• 沒有找到結果。

. All the simulations are based on 1000 simulated datasets. The following notation will be used in the presentation of the simulation results.

N/A
N/A
Info
下載
Protected

Academic year: 2021

Share ". All the simulations are based on 1000 simulated datasets. The following notation will be used in the presentation of the simulation results."

Copied!
8
0
0

加載中.... (立即查看全文)

立即下載 ( 8 頁 )

全文

(1)

We conducted simulation studies to examine the finite sample properties of the proposed three confidence intervals for ρ

(1)

− ρ

(2)

. All the simulations are based on 1000 simulated datasets. The following notation will be used in the presentation of the simulation results.

ρ

(1)

: the correlation coefficient from bivariate normal distribution 1.

ρ

(2)

: the correlation coefficient from bivariate normal distribution 2.

n

1

: the size of sample 1.

n

2

: the size of sample 2.

CPI: coverage probability of confidence interval I.

CPII: coverage probability of confidence interval II.

CPIII: coverage probability of confidence interval III.

LI: mean of the length of 100(1 − α)% C.I. of ¡

ρ

(1)

− ρ

(2)

¢

based on confidence interval I.

LII: mean of the length of 100(1 − α)% C.I. of ¡

ρ

(1)

− ρ

(2)

¢

based on confidence interval II.

LIII: mean of the length of 100(1 − α)% C.I. of ¡

ρ

(1)

− ρ

(2)

¢

based on confidence interval III.

PI: (times of CI(II) is wider than CI(III))/1000.

PII: (times of CI(I) is wider than CI(III))/1000.

PIII: (times of CI(I) is wider than CI(II))/1000.

(2)

(30, 30) 1.0 0.963 0.931 1.607 0.466 0.388 1.0 1.0 1.0 (30, 90) 1.0 0.935 0.903 1.129 0.402 0.324 1.0 1.0 1.0 (90, 30) 1.0 0.951 0.942 1.351 0.344 0.325 1.0 1.0 1.0 (100, 100) 1.0 0.945 0.923 0.904 0.248 0.225 1.0 1.0 1.0 (100, 200) 1.0 0.955 0.933 0.772 0.224 0.195 1.0 1.0 1.0 (200, 100) 1.0 0.946 0.942 0.793 0.201 0.196 1.0 1.0 1.0 (300, 300) 1.0 0.935 0.940 0.523 0.141 0.133 1.0 1.0 1.0 (300, 400) 1.0 0.951 0.933 0.486 0.136 0.124 1.0 1.0 1.0 (400, 300) 1.0 0.959 0.950 0.492 0.129 0.124 1.0 1.0 1.0

Table 1(b). ¡

ρ

(1)

, ρ

(2)

, α ¢

= (0.7, 0.8, 0.1)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII

(30, 30) 1.0 0.908 0.862 1.344 0.390 0.331 1.0 1.0 1.0

(30, 90) 0.999 0.877 0.825 1.083 0.336 0.275 0.957 1.0 1.0

(90, 30) 1.0 0.894 0.893 1.130 0.288 0.276 0.828 1.0 1.0

(100, 100) 1.0 0.889 0.871 0.756 0.206 0.189 1.0 1.0 1.0

(100, 200) 1.0 0.909 0.854 0.646 0.187 0.164 0.992 1.0 1.0

(200, 100) 1.0 0.890 0.885 0.663 0.168 0.165 0.793 1.0 1.0

(300, 300) 1.0 0.911 0.886 0.438 0.118 0.110 1.0 1.0 1.0

(300, 400) 1.0 0.903 0.872 0.407 0.114 0.104 1.0 1.0 1.0

(400, 300) 1.0 0.895 0.883 0.411 0.108 0.104 1.0 1.0 1.0

(3)

Table 2(a). ¡

ρ

(1)

, ρ

(2)

