Bootstrap-quantile ridge estimator for linear regression with applications.

Bootstrap is a simple, yet powerful method of estimation based on the concept of random sampling with replacement. The ridge regression using a biasing parameter has become a viable alternative to the ordinary least square regression model for the analysis of data where predictors are collinear. This paper develops a nonparametric bootstrap-quantile approach for the estimation of ridge parameter in the linear regression model. The proposed method is illustrated using some popular and widely used ridge estimators, but this idea can be extended to any ridge estimator. Monte Carlo simulations are carried out to compare the performance of the proposed estimators with their baseline counterparts. It is demonstrated empirically that MSE obtained from our suggested bootstrap-quantile approach are substantially smaller than their baseline estimators especially when collinearity is high. Application to real data sets reveals the suitability of the idea.

Height-for-age and weight-for-age growth charts for Pakistani infants under six months: derived from a novel case selection method using multiple indicator cluster survey data.

BACKGROUND: In the past two decades, there has been a growing recognition of the need to establish indigenous standards or reference growth charts, particularly following the WHO multicenter growth study in 2006. The availability of accurate and reliable growth charts is crucial for monitoring child health. The choice of an appropriate model for constructing growth charts depends on various data characteristics, including the distribution's tails and peak. While Pakistan has reported some reference growth charts, there is a notable absence of indigenous charts for children under two years of age, especially for infants aged 0-6 months who are exclusively breastfed. Additionally, acquiring data poses a significant challenge, particularly for low-income countries, as it demands substantial resources such as finances, time, and expertise. The Multiple Indicator Cluster Survey (MICS) constitutes a large-scale national survey conducted periodically in low-income countries under the auspices of UNICEF. In this study, we propose methods for generating selection variables utilizing the "Novel Case Selection Method," as previously published. Further our approach enables to select and fit appropriate model to the MICS data, selected, and to develop the standard growth charts. METHODS: Out of the 11,478 children under 6 months of age included in MICS-6 (Pakistan), 3,655 children (1,831 males and 1,824 females) met the specified criteria and were selected using the "Novel Case Selection Method". The sample was distributed across provinces as follows: 841 (23.0%) from KPK, 1,464 (40.1%) from Punjab, 819 (22.4%) from Sindh, and 531 (14.5%) from Balochistan. This sample encompassed both rural (76.4%) and urban (23.6%) populations. Following data cleaning and outlier removal, a total of 3,540 records for weight (1,768 males and 1,772 females) and 3,515 records for height (1,759 males and 1,756 females) were ultimately available for the development of standard charts. The Bayesian Information Criterion (BIC) was employed to determine the optimal degrees of freedom for L, M, and S using RefCurv_0.4.2. Three families within the gamlss class-namely, Box Cox Cole and Green (BCCG), Box Cox T (BCT), and Box Cox Power Exponential (BCPE)-were applied, each with three smoothing techniques: penalized splines (ps), cubic splines (cs), and polynomial splines (poly). The best-fitted model was selected from these nine combinations based on the Akaike Information Criteria. RESULTS: The Novel Case Selection Method yielded 3655 cases as per criteria. After cleaning the data, this method lead to selection of 3540 children for "weight for age" (W/A) and 3515 children for "height for age" (H/A). The "BCPE" family and "ps" as smoothing method proved to be best on AIC for all four curves, i.e. the W/A male, W/A female, H/A male, and H/A female. The optimum selected degrees of freedom for the curve "W/A", for both genders were (M = 1, L = 0, S = 0). The optimum degrees of freedom for H/A male were again (M = 1, L = 0, S = 0), but for females the selected degrees of freedom were (M = 1, L = 1, S = 1). The indigenous fitted standard curves for Pakistan were on lower trajectory in comparison to WHO standards. CONCLUSION: This study uses the Novel Case Selection Method with introduced algorithms to construct tailored growth charts for lower and middle-income countries. Leveraging extensive MICS data, the methodology ensures representative national samples. The resulting charts hold practical value and await validation from established data sources, offering valuable tools for policy makers and clinicians in diverse global contexts.

Economic policy uncertainty and CO2 emissions: a comparative analysis of developed and developing nations.

Energy consumption is essential for economic growth; however, its consumption also increases CO2 emissions, which contributes to climate change and environmental degradation. However, both environmental sustainability and sustainable development can be achieved by clean energy (CE) consumption since it consists of noncarbohydrates energy sources that seldom or do not cause CO2 emissions. Therefore, the current study considers economic policy uncertainty (EPU) to study the impacts of CE on CO2 emissions that control economic growth (GDP) and urbanization in both developed and developing nations. The findings from ARDL show that EPU significantly increases CO2 emissions in both the long and short run for both developing and developed nations. While CE and urbanization contribute to improving environmental quality. Economic growth increases CO2 emissions. The results could have a few significant practical impacts on economic policies across which policymakers could try to reduce policy uncertainty by participating in and organizing international treaties and summits. Additionally, international organizations could organize programs to reduce EPU. The role of political stability can be effective in reducing EPU in these countries. Moreover, these nations should introduce environmentally friendly innovation and clean energy technologies and give tax releases on the import and use of CE products while increasing R&D budgets.

