Transcription of Mathematical Statistics, Lecture 2 Statistical Models
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Mathematical Statistics, Lecture 2 Statistical Models
Statistical Models Statistical Models MIT Dr. Kempthorne Spring 2016 1 MIT Statistical Models Statistical Models Definitions Examples Modeling Issues Regression Models Time series Models Outline 1 Statistical Models Definitions Examples Modeling Issues Regression Models Time series Models 2 MIT Statistical Models Statistical Models Definitions Examples Modeling Issues Regression Models Time series Models Statistical Models : Definitions Def: Statistical Model Random experiment with sample space . Random vector X = (X1, X2,.., Xn) defined on . : outcome of experiment X ( ): data observations Probability distribution of X X : Sample Space = {outcomes x}FX : sigma-field of measurable events P( ) defined on (X , FX ) Statistical Model P = {family of distributions } 3 MIT Statistical Models Statistical Models Definitions Examples Modeling Issues Regression Models Time series Models Statistical Models : Definitions Def: Parameters / Parametrization Parameter identifies/specifies distribution in P.
powers of the same variable x = x. i) Fourier Series: (x. i,j = sin(jx. i) or cos(jx. i), explanatory variables are different sin/cos terms of a Fourier series expansion) Time series regressions: time indexed by i, and explanatory variables include lagged response values. Note: Linearity of ˆy. i (in regression parameters) maintained with non ...
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