAT111 2019-02-06
Wed, Feb 6, 2019

# Delta

$$ \frac{\sqrt{n}(y_n-\mu)}{\sigma} \leftarrow N(0,1) $$

$g(Y_n) \sim N(g(\mu), \sigma^2 / n (g’(\mu))^2)$

# Model

A model is a simplification of how the world works. In a parametric setting, we have this data. Let’s assume it comes from a family of distributions. What was the mean and variance of this distribution?

Models don’t have to have a finite number of parameters. A CDF could be any function that goes from 0 to 1. This is a nonparametric model.

Estimand is the thing being estimated.

Model: $N(\my, \sigma^2)$ Estimand is $\mu$ and estimator is $\hat{\mu}$ Estimate is $\sum y_i / n$

Estimator is a formula while estimate is a value after plugging values inside the estimate.