Investigation and Discrimination of Ballpoint Pen Inks by Analytical Techniques and Chemometrics.

A population study has been performed for Pakistani ballpoint pen inks of blue, black, red, and green colors (a total of four colors) commercially used in Pakistan. Ballpoint pen inks have been investigated and discriminated by using UV/Vis spectroscopy and FTIR spectroscopy. We have calculated and compared the results in terms of discriminating power (DP). The statistical techniques of principal component analysis and cluster analysis have been applied on obtained data. By visual comparison, the best DP is obtained for green ballpoint pen inks, i.e., 0.866 by using UV/Vis spectroscopy and FTIR techniques. Black and red ballpoint pen inks showed the highest DPs by using UV/Vis spectroscopy; however, blue ballpoint pen inks got the highest DP by using FTIR spectroscopy. DP has been improved by using chemometric techniques and higher DPs are obtained as compared to visual examination.

Modified Liu estimators in the linear regression model: An application to Tobacco data.

BACKGROUND: The problem of multicollinearity in multiple linear regression models arises when the predictor variables are correlated among each other. The variance of the ordinary least squared estimator become unstable in such situation. In order to mitigate the problem of multicollinearity, Liu regression is widely used as a biased method of estimation with shrinkage parameter 'd'. The optimal value of shrinkage parameter plays a vital role in bias-variance trade-off. LIMITATION: Several estimators are available in literature for the estimation of shrinkage parameter. But the existing estimators do not perform well in terms of smaller mean squared error when the problem of multicollinearity is high or severe. METHODOLOGY: In this paper, some new estimators for the shrinkage parameter are proposed. The proposed estimators are the class of estimators that are based on quantile of the regression coefficients. The performance of the new estimators is compared with the existing estimators through Monte Carlo simulation. Mean squared error and mean absolute error is considered as evaluation criteria of the estimators. Tobacco dataset is used as an application to illustrate the benefits of the new estimators and support the simulation results. FINDINGS: The new estimators outperform the existing estimators in most of the considered scenarios including high and severe cases of multicollinearity. 95% mean prediction interval of all the estimators is also computed for the Tobacco data. The new estimators give the best mean prediction interval among all other estimators. THE IMPLICATIONS OF THE FINDINGS: We recommend the use of new estimators to practitioners when the problem of high to severe multicollinearity exists among the predictor variables.

Forensic Discrimination Potential of Blue, Black, Green, and Red Colored Fountain Pen Inks Commercially Used in Pakistan, by UV/Visible Spectroscopy, Thin Layer Chromatography, and Fourier Transform Infrared Spectroscopy.

Examination and comparison of fountain pen inks are very important in forensic questioned documents examination in developing countries where the chances of fraud are greater in cases of cheques, marriage papers, entry of birth and death, etc. In this study, fountain pen inks of blue, black, green, and red colours that are commercially used in Pakistan have been discriminated by UV-Vis spectroscopy, TLC, and FTIR spectroscopy. We have calculated and compared the results in terms of discriminating power. UV/Visible Spectroscopy of fountain pen inks of different brands showed different composition despite their similar colours. TLC was effectively used to differentiate between the colored components of inks. FTIR results showed that each brand could be distinguished by studying the pattern of their absorption spectra that appeared due to the presence of different functional groups. On the basis of combined results of UV-VIS, TLC, and FTIR, the DP was found from 0.73-0.8 for blue, 0.80-1.0 for black, 0.5-1.0 for green, and 1.0 for red colored fountain pen inks. Overall, this study demonstrated the elevated worth of analysis of fountain pen inks commercially used in Pakistan as the study for fountain pen inks, while not very common, remains an interesting target study.

Reference intervals for free T3 and free T4 in Pakistani euthyroid patients: effect of age and gender on thyroid function.

OBJECTIVE: To establish reference intervals for Free Triiodothyronine (FT3) and Free Thyroxine (FT4) in euthyroid subjects and to assess the effect of age and gender on FT3 and FT4. STUDY DESIGN: Cross-sectional, analytical study. PLACE AND DURATION OF STUDY: Institute of Nuclear Medicine and Oncology (INMOL), Lahore, from January 2009 to April 2011. METHODOLOGY: FT3 and FT4 were measured in 852 euthyroid patients. Those with previous thyroid surgery, on thyroidrelated medication and severe non-thyroid illness were excluded. RESULTS: There were 215 males and 637 females with mean age of 46 years. The reference intervals, revealed by this study, for FT3 and FT4 were 2.80 - 5.39 pmol/L and 11.9 - 22.2 pmol/L respectively. The mean difference between gender groups and age groups was found statistically significant for FT3 (gender: p < 0.001; age: p < 0.001) but statistically insignificant for FT4 (gender: p=0.147; age: p=0.201). CONCLUSION: There was no effect of gender and age on FT3 and FT4. The age with serum FT3 and FT4 significantly negatively correlated but this correlation was stronger for FT3 as compared to FT4 levels. Reference intervals of FT3 and FT4 for male (2.99 - 5.63 pmol/L, 12.3 - 22.6 pmol/L) and female (2.77 - 5.29 pmol/L, 11.7 - 22.1 pmol/L) respectively are suggested.