MATHEMATICS IN STATISTICAL INFERENCE: AN INTEGRAL APPROACH
Keywords:
parameter estimation, hypothesis testing, mathematical algorithms, predictive models, data rigorAbstract
DOI: https://doi.org/10.46296/ig.v7i14edespdic.0251
This study explores the mathematical foundations of statistical inference, highlighting its essential role in analysis and decision making within various disciplines, such as engineering, economics, and social sciences. In a world increasingly driven by data analysis, the need for accurate and reliable predictive models has driven the demand for advanced statistical techniques. Statistical inference, based on sound mathematical principles, has established itself as a key tool for interpreting and drawing meaningful conclusions from observational data. The objective of this work is to examine how mathematics, particularly estimation techniques, hypothesis testing, and regression models, support statistical inference processes, improving the validity of the conclusions obtained. Through a systematic review of the literature, the impact of mathematics on each of these components and its contribution to the development of more robust predictive models is analyzed. Among the main findings, it is highlighted that the accuracy in parameter estimation directly depends on the correct application of mathematical methods, especially in large sample contexts. This translates into lower variance and greater stability in the results obtained. In addition, the implementation of advanced mathematical algorithms strengthens the capacity of inferential models, optimizing the prediction of future behaviors. The results of this study show that the rigorous use of mathematics not only improves statistical procedures, but also opens up new possibilities to address complex problems more effectively. The implications of this work underline the need to continue strengthening the training and application of mathematics in statistical processes, in order to guarantee more rigorous analysis and more informed decision-making.
Keywords: parameter estimation, hypothesis testing, mathematical algorithms, predictive models, data rigor.
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