Abstract This paper provides a comprehensive analysis of linear regression models, focusing on addressing multicollinearity challenges in breast cancer patient data. Linear regression methodologies, ...including GAM, Beta, GAM Beta, Ridge, and Beta Ridge, are compared using two statistical criteria. The study, conducted with R software, showcases the Beta regression model’s exceptional performance, achieving a BIC of − 5520.416. Furthermore, the Ridge regression model demonstrates remarkable results with the best AIC at − 8002.647. The findings underscore the practical application of these models in real-world scenarios and emphasize the Beta regression model’s superior ability to handle multicollinearity challenges. The preference for AIC over BIC in Generalized Additive Models (GAMs) is rooted in the AIC’s calculation framework, highlighting its effectiveness in capturing the complexity and flexibility inherent in GAMs.
In this paper, we consider a special class of dependent random variables (APND) that contains negative dependent random variables classes(ND,PND,NUOD,NA,NLOD,) and some classes of positive dependent ...random variables. Then we generalize Kolmogrov-Feller weak law of large numbers for i.i.d. random variables to APND random variables. we further give corresponding forms of dependence for random elements taking values in separable Banach space. This development will be of use for obtaining Banach space weak law of large numbers.
In this study, we explore the utilization of penalized likelihood estimation for the analysis of sparse photon counting data obtained from distributed target lidar systems. Specifically, we adapt the ...Poisson Total Variation processing technique to cater to this application. By assuming a Poisson noise model for the photon count observations, our approach yields denoised estimates of backscatter photon flux and related parameters. This facilitates the processing of raw photon counting signals with exceptionally high temporal and range resolutions (demonstrated here to 50 Hz and 75 cm resolutions), including data acquired through time-correlated single photon counting, without significant sacrifice of resolution. Through examination involving both simulated and real-world 2D atmospheric data, our method consistently demonstrates superior accuracy in signal recovery compared to the conventional histogram-based approach commonly employed in distributed target lidar applications.
It is a common saying that testing for conditional independence, that is, testing whether whether two random vectors X and Y are independent, given Z, is a hard statistical problem if Z is a ...continuous random variable (or vector). In this paper, we prove that conditional independence is indeed a particularly difficult hypothesis to test for. Valid statistical tests are required to have a size that is smaller than a pre-defined significance level, and different tests usually have power against a different class of alternatives. We prove that a valid test for conditional independence does not have power against any alternative.
Given the nonexistence of a uniformly valid conditional independence test, we argue that tests must be designed so their suitability for a particular problem may be judged easily. To address this need, we propose in the case where X and Y are univariate to nonlinearly regress X on Z, and Y on Z and then compute a test statistic based on the sample covariance between the residuals, which we call the generalised covariance measure (GCM). We prove that validity of this form of test relies almost entirely on the weak requirement that the regression procedures are able to estimate the conditional means X given Z, and Y given Z, at a slow rate. We extend the methodology to handle settings where X and Y may be multivariate or even high dimensional. While our general procedure can be tailored to the setting at hand by combining it with any regression technique, we develop the theoretical guarantees for kernel ridge regression. A simulation study shows that the test based on GCM is competitive with state of the art conditional independence tests. Code is available as the R package GeneralisedCovarianceMeasure on CRAN.
Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a ...coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning. We aim to provide context and explanation of the models, review current state-of-the-art literature, and identify open questions and promising future directions.
In this article, the complete convergence and the Kolmogorov strong law of large numbers for weighted sums of
-mixing random variables are presented. An application to simple linear ...errors-in-variables model is provided. Simulation studies are also carried out to support the theoretical results.
Convergence of Neutrosophic Random Variables GRANADOS, Carlos
Advances in the theory of nonlinear analysis and its applications,
03/2023, Letnik:
7, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper, we propose and study convergence of neutrosophic random variables. Besides, some relations among these convergences are proved. Besides, we define the notion of neutrosophic weak law ...of large number and neutrosophic central limit theorem, also some applications examples are shown.
This paper develops a new probabilistic optimization framework based on chance constrained programming for bi-objective optimal energy management in microgrids considering intermittent ...characteristics of wind and photovoltaic power, and customers' load profile. The proposed approach uses a method based on jointly distributed random variables to calculate the chance of meeting the load requirements while maintaining the operation cost below a present value. The framework benefits from the new improved hybrid artificial bee colony and differential evolution algorithm as the optimization technique to solve the optimal energy management of a grid-connected microgrid. A sample average approximation approach is used to verify the results of the proposed method in comparison with the scenario-based and the Monte Carlo-based stochastic programming.
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