Statistical testing

Technical

Purpose

  • To include all kinds of statistical test that I have come across in reading literature.
  • Would also be including tests used in time series analysis as well

List

T-statistic

  • Used when sample size is small and/or standard deviation is unknown

  • Z-table is used to find out the p-value and/or z-score at a given significance/confidence level

  • Its usually given by this formula

tβ^=β^β0s.e(β^) where s.e(β^) is the standard error of the estimator β^ for β and β0 is a non-random , know constant , which may or may not match actual unknown parameter value β

  • t-ratio statistic of the sample skewness is t=S^(r)6/T asymptotically a standard normal random variable

  • t-ratio statistic of the sample excess kurtosis is t=K(r)3^24/T which is asymptotically a standard normal random variable

  • Jarque-Bera test(JB) combines the two prior tests JB=S^2(r)6/T+[K(r)3^]224/T which is asymptotically distributed as chi-squared random variable with 2 degrees of freedom

  • all the above tests in this case are goodness of fit tests