Ganjealivand et al 2021b - Revision history

Rimni at 14:51, 14 December 2021

2021-12-14T14:51:10Z

Rimni at 14:50, 14 December 2021

2021-12-14T14:50:03Z

Rimni: /* Abstract */

2021-12-14T14:49:12Z

‎Abstract

Ghapani at 12:02, 9 August 2021

2021-08-09T12:02:41Z

Ghapani at 11:27, 9 August 2021

2021-08-09T11:27:31Z

Scipediacontent at 11:21, 22 July 2021

2021-07-22T11:21:52Z

Scipediacontent at 10:53, 22 July 2021

2021-07-22T10:53:11Z

Scipediacontent at 09:39, 22 July 2021

2021-07-22T09:39:38Z

Ghapani at 10:16, 19 July 2021

2021-07-19T10:16:17Z

Ghapani at 05:57, 18 July 2021

2021-07-18T05:57:44Z

← Older revision		Revision as of 14:51, 14 December 2021
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−	===4.1 Comparison the Estimator ~~<big>~~''β̃''(''k'',''d'' )~~</big>~~ with ~~<big>~~''β̃''~~</big>~~===	+	===4.1 Comparison the Estimator ''β̃''(''k'',''d'') with ''β̃''===

	The <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}</math> is <math display="inline">\mathrm{MSEM}\,(\tilde{\mathit{\boldsymbol{\beta }}})=</math><math>{\sigma }^{2}{\mathit{\boldsymbol{A}}}^{-1},</math> where <math display="inline">{\mathit{\boldsymbol{A}}}_{1}=</math><math>\left( \mathit{\boldsymbol{X}}{\mathit{\boldsymbol{H}}}^{-1}\mathit{\boldsymbol{X}}\right) ,</math> and the <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}(k,d)</math> is		The <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}</math> is <math display="inline">\mathrm{MSEM}\,(\tilde{\mathit{\boldsymbol{\beta }}})=</math><math>{\sigma }^{2}{\mathit{\boldsymbol{A}}}^{-1},</math> where <math display="inline">{\mathit{\boldsymbol{A}}}_{1}=</math><math>\left( \mathit{\boldsymbol{X}}{\mathit{\boldsymbol{H}}}^{-1}\mathit{\boldsymbol{X}}\right) ,</math> and the <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}(k,d)</math> is

← Older revision		Revision as of 14:50, 14 December 2021
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−	===4.1. Comparison the Estimator <big>''β̃''(''k'',''d'' )</big> with <big>''β̃''</big>===	+	===4.1 Comparison the Estimator <big>''β̃''(''k'',''d'' )</big> with <big>''β̃''</big>===

	The <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}</math> is <math display="inline">\mathrm{MSEM}\,(\tilde{\mathit{\boldsymbol{\beta }}})=</math><math>{\sigma }^{2}{\mathit{\boldsymbol{A}}}^{-1},</math> where <math display="inline">{\mathit{\boldsymbol{A}}}_{1}=</math><math>\left( \mathit{\boldsymbol{X}}{\mathit{\boldsymbol{H}}}^{-1}\mathit{\boldsymbol{X}}\right) ,</math> and the <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}(k,d)</math> is		The <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}</math> is <math display="inline">\mathrm{MSEM}\,(\tilde{\mathit{\boldsymbol{\beta }}})=</math><math>{\sigma }^{2}{\mathit{\boldsymbol{A}}}^{-1},</math> where <math display="inline">{\mathit{\boldsymbol{A}}}_{1}=</math><math>\left( \mathit{\boldsymbol{X}}{\mathit{\boldsymbol{H}}}^{-1}\mathit{\boldsymbol{X}}\right) ,</math> and the <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}(k,d)</math> is

← Older revision		Revision as of 14:49, 14 December 2021
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	'''Keywords''': Linear mixed model, two parameter estimation, stochastic restricted two parameter estimation, matrix mean square error		'''Keywords''': Linear mixed model, two parameter estimation, stochastic restricted two parameter estimation, matrix mean square error
−
	<!--'''Mathematics Subject''' '''Classification''' 62J05. 62J12.-->		<!--'''Mathematics Subject''' '''Classification''' 62J05. 62J12.-->

← Older revision		Revision as of 12:02, 9 August 2021
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−	'''AsupNahid Ganjealivand<sup>1</sup>, Fatemeh Ghapani<sup>*2</sup>,'''<big>''' '''</big>'''AsupZaherzadeh<sup>1,3</sup>, Farshin Hormozinejad<sup>1</sup>'''	+	'''AsupNahid Ganjealivand<sup>1</sup>, Fatemeh Ghapani<sup>*2</sup>,'''<big>''' '''</big>'''AsupZaherzadeh<sup>3</sup>, Farshin Hormozinejad<sup>1</sup>'''

	<sup>1</sup> Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran		<sup>1</sup> Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

