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Table 1 Relative bias of coefficient estimates and bias of threshold estimates of three search strategies: grid search, smooth approximation, and first order approximation

From: chngpt: threshold regression model estimation and inference

 

step

hinge

segmented

stegmented

n

250

500

250

500

250

500

250

2000

grid

        

z

0.02

0.02

0.02

0.02

0.02

0.00

0.04

0.01

x

    

0.22

0.09

0.48

0.02

I(x >e)

0.17

0.09

    

0.85

0.19

(x−e)+

  

0.15

0.05

0.23

0.11

-0.33

-0.05

e

0.00

-0.01

0.01

-0.02

0.01

0.03

-0.16

-0.02

smooth

        

z

0.01

0.02

0.02

0.02

0.03

0.01

0.03

0.01

x

    

0.20

0.10

0.43

0.02

I(x >e)

0.13

0.06

    

0.35

0.03

(x−e)+

  

0.15

0.05

0.22

0.11

-0.26

-0.03

e

-0.02

-0.01

0.01

-0.02

0.03

0.01

-0.17

-0.03

first order

        

z

  

0.02

0.02

0.02

0.00

  

x

    

0.24

0.09

  

(x−e)+

  

0.13

0.05

0.34

0.11

  

e

  

-0.00

-0.02

0.04

0.04

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