Nonparametric Kernel Method Research Articles

Hedging downside risk in agricultural commodities: A novel nonparametric kernel method

Using a nonparametric kernel method, this paper develops a weighted conditional value-at-risk hedge model to hedge downside risks in agricultural commodities. The model exhibits convexity, ensuring the acquisition of its global optimal solution. Simulations show that the nonparametric kernel method enhances the accuracy of the weighted conditional value-at-risk and hedge ratio determination, outperforming traditional estimation methods. Using major agricultural commodities, empirical evidence shows the superiority of the proposed model in reducing downside risks, compared to the minimum variance, minimum value-at-risk, and minimum conditional value-at-risk hedge models.

Beampattern analysis of cooperative beamforming with carrier frequency offsets in three-dimensional wireless networks

Cooperative beamforming (CB), where spatially distributed nodes synchronize their transmit phases to maximize the power of their combined signal at a desired receiver, can be used as an effective solution for hardware-limited nodes to achieve communication range extension. Thus, CB demonstrates effectiveness in providing higher reliability, lower latency, and extended transmission range for nodes in non-terrestrial networks (NTNs), which inherently face power and hardware limitations. In this paper, we consider the CB technique using UAVs in three-dimensional (3D) networks and analyze the average beampattern of the virtual antenna array constructed by the multiple UAVs. Further, because the mobile nature of the UAVs may cause carrier frequency offsets (CFOs), we analyze the impact of the CFO using the non-parametric kernel method. The simulation and analytical results show that the peak average beampattern degrades by about 3 dB with the CFO standard deviation of 1 kHz, which emphasizes the significance of frequency synchronization.

Kernel method for estimating overlapping coefficient using numerical integration methods

In this paper, we proposed three nonparametric kernel estimators for the overlapping Weitzman measure Δ. Due to the difficulty of finding a general expression for Δ when the nonparametric kernel method is adopted, we suggest using the numerical integration method as the first stage of our estimation process. In particular, three numerical integration rules are considered, which are known as, trapezoidal and Simpson rules. The statistical properties of the resulting estimators are studied and investigated by using the simulation technique and their performances are also compared with some existing nonparametric kernel estimators developed by Eidous and Al-Talafhah (2020). The numerical results demonstrated the superiority and usefulness of the proposed technique over that suggested by Eidous and Al-Talafhah in estimating the overlapping measure Δ.

A practical multivariate approach to testing volatility spillover

We propose an asymptotic N(0,1) inferential strategy to test for volatility spillover between markets consisting of multiple sectors. First, we use nonparametric kernel method to derive test statistics that assign flexible weight to each lag order and are able to check a growing number of lags as the sample size increases. Second, we propose a practical multivariate volatility modeling approach — which enjoys estimation consistency and simplicity — to facilitate higher dimensional spillover testing. Simulations show the reasonable finite sample performance of the proposed econometric strategy in a relatively large system. An empirical application highlights the merits of the proposed approach.

Parallel computing in finance for estimating risk-neutral densities through option prices

Option pricing is one of the most active Financial Economics research fields. Black-Scholes-Merton option pricing theory states that risk-neutral density is lognormal. However, markets' pieces of evidence do not support that assumption. More realistic assumptions impose substantial computational burdens to calculate option pricing functions. Risk-neutral density is a pivotal element to price derivative assets, which can be estimated through nonparametric kernel methods. A significant computational challenge exists for determining optimal kernel bandwidths, addressed in this study through a parallel computing algorithm performed using Graphical Processing Units. The paper proposes a tailor-made Cross-Validation criterion function used to define optimal bandwidths. The selection of optimal bandwidths is crucial for nonparametric estimation and is also the most computationally intensive. We tested the developed algorithms through two data sets related to intraday data for VIX and S&P500 indexes.

