econometrics introduction Flashcards
what is the probability framework for statistical inference?
a) Population, random variable, and distribution
b) Moments of a distribution (mean, variance, standard deviation, covariance, correlation)
c) Conditional distributions and conditional means
d) Distribution of a sample of data drawn randomly from a population: Y1,…, Yn
what is the population?
The group or collection of all possible entities of interest (e.g.school districts, population of workers in the UK etc.)
what is the random variable Y?
Numerical summary of a random outcome (e.g. outcome of rolling a die, test score in a district, STR in a district, wage of a person randomly drawn the worker population of the UK)
what is the sample space?
all the possible outcomes
what is the event?
set of one or more outcomes ie the event that an even number is rolled
what is a discrete variable?
Data that can only take certain values ie face of a dice
what is continuous variable?
data that can take any value ie time or weight
what is the variance?
the measure of the squared spread of the distribution ie E(Y-μ)^2
what is the standard deviation?
a measure of how dispersed the data is in relation to the mean. it is the square root of the variance
what is skewness?
a measure of assymetry of a distribution. if the skewness is equal to 0 then the dystribution is symmetric
what is kurtosis?
measure of the mass in tails, measure of probability of large values
what does the postive skew mean about the location of the mode median and mean?
the mode is to the left of the median and the mean is to the right
what does negative skew mean about the position of the mode median and mean?
the mode is to the right of the median and the mean is to the left
what is the covariance?
covariance is a measure of the linear association between X and Z: its units are units of X x the units of Z. a postive covariance means a postive linear relationship between X and Z
what is the correlation coefficient defined in terms of?
it is defined in terms of the covariance
what does the correlation coefficient measure?
it measures the linear association
what are conditional distributions?
the distribution of Y given values of some other random variable X, for example the distribution of test scores given the STR<20
Pr(Y=y,| X=x) = Pr(X=x, Y=y)/Pr(X=x)
what is conditional mean?
mean of the conditional distribution
E(Y| X=x) = Σy_t*Pr(Y=y_t|X=x)
what is the law of iterated expectationa?
The mean of Y is the weighted average of the conditional expectation of Y given X, weighted by the probability distribution of X.
what is the independence of two random variables?
We say that X and Y are independently distributed (or are independent) if Pr(Y=y|X=x)=Pr(Y=y)
if X and Y are independently distributed what is the covariance?
cov(X,Y)=0 but it does not mean if cov(X,Y)=0 they are independent
what does random sampling mean for different values of Y?
Y1 and Y2 are independently distributed. they are also identically distributed as they come from the same distribution
what are the features of the sampling distribution of Y^_ when n is large>
as n increases the distribution becomes more tightly centered around μ ( the law of large numbers)
moreover, the distribution of Ῡ - μ_Y becomes normal (central limit theorem
what is the definition of the consistent estimator
An estimator is consistent if the probability that its falls within an interval of the true population value tends to one as the sample size increases
