Goodness-Of-Fit Test For Standard Logistics Distribution With Outliers
Alternative to the least square coefficient of determination ( R2 OLS ), the coefficient of determination based on median absolute deviation,R 2 MAD , is an attractive consideration in the construction of goodness-of-fit test based on regression and correlation, due to its robustness. This st...
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis |
| Language: | English English |
| Published: |
2010
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/12429/1/FS_2010_11A.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Alternative to the least square coefficient of determination ( R2
OLS ), the coefficient of
determination based on median absolute deviation,R 2
MAD , is an attractive
consideration in the construction of goodness-of-fit test based on regression and
correlation, due to its robustness.
This study presents the observations made from the resulting plots and descriptive
measures obtained from contaminated standard logistic distribution. Contamination is
introduced to investigate perseverance of robustness property of R2
MAD for samples
from the standard logistic distribution. The sampling distribution of R2
MAD is
simulated for various sample sizes (n = 20, 40, 100), percentage of contamination
(5%, 15%, 25%) and distribution of the contaminants (logistic (2, 0.2), logistic (0,
0.2), logistic (2, 1) and normal (3, 0.2) contaminants). The symmetricity of the
sampling distribution of R2
MAD is observed and followed by the investigation of the confidence intervals of R2
MAD in the presence of outliers. The study of confidence
interval estimates for the mean and standard deviation of R2
MAD was conducted using
the bootstrap (BCa) method.
Tables of critical values for samples from the standard logistic distribution using
ZMAD = 1− R2 MAD and ZOLS = 1- R2OLS are constructed. The tables obtained then are used
in the power study on the goodness-of-fit tests using test statistic for alternative
distributions and contaminated alternative distributions. For lognormal, exponential
and standard logistic alternatives, Z*MAD Z and Z *OLS are simulated for various sample
sizes (n =10, 20, 30, 50, 100), percentage of contamination (5%, 15%, 25%, 40%) and
distribution of the contaminants (logistic (2, 0.2), logistic (0, 0.2), logistic (2, 1) and
normal (3, 0.2) contaminants) for different percentiles (a = 0.01, 0.025, 0.05, 0.1),
respectively. The results indicated that the test statistic ZMAD is able to discriminate
the sample that comes from alternative distributions as the test statistic ZOLS . |
|---|