Energy risk measurement and hedging analysis by nonparametric conditional value at risk model

The accurate measurement and management of energy risk have become important issues of the economic development and energy security for all countries. The existing literature generally adopts the Value at Risk (VaR). However, VaR does not satisfy the subadditivity axiom to measure the energy risk, which makes the calculation defective. In this paper, we use the Conditional VaR (CVaR) with the characteristics of coherent and convex risk measurement to measure energy risk under nonparametric kernel (NPK) framework. We consider how to use the energy derivatives to hedge the price risk of energy so that the result is more reasonable and effective. The empirical results show that the NPK method that we propose is more effective to measure the actual energy risk and carry out more effective risk hedging.

Nonparametric mean-lower partial moment model and enhanced index investment

In this study, we propose a new smooth nonparametric kernel (NPK) method to estimate downside risk as measured by the lower partial moment (LPM) and build a NPK mean-LPM model. We also use the NPK LPM to construct a novel enhanced index model for controlling downside risk. We theoretically prove that the NPK LPM estimator is a convex function when the order of the LPM is equal to or greater than 1. The numerical results show that our NPK method outperforms the moment method in terms of estimation accuracy. Our simulated experiments and empirical tests show that the NPK LPM-based enhanced index model outperforms the benchmark models and indexes when using a wide variety of performance indicators and different rebalancing strategies.

Asymptotic normality for kernel weighted averages estimation

This paper presents a set of general normality results for kernel weighted averages. We extend existing results in literature for independent data a s in Yao (2017) to stationary dependent longitudinal data. The asymptotic properties of the proposed weighted averages are investigated under \(\alpha\)-mixing conditions. These results are useful for covariance function estimation based on nonparametric kernel method.

A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations

The nonlinear autoregressive models under normal innovations are commonly used for nonlinear time series analysis in various fields. However, using this class of models for modeling skewed data leads to unreliable results due to the disability of these models for modeling skewness. In this setting, replacing the normality assumption with a more flexible distribution that can accommodate skewness will provide effective results. In this article, we propose a partially linear autoregressive model by considering the skew normal distribution for independent and dependent innovations. A semiparametric approach for estimating the nonlinear part of the regression function is proposed based on the conditional least squares approach and the nonparametric kernel method. Then, the conditional maximum-likelihood approach is used to estimate the unknown parameters through the expectation-maximization (EM) algorithm. Some asymptotic properties for the semiparametric method are established. Finally, the performance of the proposed model is verified through simulation studies and analysis of a real dataset.

Three-factor mean reverting Ornstein-Uhlenbeck process with stochastic drift term innovations: Nonlinear autoregressive approach with dependent error

This paper introduces a novel approach, withen the context of energy market, by employing a three-factor mean reverting Ornstein-Uhlenbeck process with a stochastic nonlinear autoregressive drift term having a dependent error. Initially the unique solvability for the given nonlinear system is investigated. Then, to estimate the nonlinear regression function, a semiparametric method, based on the conditional least square estimator for the parametric approach, and the nonparametric kernel method for autoregressive modification estimation have been presented . A maximum likelihood estimator has been used for parameter estimation of the Ornstein-Uhlenbeck process. Finally, some numerical simulations and real data studies have been provided to support the main conclusions of the study.

Nonparametric Assessment of Aftershock Clusters of the Maule Earthquake Mw = 8.8

We study the spatial distribution of clusters associated to the aftershocks of the megathrust Maule earthquake MW 8.8 of 27 February 2010. We used a recent clustering method which hinges on a nonparametric estimation of the underlying probability density function to detect subsets of points forming clusters associated with high density areas. In addition, we estimate the probability density function using a nonparametric kernel method for each of these clusters. This allows us to identify a set of regions where there is an association between frequency of events and coseismic slip. Our results suggest that high coseismic slip is spatially related to high aftershock frequency.