← Older revision		Revision as of 11:27, 9 August 2021
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−	'''AsupNahid Ganjealivand<sup>1</sup>, Fatemeh Ghapani<sup>*2</sup>,'''<big>''' '''</big>'''AsupZaherzadeh<sup>3</sup>, Farshin Hormozinejad<sup>1</sup>'''	+
		+	'''AsupNahid Ganjealivand<sup>1</sup>, Fatemeh Ghapani<sup>*2</sup>,'''<big>''' '''</big>'''AsupZaherzadeh<sup>1,3</sup>, Farshin Hormozinejad<sup>1</sup>'''

	<sup>1</sup> Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran		<sup>1</sup> Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

← Older revision		Revision as of 11:21, 22 July 2021
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−	===4.1. Comparison the Estimator <~~math display="inline"~~>~~\tilde{\mathit{\boldsymbol{\~~beta ~~}}}\boldsymbol{~~(~~}\mathit{\boldsymbol{~~k~~}}\boldsymbol{~~,~~}\mathit{\boldsymbol{~~d~~}}\boldsymbol{~~)}</~~math~~>~~'''~~ with ~~'''~~ <~~math display="inline"~~>~~\tilde{\mathit{\boldsymbol{\~~beta ~~}}}~~</~~math~~>===	+	===4.1. Comparison the Estimator <big>''β̃''(''k'',''d'' )</big> with <big>''β̃''</big>===

	The <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}</math> is <math display="inline">\mathrm{MSEM}\,(\tilde{\mathit{\boldsymbol{\beta }}})=</math><math>{\sigma }^{2}{\mathit{\boldsymbol{A}}}^{-1},</math> where <math display="inline">{\mathit{\boldsymbol{A}}}_{1}=</math><math>\left( \mathit{\boldsymbol{X}}{\mathit{\boldsymbol{H}}}^{-1}\mathit{\boldsymbol{X}}\right) ,</math> and the <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}(k,d)</math> is		The <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}</math> is <math display="inline">\mathrm{MSEM}\,(\tilde{\mathit{\boldsymbol{\beta }}})=</math><math>{\sigma }^{2}{\mathit{\boldsymbol{A}}}^{-1},</math> where <math display="inline">{\mathit{\boldsymbol{A}}}_{1}=</math><math>\left( \mathit{\boldsymbol{X}}{\mathit{\boldsymbol{H}}}^{-1}\mathit{\boldsymbol{X}}\right) ,</math> and the <math display="inline">MSEM</math> of <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}(k,d)</math> is

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 According to Farebrother <math display="inline">(1976),</math> if <math display="inline">{\sigma }^{2}\left( {A}_{1}^{-1}-\right. </math><math>\left. {T}_{1}{A}_{1}{T}_{1}\right) >0,</math> then the necessary and sufficient condition for <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}(k,d)</math> to be superior to <math display="inline">\tilde{\mathit{\boldsymbol{\beta }}}</math> is <math display="inline">{\mathit{\boldsymbol{\beta }}}^{'}{\left( {\mathit{\boldsymbol{T}}}_{1}{\mathit{\boldsymbol{A}}}_{1}-{\mathit{\boldsymbol{I}}}_{p}\right) }^{'}{\left[ {\sigma }^{2}\left( {\mathit{\boldsymbol{A}}}_{1}^{-1}-{\mathit{\boldsymbol{T}}}_{1}{\mathit{\boldsymbol{A}}}_{1}{\mathit{\boldsymbol{T}}}_{1}\right) \right] }^{-1}\left( {\mathit{\boldsymbol{T}}}_{1}{\mathit{\boldsymbol{A}}}_{1}-\right. </math><math>\left. {\mathit{\boldsymbol{I}}}_{p}\right) \mathit{\boldsymbol{\beta }}<1</math>.
-==5. Selection of parameters  <math display="inline">\mathit{\boldsymbol{k}}</math> and  <math display="inline">\mathit{\boldsymbol{d}}</math>==
+==5. Selection of parameters '''''k''''' and '''''d'''''==
 In the linear regression model, choosing the parameter <math display="inline">k</math> is important so many statisticians were suggested several methods for obtaining this parameter. These methods were proposed by many researchers [23-29] and others. According to Ozkale and Can [18], we rewrite model (1) in the form of a marginal model in which random effects are not explicitly defined:

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← Older revision		Revision as of 05:57, 18 July 2021
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−	'''~~Nahid~~ Ganjealivand<sup>1</sup>, Fatemeh Ghapani<sup>*2</sup>,'''<big>''' '''</big>'''AsupZaherzadeh<sup>3</sup>, Farshin Hormozinejad<sup>1</sup>'''	+	'''AsupNahid Ganjealivand<sup>1</sup>, Fatemeh Ghapani<sup>*2</sup>,'''<big>''' '''</big>'''AsupZaherzadeh<sup>3</sup>, Farshin Hormozinejad<sup>1</sup>'''

	<sup>1</sup> Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran		<sup>1</sup> Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran