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Wigner-Ville transform or Wigner-Ville distribution (WVD) associated with quaternion offset linear canonical transform (QOLCT) was proposed by Bhat and Dar. This work is devoted to the development of the theory proposed by them, which is an emerging tool in the scenario of signal processing. The main contribution of this work is to introduce WVD and ambiguity function (AF) associated with the QOLCT (WVD-QOLCT/AF-QOLCT). First, the definition of the WVD-QOLCT is proposed, and then several important properties such as dilation, nonlinearity, and boundedness are derived. Second, we derived the AF for the proposed transform. A bunch of important properties, including the reconstruction formula associated with the AF, are studied.

This paper proposes a new family of robust non-parametric estimators for regression functions by applying polynomials to construct a robust regression estimator. Theoretical results and tests on simulated and real data sets validate the efficiency and practicality of the approach. Moreover, some of its asymptotic properties are discussed and demonstrated. Experimental studies are conducted to compare this new approach with the Bernstein-Nadaraya-Watson estimator and the Nadaraya-Watson estimators. Some simulations are performed to illustrate that our robust estimator has the lowest average integrated squared error ( A I S E ¯ ). In the end, real data is utilized to assess the performance of conventional and newly presented robust regression algorithms regarding their ability to handle sensitivity to outliers. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Estimation of the population variance is of major concern in numerous examinations and ratio estimators are mainstream choices for it. It is a typical practice to utilize conventional central moments to construct variance estimators utilizing auxiliary information. However, conventional central moments give equal weight to each observation and hence highly affected by extreme values. For solving this issue, some recent developments are available in literature based on non-conventional/robust characteristics (inter-decile range, mid-range, etc.) of an auxiliary variable with conventional central moments under a simple random sampling scheme. This article initially, defines a family of ratio type variance estimators based on an adaptation of existing estimators with conventional central moments and non-conventional/robust characteristics of the auxiliary variable under a stratified random sampling scheme. After that, a novel family of variance estimators is proposed, in the presence of extreme values. The novel family of variance estimators is based on L-moments and calibration approach with some suitable constraints which can provide enhance the estimation of the population variance. We utilize L-moments characteristics (L-location, L-scale, and L-CV) for the purposes of the article. The variance expression of the novel family is also provided. Empirical illustrations are done using real and artificial data sets. The percentage relative efficiency is used for assessing the performances of adapted and novel families of estimators. [ABSTRACT FROM AUTHOR]

We consider the problem of nonparametric estimation of certain conditional models when the explanatory variable is functional. The models studied are the Conditional Expectation (CE), the Conditional Distribution Function (CDF) and the Conditional Probability Density (CPD). The estimators are constructed by combining the local linear method and the k-Nearest Neighbors (kNN) smoothing approach. For each of the three models, we define an optimal estimator associated with the best number of neighbors chosen using two bandwidth selection procedures which are the cross-validation criterion and the bootstrap smoothing rule. The asymptotic properties of these optimal kNN Local Linear Estimators ( k NN- LLE) are established under some standard conditions. The performances of the finite samples of these estimators are then examined and compared through a Monte-carlo study. In addition, an application on the riboflavin content in the yogurt using the Near-infrared curves is carried out to demonstrate the usefulness of the models proposed in the point-wise prediction as well as for the predictive interval. [ABSTRACT FROM AUTHOR]

Analyzing the co-variability between the Hilbert regressor and the scalar output variable is crucial in functional statistics. In this contribution, the kernel smoothing of the Relative Error Regression (RE-regression) is used to resolve this problem. Precisely, we use the relative square error to establish an estimator of the Hilbertian regression. As asymptotic results, the Hilbertian observations are assumed to be quasi-associated, and we demonstrate the almost complete consistency of the constructed estimator. The feasibility of this Hilbertian model as a predictor in functional time series data is discussed. Moreover, we give some practical ideas for selecting the smoothing parameter based on the bootstrap procedure. Finally, an empirical investigation is performed to examine the behavior of the RE-regression estimation and its superiority in practice. [ABSTRACT FROM AUTHOR]

