Statistics
This page reviews concepts from statistics that are useful for econometrics.
Related pages: Probability
Sampling¶
Statistic¶
Sampling distribution¶
Standard errors¶
Asymptotics I¶
Convergence in probability¶
TBD
Law of Large Numbers (LLN)¶
Asymptotics II¶
Convergence in distribution¶
TBD
Central Limit Theory (CLT)¶
Hypothesis testing¶
- Define a hypothesis.
- Select a test statistic \(T\).
- Derive the distribution of the test statistic \(T\) under the null hypothesis (e.g., a t distribution with known degrees of freedom; a normal distribution with know mean and variance).
- Select a significance level \(\alpha\) (e.g., 5%).
- Compute from the observations the observed value \(t\) of the test statistic T.
- Decide to either reject the null hypothesis in favor of the alternative or not reject it.
Null and alternative hypotheses¶
\(H_0\) and \(H_1\)
Significance levels¶
TBD
P-value¶
Type I and type II errors¶
False positive and false negative.