In this paper, we consider a new method dealing with the problem of estimating the scoring function ${\gamma }_a$, with a constant $a$, in functional space and an unknown scale parameter under a nonparametric robust regression model. Based on the $k$ Nearest Neighbors ( $k$NN) method, the primary objective is to prove the asymptotic normality aspect in the case of a stationary ergodic process of this estimator. We begin by establishing the almost certain convergence of a conditional distribution estimator. Then, we derive the almost certain convergence (with rate) of the conditional median (scale parameter estimator) and the asymptotic normality of the robust regression function, even when the scale parameter is unknown. Finally, the simulation and real-world data results reveal the consistency and superiority of our theoretical analysis in which the performance of the $k$NN estimator is comparable to that of the well-known kernel estimator, and it outperforms a nonparametric series (spline) estimator when there are irrelevant regressors.

This paper aims to investigate a semi-functional partial linear regression model in the presence of missing data in the response variable under the missing at random mechanism. We construct estimators using the kNN-local linear method and establish the asymptotic distribution of the parametric component. Additionally, the uniform almost complete consistency rates for the nonparametric component with respect to the number of neighbors under appropriate conditions is derived. Through simulations and real data analysis, we assess the effectiveness of the proposed approach and demonstrate its superiority by comparing it with existing methods for semi-functional partial linear regression models.

To improve the performance of genetic algorithms (GAs) in complex optimization settings, this work offered two novel real-coded crossover operators: one based on the Gumbel distribution (GX) and the other on the Rayleigh distribution (RX). These innovative operators, when combined with three different mutation techniques, created a significant improvement in GA methodology. Our meticulous simulations showed that the GX operator significantly outperformed RX and other traditional operators, demonstrating its superior capacity to address complex optimization problems. The GX operator's unusual robustness was further validated through detailed performance analysis utilizing the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) multi-criteria decision-making technique, setting a new standard in crossover operator design and significantly improving the state of the art in GAs.

Analyzing the real impact of spatial dependency in financial time series data is crucial to financial risk management. It has been a challenging issue in the last decade. This is because most financial transactions are performed via the internet and the spatial dependency between different international stock markets is not standard. The present paper investigates functional expectile regression as a spatial financial risk model. Specifically, we construct a nonparametric estimator of this functional model for the functional single index regression (FSIR) structure. The asymptotic properties of this estimator are elaborated over general spatial settings. More precisely, we establish Borel-Cantelli consistency (BCC) of the constructed estimator. The latter is obtained with the precision of the convergence rate. A simulation investigation is performed to show the easy applicability of the constructed estimator in practice. Finally, real data analysis about the financial data (Euro Stoxx-50 index data) is used to illustrate the effectiveness of our methodology.

Financial risk management using the generalized autoregressive conditional heteroskedasticity model is a primordial topic in financial data analysis. It helps to improve risk assessment accuracy by taking into account the time-varying volatility. In this paper, we improved this feature by analyzing the functional nature of the high-frequency financial data. Specifically, we investigated the nonparametric estimation method of the multifunctional expectile function based on a kernel technique, developed the estimator, and established its stochastic consistency. The obtained asymptotic result provided a good mathematical foundation allowing us to enhance the expectile applicability in financial risk analysis. We assessed the algorithm's efficiency through empirical testing, and illustrated the practical value of expectile estimation in multi-asset risk management by applying it to real-world financial data with diverse scenarios.

Functional statistics is a new technique for dealing with data that can be viewed as curves or images. Parallel to this approach, the Near-Infrared Reflectance (NIR) spectroscopy methodology has been used in modern chemistry as a rapid, low-cost, and exact means of assessing an object’s chemical properties. In this research, we investigate the quality of corn and cookie dough by analyzing the spectroscopic technique using certain cutting-edge statistical models. By analyzing spectral data and applying functional models to it, we could predict the chemical components of corn and cookie dough. Kernel Functional Classical Estimation (KFCE), Kernel Functional Quantile Estimation (KFQE), Kernel Functional Expectile Estimation (KFEE), Semi-Partial Linear Functional Classical Estimation (SPLFCE), Semi-Partial Linear Functional Quantile Estimation (SPLFQE), and Semi-Partial Linear Functional Expectile Estimation (SPLFEE) are models used to accurately estimate the different quantities present in Corn and Cookie dough. The selection of these functional models is based on their ability to construct a forecast region with a high level of confidence. We demonstrate that the considered models outperform traditional models such as the partial least-squares regression and the principal component regression in terms of prediction accuracy. Furthermore, we show that the proposed models are more robust than competing models such as SPLFQE and SPLFEE in the sense that data heterogeneity has no effect on their efficiency.