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.
distributions with mean µ {E. j} are i.i.d. with distribution function G (·), where G ∈G, the class of symmetric distributions with mean 0. Non-Parametric. Model: X 1,..., X n are i.i.d. with distribution function G (·) where G ∈G, the class of all distributions on the sample space X (with center µ) íí MIT 18.655 Statistical Models
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