Estimation of the reliability function of the Rayleigh distribution using some robust and kernel methods

The research presents the reliability. It is defined as the probability of accomplishing any part of the system within a specified time and under the same circumstances. On the theoretical side, the reliability, the reliability function, and the cumulative function of failure are studied within the one-parameter Raleigh distribution. This research aims to discover many factors that are missed the reliability evaluation which causes constant interruptions of the machines in addition to the problems of data. The problem of the research is that there are many methods for estimating the reliability function but no one has suitable qualifications for most of these methods in the data such as the presence of anomalous values or extreme values or the appropriate distribution of these data is unknown. Therefore, the data need methods through which can be dealt with this problem. Two of the estimation methods have been used: the robust (estimator M) method and the nonparametric Kernel method. These estimation methods are derived to arrive at the formulas of their capabilities. A comparison of these estimations is made using the simulation method as it is implemented. Simulation experiments using different sample sizes and each experiment is repeated (1000) times to achieve the objective. The results are compared by using one of the most important statistical measures which is the mean of error squares (MSE). The best estimation method has been reached is the robust (M estimator) method. It has been shown that the estimation of the reliability function gradually decreases with time, and this is identical to the properties of this function.

Longitudinal Deep Kernel Gaussian Process Regression

Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, \ie irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They rely on ad hoc heuristics or expensive trial and error to choose the effective kernels, and (ii) They fail to handle multilevel correlation structure in the data. We introduce Longitudinal deep kernel Gaussian process regression (L-DKGPR) to overcome these limitations by fully automating the discovery of complex multilevel correlation structure from longitudinal data. Specifically, L-DKGPR eliminates the need for ad hoc heuristics or trial and error using a novel adaptation of deep kernel learning that combines the expressive power of deep neural networks with the flexibility of non-parametric kernel methods. L-DKGPR effectively learns the multilevel correlation with a novel additive kernel that simultaneously accommodates both time-varying and the time-invariant effects. We derive an efficient algorithm to train L-DKGPR using latent space inducing points and variational inference. Results of extensive experiments on several benchmark data sets demonstrate that L-DKGPR significantly outperforms the state-of-the-art longitudinal data analysis (LDA) methods.

Generalized Birnbaum–Saunders kernel for hazard rate function estimation

This paper proposes the nonparametric kernel method for the hazard rate (HR) function estimation in the context of positively skewed data. The class of generalized Birnbaum-Saunders (GBS) kernels is considered because of its several interesting properties and flexibility. Some asymptotic properties, such as bias, variance and mean integrated squared error (MISE) are established for the proposed estimator. In addition, we demonstrate that, the GBS-HR estimator is strongly consistent and asymptotically normal. The choice of bandwidth is also investigated by rule of thumb and unbiased cross validation approaches. Finally, performances of the HR estimator based on GBS kernels and comparison of the two bandwidth selection methods are illustrated by a simulation study and real applications.

ESTIMATION OF TIME-VARYING COVARIANCE MATRICES FOR LARGE DATASETS

Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently, there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or nonparametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible dependence and heavy-tailed distributions. In this paper, we introduce a nonparametric version of regularization techniques for sparse large covariance matrices, developed by Bickel and Levina (2008) and others. We focus on the robustness of such a procedure to time variation, dependence and heavy-tailedness of distributions. The paper includes a set of results on Bernstein type inequalities for dependent unbounded variables which are expected to be applicable in econometric analysis beyond estimation of large covariance matrices. We discuss the utility of the robust thresholding method, comparing it with other estimators in simulations and an empirical application on the design of minimum variance portfolios.

Density estimation on an unknown submanifold

We investigate the estimation of a density f from a n-sample on an Euclidean space RD, when the data are supported by an unknown submanifold M of possibly unknown dimension d<D, under a reach condition. We investigate several nonparametric kernel methods, with data-driven bandwidths that incorporate some learning of the geometry via a local dimension estimator. When f has Holder smoothness β and M has regularity α, our estimator achieves the rate n−α∧β∕(2α∧β+d) for a pointwise loss. The rate does not depend on the ambient dimension D and we establish that our procedure is asymptotically minimax for α≥β. Following Lepski’s principle, a bandwidth selection rule is shown to achieve smoothness adaptation. We also investigate the case α≤β: by estimating in some sense the underlying geometry of M, we establish in dimension d=1 that the minimax rate is n−β∕(2β+1) proving in particular that it does not depend on the regularity of M. Finally, a numerical implementation is conducted on some case studies in order to confirm the practical feasibility of our estimators.

