On some two parameter estimators for the linear regression models with correlated predictors: simulation and application

Khan, Muhammad Shakir; Ali, Amjad; Suhail, Muhammad; Kibria, B. M. Golam

doi:10.1080/03610918.2024.2369809

Communications in Statistics - Simulation and Computation

2024

DOI: 10.1080/03610918.2024.2369809

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On some two parameter estimators for the linear regression models with correlated predictors: simulation and application

Muhammad Shakir Khan,

Amjad Ali,

Muhammad Suhail

et al.

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2024

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Cited by 2 publications

References 24 publications

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Spectral Estimation of Chlorophyll for Non-Invasive Assessment in Apple Orchards

Szabó,

Tamás,

Nagy

2024

Horticulturae

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The main aim of our research was to develop a methodology of chlorophyll content in the leaves of apple trees non-invasive assessment in apple orchards and its adaptation to Early Gold and Golden Reinders based on spectral characteristics of chlorophyll content in the canopy. In each measurement period, 30 samples were collected from each of the two apple cultivars studied. For spectral data collection of leaf samples, an AvaSpec 2048 spectrometer was used in the wavelength range 400–1000 nm in three replicates. Principal component analysis (PCA) with varimax rotation was used to identify the wavelength with the highest factor weight to identify the chlorophyll-sensitive wavelength. The models were calibrated with 2/3 of the values in the database and validated with the remaining 1/3. The simple linear regression method generated the model for estimating chlorophyll. The coefficient of determination (R2) was used to compare the strength of the regression models, and the Root Mean Square Error (RMSE), Normalized Root Mean Square Error (NRMSE), Nash–Sutcliffe efficiency (NSE), Mean Absolute Error (MAE) and Mean Bias Error (MBE) functions were used to measure the accuracy of the estimator models. These metrics help to quickly assess how reliable and accurate a model’s predictions are. Nine indices were obtained based on the precision values, and CHLapple1 performed best (R2 = 0.633, RMSE = 298.28 µg/g, NRMSE = 9.61%, NSE = 0.60 MBE = 84.59, and MAE = 243.39).

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Spectral Estimation of Chlorophyll for Non-Invasive Assessment in Apple Orchards

Szabó,

Tamás,

Nagy

2024

Horticulturae

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Mitigating Multicollinearity in Regression: A Study on Improved Ridge Estimators

Akhtar,

Alharthi,

Khan

2024

Mathematics

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Multicollinearity, a critical issue in regression analysis that can severely compromise the stability and accuracy of parameter estimates, arises when two or more variables exhibit correlation with each other. This paper solves this problem by introducing six new, improved two-parameter ridge estimators (ITPRE): NATPR1, NATPR2, NATPR3, NATPR4, NATPR5, and NATPR6. These ITPRE are designed to remove multicollinearity and improve the accuracy of estimates. A comprehensive Monte Carlo simulation analysis using the mean squared error (MSE) criterion demonstrates that all proposed estimators effectively mitigate the effects of multicollinearity. Among these, the NATPR2 estimator consistently achieves the lowest estimated MSE, outperforming existing ridge estimators in the literature. Application of these estimators to a real-world dataset further validates their effectiveness in addressing multicollinearity, underscoring their robustness and practical relevance in improving the reliability of regression models.

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On some two parameter estimators for the linear regression models with correlated predictors: simulation and application

Cited by 2 publications

References 24 publications

Spectral Estimation of Chlorophyll for Non-Invasive Assessment in Apple Orchards

Spectral Estimation of Chlorophyll for Non-Invasive Assessment in Apple Orchards

Mitigating Multicollinearity in Regression: A Study on Improved Ridge Estimators

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