, α ¢

= (0.4, 0.7, 0.05)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII (30, 30) 0.999 0.945 0.899 1.379 0.713 0.564 1.0 1.0 1.0 (30, 90) 0.996 0.919 0.830 1.068 0.633 0.469 1.0 1.0 1.0 (90, 30) 0.999 0.935 0.926 1.200 0.512 0.472 1.0 1.0 1.0 (100, 100) 1.0 0.935 0.900 0.775 0.385 0.324 1.0 1.0 1.0 (100, 200) 0.998 0.951 0.886 0.642 0.357 0.281 1.0 1.0 1.0 (200, 100) 1.0 0.943 0.927 0.697 0.308 0.281 1.0 1.0 1.0 (300, 300) 1.0 0.955 0.912 0.448 0.222 0.189 1.0 1.0 1.0 (300, 400) 1.0 0.954 0.909 0.411 0.215 0.177 1.0 1.0 1.0 (400, 300) 1.0 0.960 0.926 0.426 0.201 0.178 1.0 1.0 1.0

Table 2(b). ¡

ρ

(1)

, ρ

(2)

, α ¢

= (0.4, 0.7, 0.1)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII

(30, 30) 0.995 0.894 0.816 1.154 0.597 0.477 1.0 1.0 0.998

(30, 90) 0.982 0.850 0.752 0.894 0.530 0.396 1.0 1.0 1.0

(90, 30) 0.994 0.892 0.879 1.00 0.428 0.398 1.0 1.0 1.0

(100, 100) 1.0 0.889 0.828 0.648 0.322 0.272 1.0 1.0 1.0

(100, 200) 0.994 0.901 0.802 0.537 0.299 0.235 1.0 1.0 1.0

(200, 100) 0.999 0.893 0.868 0.583 0.258 0.236 1.0 1.0 1.0

(300, 300) 1.0 0.905 0.843 0.375 0.186 0.158 1.0 1.0 1.0

(300, 400) 0.995 0.913 0.842 0.344 0.180 0.148 1.0 1.0 1.0

(4)

(30, 30) 0.939 0.943 0.980 1.126 0.916 0.821 1.0 0.961 0.874 (30, 90) 0.917 0.930 0.975 0.922 0.745 0.694 1.0 0.954 0.862 (100, 100) 0.937 0.938 0.984 0.624 0.503 0.485 1.0 0.998 0.987 (100, 200) 0.944 0.949 0.980 0.539 0.435 0.424 1.0 1.0 1.0 (300, 300) 0.949 0.949 0.988 0.360 0.290 0.287 1.0 1.0 1.0 (300, 400) 0.956 0.956 0.984 0.336 0.272 0.269 1.0 1.0 1.0

Table 3(b). ¡

ρ

(1)

, ρ

(2)

, α ¢

= (0.3, 0.3, 0.1)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII

(30, 30) 0.952 0.876 0.885 0.942 0.767 0.701 1.0 0.946 0.874

(30, 90) 0.939 0.859 0.872 0.771 0.623 0.589 1.00 0.943 0.862

(100, 100) 0.946 0.887 0.887 0.522 0.420 0.409 1.0 0.997 0.987

(100, 200) 0.956 0.881 0.883 0.451 0.364 0.357 1.0 0.994 0.987

(300, 300) 0.962 0.900 0.902 0.301 0.243 0.241 1.0 1.0 1.0

(300, 400) 0.958 0.903 0.903 0.281 0.228 0.226 1.0 1.0 1.0

(5)

Table 4(a). ¡

ρ

(1)

, ρ

(2)

