limited_dep介绍与使用方法.pdf

ModelsofLimitedDependentVariables

ZhentaoShi

TheChineseUniversityofHongKong

Limited1/41

FundamentalTask

UseXtopredicty

Beyondcontinuousrandomvariables

Binary

Multi-responses

Integer

Mixedtype:censoring,truncation

Self-selection

Appliedmicroeconomics

Biostatistics

Limited2/41

PanoramicView

MLEisaunifyingframework

RegressorsXenterthemodelasasingleindexX

ii

Distributionalassumptionsarechosenforconvenience

Economicsinterpretsthesingleindexasutility

Numericaldemon:NormalMLE

/code/frankshi0/normal-mle

Limited3/41

Section1

BinaryChoices

Limited4/41

BinaryOutcome

Outcomey0,1

i

Classification

Unsupervisedlearning:k-means

algorithms

Binaryregression(Supervised

learning)

Collegeentrance

Loandecision

Spamfilter

Limited5/41

LinearProbabilityModels

KeepusinglinearregressionyX

iii

Conditionalmean

Pry1XEyXX

iiiii

ErrortermiX,1Xisbinary.ii

Conditionalheteroskedast