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In this paper, we propose and study a new global test, namely, GPF test, for the one-way ANOVA problem for functional data, obtained via globalizing the usual pointwise F-test. The asymptotic random expressions of the test statistic are derived, and its asymptotic power is investigated. The GPF test is shown to be root-n consistent. It is much less computationally intensive than a parametric bootstrap test proposed in the literature for the one-way ANOVA for functional data. Via some simulation studies, it is found that in terms of size-controlling and power, the GPF test is comparable with two existing tests adopted for the one-way ANOVA problem for functional data. A real data example illustrates the GPF test.

Linear regression is widely used in biomedical and psychosocial research. A critical assumption that is often overlooked is homoscedasticity. Unlike normality, the other assumption on data distribution, homoscedasticity is often taken for granted when fitting linear regression models. However, contrary to popular belief, this assumption actually has a bigger impact on validity of linear regression results than normality. In this report, we use Monte Carlo simulation studies to investigate and compare their effects on validity of inference.

In this article, we propose a new class of semiparametric instrumental variable models with partially varying coefficients, in which the structural function has a partially linear form and the impact of endogenous structural variables can vary over different levels of some exogenous variables. We propose a three-step estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic normality of these proposed estimators are established. Moreover, a generalized F-test is developed to test whether the functional coefficients are of particular parametric forms with some underlying economic intuitions, and furthermore, the limiting distribution of the proposed generalized F-test statistic under the null hypothesis is established. Finally, we illustrate the finite sample performance of our approach with simulations and two real data examples in economics.

As the dimensionality of the alternative hypothesis increases, the power of classical tests tends to diminish quite rapidly. This is especially true for high dimensional data in which there are more parameters than observations. We discuss a score test on a hyperparameter in an empirical Bayesian model as an alternative to classical tests. It gives a general test statistic which can be used to test a point null hypothesis against a high dimensional alternative, even when the number of parameters exceeds the number of samples. This test will be shown to have optimal power on average in a neighbourhood of the null hypothesis, which makes it a proper generalization of the locally most powerful test to multiple dimensions. To illustrate this new locally most powerful test we investigate the case of testing the global null hypothesis in a linear regression model in more detail. The score test is shown to have significantly more power than the F-test whenever under the alternative the large variance principal components of the design matrix explain substantially more of the variance of the outcome than do the small variance principal components. The score test is also useful for detecting sparse alternatives in truly high dimensional data, where its power is comparable with the test based on the maximum absolute t-statistic.

In real data analysis, it is often interesting to consider a general linear hypothesis testing (GLHT) problem for functional data, which includes the one-way ANOVA, post hoc, or contrast analysis as special cases. Existing tests for this GLHT problem include an L 2 -norm-based test and an F-type test but their theoretical properties have not been investigated. In addition, for functional one-way ANOVA, simulation studies in the literature indicate that they are less powerful than the globalizing pointwise F (GPF) test and the F max  -test. The GPF and F max  -test enjoy several other good properties. They are scale-invariant in the sense that their test statistics do not change if we multiply each of functional curves with a nonzero function of the observed locations. In this article, the GPF and F max  -test are adapted to the above GLHT problem. Their theoretical properties, for example, root-n consistency as well as those of the L 2 -norm-based and F-type tests are established. Intensive simulation studies are carried out to compare the finite-sample behavior of the tests under consideration in scenarios reflecting various practical characteristics of functional data. Simulation results indicate that the GPF test has higher power than other tests when the functional data are less correlated, and the F max  -test has higher power than other tests when the functional data are moderately or highly correlated. These results are also confirmed by application of the GPF and F max  tests to the corneal surface data coming from medical industry. This application suggests the new methods may help to make more clear and sure decisions in practice. For a convenient application of the considered testing procedures, their implementation is developed in the R programming language. Supplementary materials for the article are available online.

To improve the quality of construction and increase the durability of engineering structures under construction, complex geodetic works should be performed, including geodetic observations of deformations of structures. These observations are carried out during the construction of buildings and structures and their operation, mainly before the period of deformation stabilization. In this regard, a reliable statistical definition of deformations close to the limit is necessary, based on the data of geodetic observations. The research helps to improve the definition of deformations of structures using the Fischer’s F-test and the Foster-Stuart test, based on analysis of the measurements of horizontal and vertical monitoring of industrial structures. According to the results, the magnitude of the subsidence plays a more significant role from than its absolute value, thus the value of the deformation intensity is of primary importance in justifying observation periodicity.

We discuss the role that the null hypothesis should play in the construction of a test statistic used to make a decision about that hypothesis. To construct the test statistic for a point null hypothesis about a binomial proportion, a common recommendation is to act as if the null hypothesis is true. We argue that, on the surface, the one-sample t -test of a point null hypothesis about a Gaussian population mean does not appear to follow the recommendation. We show how simple algebraic manipulations of the usual t-statistic lead to an equivalent test procedure consistent with the recommendation. We provide geometric intuition regarding this equivalence and we consider extensions to testing nested hypotheses in Gaussian linear models. We discuss an application to graphical residual diagnostics where the form of the test statistic makes a practical difference. By examining the formulation of the test statistic from multiple perspectives in this familiar example, we provide simple, concrete illustrations of some important issues that can guide the formulation of effective solutions to more complex statistical problems.

There is growing interest in the use of recycled materials in the building sector as a way to reduce waste and improve environmental sustainability. Polyethylene terephthalate (PET) is a thermoplastic polymer that has attracted the attention of researchers due to its application in the building industry. In the recent past, many studies have reported on the application of PET aggregates in structural lightweight concrete. This paper presents a review of the findings of 20 studies conducted between 2010 and 2022 randomly. The preliminary findings highlighted include the method of production of PET aggregates and their physical/thermal properties. The review extended further to focus on the extent of incorporation, physical properties, strength properties, and durability of concrete with PET aggregates. The substitution of PET aggregates up to 20% reflected positively on the compressive strength, while tensile and flexural strength had positive responses up to 10%. Water absorption as a measure of concrete durability increased with the addition of PET aggregates. A meta-analysis of these findings was performed using hypothesis testing (t-test and f-test) to identify significant differences between the experimental outcomes of PET incorporation in concrete. Experimental procedures with greater tolerance for PET inclusion and satisfactory concrete properties were highlighted. The paper recommends the formulation of hybrid mix proportions, developed from experimental designs with noteworthy inclusion of PET aggregates and those that attained high values of desired concrete properties. Furthermore, optimization should be performed to provide robust mix designs for high-strength or lightweight concrete with PET aggregates.

Permutation tests based ondistances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo-F tests arising from a distance-based extension of multivariate analysis of variance. In this article, we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data.