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Instead of relying on null-hypothesis significance testing (NHST), researchers are consistently advised to use effect sizes (ESs) and confidence intervals (CIs) to convey research findings. However, typical ES measures for most linear models (e.g., multiple regression) assume data normality, a condition that is often violated in behavioral research. This may lead to inaccurate interpretation of ES. In multiple regression models, Cohen's f2, R2 and R adj 2 are employed by researchers, but no study has systematically evaluated their robustness in practice. Thus, this Monte Carlo simulation study evaluates the robustness of f2, R2 and R adj 2 and the associated CIs based on manipulated levels of sample sizes, magnitudes of ESs, numbers of predictors, and data violations (i.e., heavy-tailed, skewed, contaminated, lognormal, and heteroscedastic distributions of errors). This study offers guidelines regarding how robust these ESs are so that researchers can report the most appropriate ES in their research studies. [ABSTRACT FROM AUTHOR]

Data analysis techniques that rely on standard statistical tools and algorithms often encounter problems when dealing with data sets that have large sample sizes. In this study, two statistical tests done in conducting simple linear regression analysis were revisited. In particular, the study simulated the effects of large sample sizes and amount of contamination in the data due to non-sampling errors on the false positive rate of the Kolmogorov-Smirnov (K-S) test in testing for normality of error terms. The study also characterized the effects of varying sample size and amount of contamination in the data on the false negative rate of the t-test in testing the significance of a regression coefficient. Lastly, an optimality index was developed to determine the sample sizes and the values of the percent noise at which both the false positive rate of the K-S test and the false negative rate of the t-test are minimized. [ABSTRACT FROM AUTHOR]

We propose a kernel density based estimation for nonlinear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. For the hypothesis testing of parametric components, restricted estimators under the null hypothesis and test statistics are proposed. The asymptotic properties for the estimators and test statistics are established. A bootstrap procedure is proposed to calculate critical values. Lastly, we make some comparisons between the proposed estimator and nonlinear least squares estimator through the simulation. Our simulation studies indicate that the kernel density based estimator provides a better alternative under some settings, particularly for multimodal distribution of the error term. [ABSTRACT FROM AUTHOR]

In a high-dimensional linear regression model, this article is concerned with testing statistical significance of a subset of regression coefficients. The conventional partial F-test is not applicable in high-dimensional situations. Several methods for testing whether any of the discarded covariates is significant conditional on relative importance of predictors have been proposed in the recent literature, but they are adversely affected by the overestimation of the variance. To overcome this issue, we propose a novel nonparametric testing procedure to avoid this problem and enhance the empirical power. In addition, the new test is very effective when error distribution deviates from the normal scenario and can integrate all the individual information of the discarded covariates. Under the high-dimensional null and alternative hypotheses, we derive the asymptotic distribution of the proposed test statistic, which allows power evaluation of the test. Numerical studies are carried out to examine the numerical performance of the test. The results show that the test proposed here behaves well in terms of sizes and power and significantly outperforms the existing choices in a range of settings. [ABSTRACT FROM AUTHOR]

We consider the estimation and hypothesis test for single-index model by proposing a profile mean squares relative error estimation method, coupling with a leave-one-component-out method. The asymptotic normality for the PMSRE estimator is studied. For the hypothesis test of the single-index parameter, a restricted estimator under the null hypothesis and test statistics are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Lastly, we make some comparisons between the proposed estimator and the profile least squares estimator and the profile least product relative estimator through the simulation. Our simulation studies indicate that the profile mean squares relative error estimator provides a better alternative under some settings, particularly for multimodal or asymmetric distributions of the error term. [ABSTRACT FROM AUTHOR]

In this article, we mainly discuss hypothesis tests to assess whether nonparametric function satisfies monotonicity or convexity in semiparametric partially linear model. For this purpose, we propose a new test statistic for monotonicity or convexity of nonparametric function based on Bernstein polynomials. Furthermore, we employ likelihood ratio statistic to test the significance of regression parameters of the model. We discuss the asymptotic properties of the tests for both nonparametric function and regression parameters. A simulation study is conducted to evaluate the finite sample performance compared with the other methods for shape tests. The method is illustrated by the fuel efficiency study. [ABSTRACT FROM AUTHOR]