New Results on Elliptic Equations with Nonlocal Boundary Coefficient-Operator Conditions in UMD Spaces: Noncommutative Cases

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Predicting temperature curve based on fast kNN local linear estimation of the conditional distribution function

Predicting the yearly curve of the temperature, based on meteorological data, is essential for understanding the impact of climate change on humans and the environment. The standard statistical models based on the big data discretization in the finite grid suffer from certain drawbacks such as dimensionality when the size of the data is large. We consider, in this paper, the predictive region problem in functional time series analysis. We study the prediction by the shortest conditional modal interval constructed by the local linear estimation of the cumulative function of $Y$Y given functional input variable $X$X . More precisely, we combine the $k$k -Nearest Neighbors procedure to the local linear algorithm to construct two estimators of the conditional distribution function. The main purpose of this paper is to compare, by a simulation study, the efficiency of the two estimators concerning the level of dependence. The feasibility of these estimators in the functional times series prediction is examined at the end of this paper. More precisely, we compare the shortest conditional modal interval predictive regions of both estimators using real meteorological data

Estimating the Conditional Density in Scalar-On-Function Regression Structure: <i>k</i>-N-N Local Linear Approach

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator

Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data

In this paper, we study the nonparametric estimation of the expected shortfall regression when the exogenous observation is functional. The constructed estimator is obtained by combining the double kernels estimator of both conditional value at risk and conditional density function. The asymptotic proprieties of this estimator are established under weak dependency condition. Precisely, we assume that the observations are generated from quasi-associated functional time series and we prove the almost complete convergence of the constructed estimator. This asymptotic result is obtained under a standard condition of functional time series analysis. The finite sample performance of this estimator is evaluated using artificial data

Estimating the Conditional Density in Scalar-On-Function Regression Structure: k-N-N Local Linear Approach

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator