The analysis of high-dimensional count data presents a unique set of challenges, including overdispersion, zero-inflation, and complex nonlinear relationships that traditional generalized linear models and standard machine learning approaches often fail to adequately address. This study introduces and validates a novel Random Forest framework specifically developed for high-dimensional Poisson and Negative Binomial regression, designed to overcome the limitations of existing methods. Through comprehensive simulations and a real-world genomic application to the Norwegian Mother and Child Cohort Study, we demonstrate that the proposed methods achieve superior predictive accuracy, quantified by lower root mean squared error and deviance, and critically produced exceptionally stable and interpretable feature selections. Our theoretical and empirical results show that these distribution-optimized ensembles significantly outperform both penalized-likelihood techniques and naive-transformation-based ensembles in balancing statistical robustness with biological interpretability. The study concludes that the proposed frameworks provide a crucial methodological advancement, offering a powerful and reliable tool for extracting meaningful insights from complex count data in fields ranging from genomics to public health.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests having been developed. However, most previously developed testing procedures for fractional cointegration are primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test’s development is based on a bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between $[0,1]$, and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections, out of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behaviour of our proposed test is examined through extensive Monte Carlo experiments under various data generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labour wage of 36 countries agricultural markets.

Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behavior of our proposed test is examined through extensive Monte Carlo experiments under various data-generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels, even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labor wage of 36 countries’ agricultural markets.