2- Review of statistical theory Flashcards
What is a population?
The group or collection of all possible entities of interest
What is a random variable?
Numerical summary of a random outcome
What is the expected value of a variable e.g Y?
The expected value (or mean) of Y is the average value of Y over repeated realisations of Y
What does the variance measure?
It measures the spread of the distribution of Y
What does the standard deviation measure?
Measures the average deviation of Y from its mean
What does covariance tell us?
Covariance describes a linear association between X and Y
What do the values of a correlation coefficient represent?
1 implies perfect positive linear association, -1 implies perfect negative linear association, 0 implies no linear association
What is the conditional mean as a function of the conditional distribution?
It is the mean of the conditional distribution
What does it mean when 2 random variables are independent and identically distributed (i.i.d)?
If each random variable has the same probability distribution as the others and all are mutually independent
What is the sampling distribution?
The distribution of a moment across all possible random samples
What do we do if we want to know the population mean µY but cannot measure it?
Use the sample mean Ybar to estimate it from the random sample
How can we gain an understanding of how much we can learn from one sample?
We need to look at the sampling variance; the larger the sample size, the lower the variance and the more reliable the estimates
What is the law of large numbers?
As the sample size increases, the distribution of E(Y)
becomes more tightly centred around the population mean, µY
What is the tenet of consistency in Econometrics?
As the sample size goes to infinity, the distribution of
estimates collapses to the population parameter
What are the 2 ideal properties for estimators?
- Unbiased
- Consistent
