Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

Nkurunziza, Sévérien; Ahmed, S. Ejaz

doi:10.1111/j.1467-9574.2011.00491.x

Cited by 12 publications

(6 citation statements)

References 16 publications

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“…A discussion of the pretest and the shrinkage estimation methodologies and their relative merits with respect to absolute penalty estimators can be found in AHMED et al (), AHMED (), AHMED and RAHEEM (), NKURUNZIZA and AHMED (), and Hussein Nkurunziza and Tomanelli (). For instance, AHMED and RAHEEM () compared shrinkage and pretest estimators to some absolute penalty estimators including the LASSO in the context of linear regression models.…”

Section: Introductionmentioning

confidence: 99%

Penalty and related estimation strategies in the spatial error model

Al-Momani

Hussein

Ahmed

2016

Statistica Neerlandica

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Spatial autoregressive models are powerful tools in the analysis of data sets from diverse scientific areas of research such as econometrics, plant species richness, cancer mortality rates, image processing, analysis of the functional Magnetic Resonance Imaging (fMRI) data, and many more. An important class in the host of spatial autoregressive models is the class of spatial error models in which spatially lagged error terms are assumed. In this paper, we propose efficient shrinkage and penalty estimators for the regression coefficients of the spatial error model. We carry out asymptotic as well as simulation analyses to illustrate the gain in efficiency achieved by these new estimators. Furthermore, we apply the new methodology to housing prices data and provide a bootstrap approach to compute prediction errors of the new estimators.

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Section: Introductionmentioning

confidence: 99%

Penalty and related estimation strategies in the spatial error model

Al-Momani

Hussein

Ahmed

2016

Statistica Neerlandica

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“…The proof of the proposition is lengthy and hence omitted, but with the help of the joint asymptotic normality of the restricted and unrestricted estimators given in the last proposition, one can work out the proof along the same lines as in Ahmed et al . (), Nkurunziza & Ahmed () and Tomanelli ().…”

Section: The Proposed Methodologymentioning

confidence: 99%

“…In the following proposition we state the risk dominance of the proposed shrinkage estimators with respect to the restricted and unrestricted estimators. The proof of the proposition is lengthy and hence omitted, but with the help of the joint asymptotic normality of the restricted and unrestricted estimators given in the last proposition, one can work out the proof along the same lines as in Ahmed et al (2007), Nkurunziza & Ahmed (2011) and Tomanelli (2012).…”

Section: The Shrinkage Estimators and Their Asymptotic Performancementioning

confidence: 99%

Nonparametric Shrinkage Estimation for Aalen's Additive Hazards Model

Hussein

Nkurunziza

Tomanelli

2014

Aust. N. Z. J. Stat.

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Aalen's nonparametric additive model in which the regression coefficients are assumed to be unspecified functions of time is a flexible alternative to Cox's proportional hazards model when the proportionality assumption is in doubt. In this paper, we incorporate a general linear hypothesis into the estimation of the time-varying regression coefficients. We combine unrestricted least squares estimators and estimators that are restricted by the linear hypothesis and produce James-Stein-type shrinkage estimators of the regression coefficients. We develop the asymptotic joint distribution of such restricted and unrestricted estimators and use this to study the relative performance of the proposed estimators via their integrated asymptotic distributional risks. We conduct Monte Carlo simulations to examine the relative performance of the estimators in terms of their integrated mean square errors. We also compare the performance of the proposed estimators with a recently devised LASSO estimator as well as with ridge-type estimators both via simulations and data on the survival of primary billiary cirhosis patients.

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“…According to Nkurunziza and S. Ejaz Ahmed the estimation methods mostly used are the multivariate least square estimation [16].…”

Section: σ =mentioning

confidence: 99%

Determine Joint Factors that Affect Maternal Weight and Body Mass Index Among Pregnant Women in Ethiopia: A Bi-variate Analysis

Zeru¹,

Gebre²

2019

AJTAS

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Introduction: A low maternal body mass index and sub-optimal weight gain during pregnancy are long recognized risk factors for delivery of infants too small for gestational age, low birth weight as well as to increase the risk of subsequent obesity and hypertension in the offspring. Maternal body mass index and maternal weight is positively associated with infant obesity risk. The main objective of this research was to determine the determinants of maternal body mass index and maternal weight simultaneously based on Ethiopia demographic health survey 2016 which was implemented in statistical package R. Methodology: Cross sectional study design was used from Ethiopia demographic health survey 2016. Bi-variate linear regression model was used to determine the factors that affect maternal body mass index and maternal weight simultaneously. Result: The bi-variate analysis of maternal pregnancy weight and body mass index identified that the co-variate husband educational level, preferred waiting time for birth, region, family size, frequency of watching television, maternal height, desire for more children and number of tetanus injections before pregnancy were statistically associated with maternal pregnancy weight. Moreover, educational level of husband, preferred waiting time for birth, region, family size, desire for more children, frequency of watching television and number of tetanus injections before pregnancy were statistically significant for maternal pregnancy body mass index in Ethiopia (p≤0.05). Conclusion: The risk of over pregnancy weight and body mass index increased when parent prefer high number of waiting time to birth another child in Ethiopia. In addition the risk of over pregnancy weight and body mass index increased when mother received more tetanus injection during pregnancy.

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Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

Cited by 12 publications

References 16 publications

Penalty and related estimation strategies in the spatial error model

Penalty and related estimation strategies in the spatial error model

Nonparametric Shrinkage Estimation for Aalen's Additive Hazards Model

Determine Joint Factors that Affect Maternal Weight and Body Mass Index Among Pregnant Women in Ethiopia: A Bi-variate Analysis

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