A nonparametric method using the trimmed mean is proposed to estimate the slope parameter of the replicated linear functional relationship model (LFRM). This study considers the replicated LFRM when the error terms are not assumed to have a normal distribution. The maximum likelihood estimation method requires the assumption of normality and may lead to errors when outliers are present in the data. The performance of the proposed method is compared with the maximum likelihood estimation method in terms of estimated bias and mean square error. Results simulation study highlighted that the proposed method provides a better estimate of the slope parameter in the presence of outliers as compared to the maximum likelihood estimation method.

Topics
Computer simulation, Estimation theory, Gaussian processes
1.
W. A.
Fuller
,
Measurement Error Models
.
John Wiley & Sons
,
1987
.
Google Scholar
Crossref
Search ADS
 
2.
Y.
Hu
 and
T.
Wansbeek
, “
Measurement Error Models: Editors’ Introduction
,”
J. Econom.
, vol.
200
, no.
2
, pp.
151
–
153
,
2017
.
https://doi.org/10.1016/j.jeconom.2017.06.001
Google Scholar
Crossref
Search ADS
 
3.
D. V.
Lindley
, “
Estimation of a Functional Relationship
,”
Biometrika
, vol.
40
, no.
1/2
, pp.
47
–
49
,
1953
.
https://doi.org/10.2307/2333095
Google Scholar
Crossref
Search ADS
 
4.
M. G.
Kendall
 and
A.
Stuart
,
The Advanced Theory of Statistics. Vol 2: Inference and Relationship
, 4th ed., vol.
2
.
London
:
Griffin
,
1979
.
Google Scholar
 
5.
A. G.
Hussin
,
N.
Fieller
, and
E.
Stillman
, “
Pseudo-replicates in the Linear Circular Functional Relationship Model
,”
J. Appl. Sci.
, vol.
5
, no.
1
, pp.
138
–
143
,
2005
.
https://doi.org/10.3923/jas.2005.138.143
Google Scholar
Crossref
Search ADS
 
6.
M.
Dorff
 and
J.
Gurland
, “
Estimation of the Parameters of a Linear Functional Relation
,”
J. R. Stat. Soc. Ser. B
, vol.
23
, no.
1
, pp.
160
–
170
,
1961
.
Google Scholar
 
7.
W. M.
Patefield
, “
Information from the Maximized Likelihood Function
,”
Biometrika
, vol.
72
, no.
3
, pp.
664
–
668
,
1985
.
https://doi.org/10.1093/biomet/72.3.664
Google Scholar
Crossref
Search ADS
 
8.
A. A.
Ghapor
,
Y. Z.
Zubairi
,
A. S. M.
Al Mamun
, and
A. H. M. R.
Imon
, “
A Robust Nonparametric Slope Estimation in Linear Functional Relationship Model
,”
Pak. J. Stat.
, vol.
31
, no.
3
, pp.
339
–
350
,
2015
.
Google Scholar
 
9.
A. D.
Al-Nasser
 and
M. A. H.
Ebrahem
, “
A New Nonparametric Method for Estimating the Slope of Simple Linear Measurement Error Model in the Presence of Outliers
,”
Pak. J. Stat.
, vol.
21
, no.
3
, pp.
265
–
274
,
2005
.
Google Scholar
 
10.
A. S. M.
Al Mamun
,
A. G.
Hussin
,
Y. Z.
Zubairi
, and
A. H. M. R.
Imon
, “
A nonparametric robust estimator for slope of linear structural relationship model
,”
Pak. J. Stat.
, vol.
28
, no.
3
, pp.
385
–
394
,
2012
.
Google Scholar
 
11.
A. Mohd
Arif
,
Y. Z.
Zubairi
, and
A. G.
Hussin
, “
Nonparametric Estimation for a Slope of a Replicated Linear Functional Relationship Model
,”
ASM Sci. J.
, vol.
13
, pp.
1
–
5
,
2020
.
https://doi.org/10.32802/asmscj.2020.sm26(1.15)
Google Scholar
Crossref
Search ADS
 
12.
R. R.
Wilcox
, “
Trimmed Means
,”
Encycl. Stat. Behav. Sci.
, vol.
4
, pp.
2066
–
2067
,
2005
.
Google Scholar
 
13.
V. D.
Barnett
, “
Fitting Straight Lines-The Linear Functional Relationship with Replicated Observations
,”
Appl. Stat.
, vol.
19
, no.
2
, pp.
135
–
144
,
1970
.
https://doi.org/10.2307/2346543
Google Scholar
Crossref
Search ADS
 
14.
A. G.
Hussin
, “
Approximating Fisher’s Information for the Replicated Linear Circular Functional Relationship Model
,”
Bull. Malaysian Math. Sci. Soc.
, vol.
28
, no.
2
, pp.
131
–
139
,
2005
.
Google Scholar
 
15.
A. Mohd
Arif
,
Y. Z.
Zubairi
, and
A. G.
Hussin
, “
Maximum Likelihood Estimation of Replicated Linear Functional Relationship Model
,” vol.
10
, no.
1
, pp.
301
–
308
,
2021
.
Google Scholar
 
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