, α ¢

= (0, 0.2, 0.05)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII (30, 30) 0.969 0.923 0.929 1.045 0.976 0.868 1.0 0.880 0.645 (30, 90) 0.956 0.920 0.927 0.843 0.805 0.737 1.0 0.806 0.598 (90, 30) 0.953 0.926 0.940 0.862 0.789 0.734 1.0 0.802 0.635 (100, 100) 0.956 0.941 0.939 0.571 0.541 0.514 1.0 0.875 0.735 (100, 200) 0.956 0.938 0.933 0.489 0.471 0.448 1.0 0.829 0.677 (200, 100) 0.956 0.938 0.933 0.489 0.471 0.448 1.0 0.829 0.677 (300, 300) 0.963 0.944 0.941 0.329 0.313 0.303 1.0 0.932 0.858 (300, 400) 0.963 0.950 0.943 0.306 0.293 0.284 1.0 0.934 0.844 (400, 300) 0.957 0.943 0.939 0.308 0.292 0.284 1.0 0.931 0.854

Table 4(b). ¡

ρ

(1)

, ρ

(2)

, α ¢

= (0, 0.2, 0.1)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII

(30, 30) 0.917 0.872 0.872 0.874 0.817 0.739 1.0 0.837 0.645

(30, 90) 0.900 0.854 0.856 0.705 0.674 0.624 1.0 0.782 0.598

(90, 30) 0.899 0.865 0.877 0.721 0.660 0.622 1.0 0.773 0.635

(100, 100) 0.905 0.883 0.881 0.477 0.452 0.433 1.0 0.851 0.735

(100, 200) 0.889 0.876 0.872 0.409 0.394 0.377 1.0 0.810 0.677

(200, 100) 0.916 0.889 0.888 0.417 0.389 0.376 1.0 0.846 0.767

(300, 300) 0.917 0.900 0.896 0.27 0.262 0.254 1.0 0.926 0.858

(300, 400) 0.909 0.902 0.893 0.256 0.245 0.238 1.0 0.933 0.844

(6)

(30, 30) 0.971 0.929 0.932 1.105 0.932 0.833 1.0 0.949 0.833 (30, 90) 0.971 0.924 0.929 0.888 0.773 0.707 1.0 0.921 0.766 (90, 30) 0.967 0.925 0.935 0.905 0.756 0.710 1.0 0.902 0.812 (100, 100) 0.979 0.948 0.949 0.602 0.517 0.496 1.0 0.977 0.940 (100, 200) 0.971 0.942 0.942 0.517 0.451 0.433 1.0 0.973 0.935 (200, 100) 0.974 0.944 0.945 0.526 0.444 0.434 1.0 0.981 0.960 (300, 300) 0.977 0.941 0.941 0.349 0.299 0.293 1.0 0.999 0.9980 (300, 400) 0.980 0.948 0.946 0.325 0.280 0.275 1.0 0.999 0.999 (400, 300) 0.974 0.941 0.942 0.328 0.278 0.274 1.0 0.999 0.997

Table 5(b). ¡

ρ

(1)

, ρ

(2)

, α ¢

= ( −0.2, −0.3, 0.1)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII

(30, 30) 0.928 0.871 0.876 0.925 0.780 0.710 1.0 0.924 0.833

(30, 90) 0.930 0.869 0.871 0.743 0.646 0.600 1.0 0.905 0.766

(90, 30) 0.930 0.870 0.886 0.757 0.632 0.602 1.0 0.887 0.812

(100, 100) 0.946 0.898 0.897 0.504 0.432 0.418 1.0 0.972 0.940

(100, 200) 0.929 0.886 0.884 0.433 0.377 0.364 1.0 0.966 0.935

(200, 100) 0.944 0.899 0.903 0.440 0.371 0.365 1.0 0.977 0.960

(300, 300) 0.936 0.887 0.885 0.292 0.250 0.246 1.0 0.999 0.998

(300, 400) 0.941 0.887 0.884 0.272 0.234 0.230 1.0 0.999 0.999

(400, 300) 0.938 0.884 0.884 0.274 0.233 0.230 1.0 0.998 0.997

(7)

Table 6(a). ¡

ρ

(1)

, ρ

(2)

