Please enable JavaScript.
Coggle requires JavaScript to display documents.
Element of Econometrics - Coggle Diagram
Element of Econometrics
Random Variable, Sampling, Estimation
-
Variance Rule:
1) Var(Y) = Cov (Y,Y)
2) Var(Y) = Var(V+W) = Var(V) + Var(W) + 2Cov(V,W)
3) If Y = aZ where a is constant, Var(Y) = Var(aZ) = a^2var(Z)
-
-
Estimator
Properties of Estimators:
1) Unbiasedness if small sample is unbiased = big sample is unbiased, not vice-versa
2) Consistency
3) Efficiency*
4) Minimum Square Error
Unbiasedness
Small Sample Property
If E(sample estimator) = population parameter
Bias of sample estimator = E(sample estimator) - population parameter
Efficiency - Comparative Concept
Estimators must first be unbiased
Estimator with lowest variance will be efficient
Minimum Mean Square Error
MSE(estimator) = Var(estimator) + [Bias(estimator)]^2
MSE(sample estimator) = E(sample estimator - parametor)^2
Consistent: Large Sample Concept
Estimator converges in probability to titer as n approaches infinity
Consistent does not mean that it'll be unbiased
Law of large numbers & Consistency, sample mean converges to population mean, plim(sample mean) = population mean
Law of Large Number:
only applicable to:
plim sample mean = population mean
plim sample variance = population variance
plim sample cov = population covariance
Sufficient Condition to be consistent:
lim[E(sample estimator)] = population estimator
lim[var(sample estimator)] = 0
both condition must be met to be consistent
-
-
-
-
-
-
-
-
-
-
-
-
-
-