Traditionally, regression problems are examined using univariate characteristics, including the scale function, marginal density, regression error, and regression function. When the correlation between the response and the predictor is reasonably straightforward, these qualities are helpful and instructive. Given the predictor, the response's conditional density provides more specific information regarding the relationship. This study aims to examine a nonparametric estimator of a scalar response variable's function of a density and mode, given a functional variable when the data are spatially dependent. The estimator is then derived and established by combining the local linear and the k nearest neighbors methods. Next, the suggested estimator's uniform consistency in the number of neighbors (UNN) is proved. Finally, to demonstrate the efficacy and superiority of the acquired results, we applied our new estimator to simulated and real data and compared it to the existing competing estimator. Traditionally, regression problems are examined using univariate characteristics, including the scale function, marginal density, regression error, and regression function. When the correlation between the response and the predictor is reasonably straightforward, these qualities are helpful and instructive. Given the predictor, the response's conditional density provides more specific information regarding the relationship. This study aims to examine a nonparametric estimator of a scalar response variable's function of a density and mode, given a functional variable when the data are spatially dependent. The estimator is then derived and established by combining the local linear and the nearest neighbors methods. Next, the suggested estimator's uniform consistency in the number of neighbors (UNN) is proved. Finally, to demonstrate the efficacy and superiority of the acquired results, we applied our new estimator to simulated and real data and compared it to the existing competing estimator. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new method dealing with the problem of estimating the scoring function γ 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. [ABSTRACT FROM AUTHOR]

Nonparametric (distribution-free) control charts have been introduced in recent years when quality characteristics do not follow a specific distribution. When the sample selection is prohibitively expensive, we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts. In this study, we proposed a nonparametric homogeneously weighted moving average based on the Wilcoxon signed-rank test with ranked set sampling (NPHWMARSS) control chart for detecting shifts in the process location of a continuous and symmetric distribution. Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed NPHWMARSS control chart. The proposed NPHWMARSS control chart’s performance is compared to that of parametric and nonparametric control charts. These control charts include the exponentially weighted moving average (EWMA) control chart, Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart, the nonparametric EWMA sign control chart, Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart, and the homogeneously weighted moving average control charts. The findings show that the proposed NPHWMARSS control chart performs better than its competitors, particularly for the small shifts. Finally, an example is presented to demonstrate how the proposed scheme can be implemented practically. [ABSTRACT FROM AUTHOR]

At present Bayesian Networks (BN) are being used widely for demonstrating uncertain knowledge in many disciplines, including biology, computer science, risk analysis, service quality analysis, and business. But they suffer from the problem that when the nodes and edges increase, the structure learning difficulty increases and algorithms become inefficient. To solve this problem, heuristic optimization algorithms are used, which tend to find a near-optimal answer rather than an exact one, with particle swarm optimization (PSO) being one of them. PSO is a swarm intelligence-based algorithm having basic inspiration from flocks of birds (how they search for food). PSO is employed widely because it is easier to code, converges quickly, and can be parallelized easily. We use a recently proposed version of PSO called generalized particle swarm optimization (GEPSO) to learn bayesian network structure. We construct an initial directed acyclic graph (DAG) by using the max-min parent’s children (MMPC) algorithm and cross relative average entropy. This DAG is used to create a population for the GEPSO optimization procedure. Moreover, we propose a velocity update procedure to increase the efficiency of the algorithmic search process. Results of the experiments show that as the complexity of the dataset increases, our algorithm Bayesian network generalized particle swarm optimization (BN-GEPSO) outperforms the PSO algorithm in terms of the Bayesian information criterion (BIC) score. [ABSTRACT FROM AUTHOR]

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 leasts-quares 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. [ABSTRACT FROM AUTHOR]