Easy Peasy
What is iid?
Independently and identically distributed (same probability for each)
Define point estimation
Process of estimating unknown parameters of a population using sample data; different samples lead to different values of p hat (estimator is a random variable)
Continuous Mapping Theorem
if xn → x then g(xn) → g(x).
Define confidence interval
Method that uses a range to estimate unknown parameter theta
Define hypothesis testing
Method used to make decisions about the population based on sample data
What are three methods of statistical inference?
What are the steps to MLE?
1. Write down log-likelihood l(theta) = log L(theta)
2. Take derivative of l(theta) and equal it to 0
3. Solve for theta hat
4. Check its max using 2nd derivative (should be negative)
Theorem that shows that Xn converges in probability to mu
Law of Large Numbers
Pivotal quantities, bootstrap, CLT
Name the two hypotheses
Null hypothesis (H0) and Alternative Hypothesis (Ha or H1)
What are 3 general approaches to construct estimators?
MLE, MOM, and Bayes
How does MOM work?
It matches population moments to sample moments from data
Central Limit Theorem
standardized sample mean converges in distribution to a standard Normal as the sample size increases
concept that describes how a sequence of rvs behaves as the sample size increases (sequence of distributions getting closer to another distribution as n goes to infinity)
What does "reject H0" and "fail to reject H0" mean?
Reject H0: data is unlikely under the null (enough evidence to support H1)
Fail to Reject H0: Data is not unlikely under the null; insufficient evidence to conclude H0 isn't true
The lower the bias, the ____ the variance
higher
What is the kernel trick?
It recognizes distributions based on their form without needing to compute constants
Interpret what a 95% CI means
If we independently repeat the process of sampling n observations, approximately 95% of the times the random CI will include the true theta value.
Which error is this? You reject the null hypothesis when it's actually true.
Type I Error
Define convergence in probability.
As we take more samples (increase in n) from a random process, the values will be more and more likely to the true value.
Xn -> (p) z* as n -> infinity
What is the Bayes Rule for random variables?
What are the 3 sampling distributions and what are they used to do?
Which test to use for a mean of a normal distribution with unknown variance?
1 sample t-test (two-sided)