, α ¢

= ( −0.4, −0.7, 0.05)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII (30, 30) 1.0 0.935 0.888 1.391 0.702 0.556 1.0 1.0 1.0 (30, 90) 0.991 0.919 0.845 1.070 0.634 0.465 1.0 1.0 0.999 (90, 30) 1.0 0.947 0.935 1.195 0.513 0.473 1.0 1.0 1.0 (100, 100) 1.0 0.939 0.907 0.770 0.386 0.323 1.0 1.0 1.0 (100, 200) 0.999 0.935 0.872 0.641 0.357 0.280 1.0 1.0 1.0 (200, 100) 1.0 0.942 0.926 0.695 0.308 0.282 1.0 1.0 1.0 (300, 300) 0.999 0.940 0.894 0.447 0.222 0.188 1.0 1.0 1.0 (300, 400) 1.0 0.943 0.884 0.412 0.214 0.177 1.0 1.0 1.0 (400, 300) 1.0 0.947 0.902 0.426 0.201 0.177 1.0 1.0 1.0

Table 6(b). ¡

ρ

(1)

, ρ

(2)

, α ¢

= ( −0.4, −0.7, 0.1)

(n

1

, n

2

) CPI CPII CPIII LI LII LIII PI PII PIII

(30, 30) 0.991 0.878 0.813 1.164 0.588 0.471 1.0 1.0 1.0

(30, 90) 0.979 0.860 0.770 0.895 0.531 0.392 1.0 1.0 0.999

(90, 30) 0.997 0.889 0.869 1.0 0.429 0.399 1.0 1.0 1.0

(100, 100) 0.999 0.89 0.841 0.644 0.323 0.271 1.0 1.0 1.0

(100, 200) 0.994 0.885 0.797 0.536 0.299 0.235 1.0 1.0 1.0

(200, 100) 1.00 0.901 0.878 0.581 0.258 0.237 1.0 1.0 1.0

(300, 300) 0.997 0.887 0.836 0.374 0.186 0.158 1.0 1.0 1.0

(300, 400) 0.998 0.893 0.816 0.344 0.179 0.148 1.0 1.0 1.0

(8)

the two population correlations are large in magnitude.

3. The confidence interval III tends to have CPs lower than norminal values when one of the two population correlations is large in magnitude and the sample sizes are highly imbalanced among the two samples.

4. Regarding the precision (length) of the confidence interval, the length of confidence

interval III is almost always shorter than that of the confidence interval II, and the length

of confidence interval II tends to be shorter than that of confidence interval I. Therefore,

for practical applications, we would suggest using the confidence interval III when the two

correlations are moderate in magnitude or when the two sample sizes are balenced, while in

other situations the confidence interval II is a better choice.

參考文獻

立即下載 ( PDF - 8 頁 - 75.71 KB )

相關文件

s[In The Concept of Nirvāna in Mādhyamika

6 《中論·觀因緣品》，《佛藏要籍選刊》第 9 冊，上海古籍出版社 1994 年版，第 1

Mathematical modeling of the eyespots in butterfly wings

The first row shows the eyespot with white inner ring, black middle ring, and yellow outer ring in Bicyclus anynana.. The second row provides the eyespot with black inner ring

of the Atom

You are given the wavelength and total energy of a light pulse and asked to find the number of photons it

In the text?

Robinson Crusoe is an Englishman from the 1) t_______ of York in the seventeenth century, the youngest son of a merchant of German origin. This trip is financially successful,

PRACTICES IN THE

fostering independent application of reading strategies Strategy 7: Provide opportunities for students to track, reflect on, and share their learning progress (destination). •

Areas to be covered in the talk

Now, nearly all of the current flows through wire S since it has a much lower resistance than the light bulb. The light bulb does not glow because the current flowing through it

The hidden dimensions of the Universe

volume suppressed mass: (TeV) 2 /M P ∼ 10 −4 eV → mm range can be experimentally tested for any number of extra dimensions - Light U(1) gauge bosons: no derivative couplings. =>

of the QCDVacuum

incapable to extract any quantities from QCD, nor to tackle the most interesting physics, namely, the spontaneously chiral symmetry breaking and the color confinement.. 