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In genomic studies, univariate analysis is commonly used to discover susceptible variants. It applies univariate regression for each variant and tests the significance of the regression coefficient or slope parameter. This strategy, however, may miss signals that are jointly detectable with other variants. Multivariate analysis is another popular approach, which tests grouped variants with a predefined group, e.g., based on a gene, pathway, or physical location. However, the power will be diminished if the modeling assumption is not suited to the data. Therefore, data-adaptive testing that relies on fewer modeling assumptions is preferable. Possible approaches include a data-adaptive test proposed by Ueki (2021), which applies to various data-adaptive regression models using a generalization of Yanai's generalized coefficient of determination. While several regression models are possible choices for the data-adaptive test, this paper focuses on the fused lasso that can count for the effect of adjacent variants and investigates its performance through comparison with other existing tests. Simulation studies demonstrate that the test using fused lasso has a high power compared to the existing tests including the univariate regression test, saturated regression test, SKAT (sequence kernel association test), burden test, SKAT-O (optimized sequence kernel association test), and the tests using lasso, ridge, and elastic net when assuming a similar effect of adjacent variants. [ABSTRACT FROM AUTHOR]

The internal validity of a causal inference made based on an observational study is often subject to debate. The potential outcomes framework of causal inference stipulates that causal inference is essentially a missing data problem, and we follow this spirit to define the ideal sample as the combination of the observed data and the missing/counterfactual data for regression models. The robustness of a causal inference can be quantified by the probability of a robust inference for internal validity in regression, i.e., the PIVR, which is the probability of rejecting the null hypothesis again for the ideal sample provided the same null hypothesis has been already rejected for the observed sample. Drawing on the relationship between the PIVR and the mean counterfactual outcomes, we formalize a conceptual framework of quantifying the robustness of a regression-based causal inference based on a joint distribution about the mean counterfactual outcomes, holding the observed sample fixed. Interpretatively, the PIVR is the statistical power of the null hypothesis significance testing that is thought to be built on the ideal sample. We demonstrate the conceptual framework of quantifying the robustness of a regression-based causal inference with an empirical example. [ABSTRACT FROM AUTHOR]

The paper focuses on analysing the current tax behaviour of Slovak citizens and their inclination to tax evasion. Inclination to tax evasion is defined in this research based on respondents' answers to questions focused on their tax morale. The data processed in this research was obtained from a questionnaire survey on a sample of 1067 respondents. Intentional sampling was used to ensure the same structure of respondents. In terms of tax evasion acceptance, we identified three groups of people: honest, dishonest, and unconscious. The research confirmed that 78% of the population is prone to tax evasion, and only 22% have never evaded paying taxes and would not do so knowingly or unconsciously. By applying the statistical hypothesis testing, we also found out that except for sex (women are less prone to tax evasion), inclination to tax evasion also depends on education, age, main source of income and experience. Finally, three types of logistic regression models to predict the inclination of a specific tax behaviour were constructed and evaluated based on the total accuracy metric and validated on the ex-post set. [ABSTRACT FROM AUTHOR]

This paper uses the median-of-means (MOM) method to estimate the parameters of the nonlinear regression models and proves the consistency and asymptotic normality of the MOM estimator. Especially when there are outliers, the MOM estimator is more robust than nonlinear least squares (NLS) estimator and empirical likelihood (EL) estimator. On this basis, we propose hypothesis testing Statistics for the parameters of the nonlinear regression models using empirical likelihood method, and the simulation performance shows the superiority of MOM estimator. We apply the MOM method to analyze the top 50 data of GDP of China in 2019. The result shows that MOM method is more feasible than NLS estimator and EL estimator. [ABSTRACT FROM AUTHOR]

We introduce a new multivariate regression model based on the generalized Poisson distribution, which we called geographically-weighted multivariate generalized Poisson regression (GWMGPR) model, and we present a maximum likelihood step-by-step procedure to obtain parameters for it. We use the maximum likelihood ratio test to examine the significance of the regression parameters and to define their critical region. [ABSTRACT FROM AUTHOR]