Density Estimation and Combination under Model Ambiguity



10 Tables

True:G(9,3)

h к n 1/4.5

N=400

t=1000

Gamma
par(1)

par(2)

Normal

par(1)

par(2)

Weibull
par(1)

par(2)

NPQMLE

estim.θ

8.22

3.33

25.55

9.31

0.000031

3.11

st.dev.

. ʌ .
KI(g,f (b))

0.701

0.298

0.0084

0.545

0.425

0.023

0.000015

0.136

0.025

QMLE

estim.θ

9.034

3.03

27.002

9.001

0.000022

3.173

st.dev.

. ʌ .
KI(g,f (b))

0.629

0.213

0.0037

0.449

0.367

0.044

0.000013

0.131

0.0445

Table 1

True:G(9,3)

h к n 1/4

N=400

t=1000

Gamma

Normal

Weibull

par(1)

par(2)

par(1)

par(2)

par(1)

par(2)

NPQMLE

estim.θ

8.586

3.194

25.536

9.103

0.000026

3.17

st.dev.

0.756

0.291

0.543

0.425

0.000014

0.143

. ʌ .

KI(g,f (b))

0.0062

0.0211

0.0236

Table 2

True:G(9,3)

h к n 1/4.5

N=800

_________t=1000__________________________

Gamma
par(1)

par(2)

Normal

par(1)

par(2)

Weibull
par(1)

par(2)

NPQMLE

estim.θ

8.36

3.27

25.53

9.21

0.000027

3.143

st.dev.

. ʌ .
KI(g,f (b))

0.521

0.214

0.0049

0.379

0.315

0.019

0.000009

0.101

0.0222

QMLE

estim.θ

9.007

3.009

27.011

9.012

0.000021

3.166

st.dev.

. ʌ .
KI(g,f (b))

0.469

0.161

0.002

0.322

0.276

0.042

0.000073

0.098

0.0432

Table 3

True:G(9,3)

h к n 1/4

N=800_________

t=1000___________________________

Gamma

Normal

Weibull.

par(1)

par(2)

par(1)

par(2)

par(1)

par(2)

NPQMLE

estim.θ

8.65

3.15

25.511

9.05

0.000024

3.183

st.dev.

0.555

0.212

0.384

0.317

0.000008

0.105

. ʌ .

KI(g,f (b))

0.0035

0.0186

0.0211

Table 4

37



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