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Marek Pokropski's "Mechanisms and Consciousness Integrating Phenomenology with Cognitive Science" reopens the question about the possibility of naturalization of phenomenology. The author adopts the position of nonreductive mechanistic integration, which, he claims, has offered new methodological perspectives for studying complex mental phenomena such as consciousness. In this paper, I outline the context of the discussions on the relationship between phenomenology and cognitive sciences, and (§2) discuss the approach proposed by Pokropski, pointing out the main arguments and the most important research achievements. Then I focus on some difficulties of this position. The first of these I associate with a procedure which I call a dismemberment of phenomenology (§3). The second (§4) concerns the concept of constraint, which is key to Pokropski's analyzes, and some consequences of its application and alternative reading. Finally, in §5 I draw attention to two difficulties. The first is whether it is possible to read phenomenology in terms of functional analysis; the second is related to the doubt whether psychological or phenomenological functional explanations can be treated as mechanistic (which is a strong premise of Pokropski's argument). In Conclusion I make an overall assessment of the presented approach. [ABSTRACT FROM AUTHOR]

This paper develops a new nonparametric estimator of the scalar-on function modal regression that is used to analyse the co-variability between a functional regressor and a scalar output variable. The new estimator inherits the smoothness of the kernel method and the robustness of the quantile regression. We assume that the functional observations are structured as a strong mixing functional time series data and we establish the almost complete consistency (with rate) of the constructed estimator. A discussion highlighting the impact of this new estimator in nonparametric functional data analysis is also given. The usefulness of this new estimator is shown using an artificial data example. [ABSTRACT FROM AUTHOR]

Tecator dataset has been widely used in the content of functional data analysis. As far as we know, this dataset is only considered under mean regression, which is easily affected by outliers. However, there are 8 more fat samples and 17 more protein samples in this dataset, so, in this paper, we explore this dataset by quantile regression, which is a robust method. Single-index partially functional linear quantile regression is proposed, and B-splines are used to estimate the unknown link function in the single-index component and the unknown slope function in the functional linear component. We establish the convergence rates and asymptotic normality of the estimators. Simulation studies and a real data application are presented to illustrate the performance of the proposed methodologies. [ABSTRACT FROM AUTHOR]

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for the use of smoothing techniques that annihilate the noise. At the same time, imposing the smoothness assumption excludes a considerable range of stochastic processes, most notably diffusion processes. Under perfect observation of the sample paths, such processes would not need to be excluded from the realm of functional data analysis. In this paper, we introduce a careful modification of existing methods, dubbed the 'reflected triangle estimator', and show that this allows for the functional data analysis of processes with nowhere differentiable sample paths, even when these are discretely and noisily observed, including under irregular and sparse designs. Our estimator matches the established rates of convergence for processes with smooth paths, and furthermore attains the same optimal rates as one would get under perfect observation. Thus, with reflected triangle estimation, the scope of applicability of much of the methodology developed for discretely/irregularly/noisily/sparsely sampled functional data is considerably extended. By way of simulation it is shown that the advantages furnished are reflected in practice, hinting at potential closer links with the field of diffusion inference. [ABSTRACT FROM AUTHOR]

In Selk, L., and Gertheiss, J. [(2022), 'Nonparametric Regression and Classification with Functional, Categorical, and Mixed Covariates', Advances in Data Analysis and Classification] a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, so that both classification and regression problems are considered. In the paper at hand the asymptotic properties of this method are studied. A uniform convergence rate for the regression / classification estimator is given. It is further shown that a data-driven least squares cross-validation method can asymptotically remove irrelevant noise variables automatically. [ABSTRACT FROM AUTHOR]