Statistics Flashcards
Define a random sample
A set of random variables, which are independently and identically distributed
Define the sample mean
1/n times the sum of the variables
Define the sample variance
S^2 = 1/(n-1) times the sum of (X - Xbar)^2
Define the sample standard deviation
The square root of the sample variance
Define likelihood
If a sample has joint pdf/pmf f(x;θ), then L(θ) = f(x;θ)
Define the maximum likelihood estimate
The value of θ that maximised the likelihood for given measurements x.
Define a statistic
A function of X that does not depend on θ.
Define an unbiased estimator
An estimator T(X) is unbiased for θ if E[T] = θ.
Define the mean squared error of an estimator
The mean squared error of T is E[(T-θ)^2]
Define the bias of an estimator
The bias of T is E[T] - θ
Define a confidence interval
If a(X) and b(X) are two statistics and 0<α<1, the interval (a(X),b(X)) is a confidence interval with confiedence level 1-α if for all θ, P(a(X)<θ<b(X)) = 1-α.
Define the standard error of an estimator
If θhat is an estimator of θ based on X, SE(θhat) = sqrt(var(θhat))
Define a fitted value of a model
The ith fitted value of a model Y is yhat = αhat + (βhat)(xi)
Define a residual
The ith residual e_i is given by e_i = y_i - yhat_i.
Define the residual sum of squares
The sum of the squares of the residuals.