교차검증 대역폭 결정 기반의 커널평탄화 기법을 응용한 2단계 포트폴리오 최적화

Well-known portfolio selection processes often employ either a mean-variance or expected utility framework. This paper deals with a portfolio selection process based on shortfall chance. Onerecent portfolio selection study based on shortfall chance used the nonparametric kernel method with Silverman’s bandwidth choice. This bandwidth choice assumes that the data distribution of interest is Gaussian. However, this bandwidth choice may be ineffective, as numerous empirical studies refer that financial asset returns are not Gaussian. Accordingly, an alternative method is proposed in this paper, based on the bandwidth choice with cross-validation criterion. In order to show the effectiveness of the proposed method, it is applied to simulated data from three non-Gaussian distributions and empirical data from three stock markets. The results of these experiments illustrate that the proposed method performs similarly or better than three conventional portfolio selection methods that respectively rely on Silverman’s bandwidth choice, Sharpe Ratio, and Stutzer’s PPI.

A new family of kernels from the beta polynomial kernels with applications in density estimation

One of the fundamental data analytics tools in statistical estimation is the non-parametric kernel method that involves probability estimates production. The method uses the observations to obtain useful statistical information to aid the practicing statistician in decision making and further statistical investigations. The kernel techniques primarily examine essential characteristics in a data set, and this research aims to introduce new kernel functions that can easily detect inherent properties in any given observations. However, accurate application of kernel estimator as data analytics apparatus requires the kernel function and smoothing parameter that regulates the level of smoothness applied to the estimates. A plethora of kernel functions of different families and smoothing parameter selectors exist in the literature, but no one method is universally acceptable in all situations. Hence, more kernel functions with smoothing parameter selectors have been propounded customarily in density estimation. This article proposes a distinct kernel family from the beta polynomial kernel family using the exponential progression in its derivation. The newly proposed kernel family was evaluated with simulated and life data. The outcomes clearly indicated that this kernel family could compete favorably well with other kernel families in density estimation. A further comparison of numerical results of the new family and the existing beta family revealed that the new family outperformed the classical beta kernel family with simulation and real data examples with the aid of asymptotic mean integrated squared error (AMISE) as criterion function. The information obtained from the data analysis of this research could be used for decision making in an organization, especially when human and material resources are to be considered. In addition, Kernel functions are vital tools for data analysis and data visualization; hence the newly proposed functions are vital exploratory tools.

Probabilistic Data-Driven Prognostic Methodology for Proton Exchange Membrane Fuel Cells

&#x0D; &#x0D; &#x0D; Hydrogen fuel cells, particularly proton exchange membrane fuel cells (PEMFC), are promising, robust, clean energy sources. However, their high cost and short lifespan under dynamic loads impedes their widespread usage. Accurate and real-time prognostics, especially remaining useful time (RUL) estimation, can help ameliorate the commercial viability of PEMFCs. Data-driven methods are increasingly considered for RUL estimation. This paper looks at two such methods – Gaussian Process Regression (GPR) and Long-Short Term Memory (LSTM) Networks and assesses them in terms of accuracy and suitability for real-time applications when tested against the IEEE PHM Challenge 2014 data set. Gaussian Process Regression is a non-parametric kernel method. LSTM, on the other hand, is a recurrent neural network based architecture that is effective at detecting both long term and short term trends in time series predictions. For the cases investigated here, the results derived using LSTM are more accurate, especially since they effectively capture long term trends. However, GPR assigns a probability to its prediction - a desirable aspect in a real-time setting so that corrective action can be applied appropriately. The paper then proposes the use of a variant of these methods - Gaussian Process-Long Short Term Memory Network (GP-LSTM) as an alternative that combines the higher accuracies of the LSTM method and the probabilistic output from GPR. The results attained using GP-LSTM are close in accuracy to the LSTM results and have a probability associated with them, making them suitable for real-time applications. The effectiveness of GP-LSTM is further proven using a dynamic data set and strategies are suggested to appropriately apply GP-LSTM to real-world scenarios.&#x0D; &#x0D; &#x0D;

Nonparametric estimation of time varying correlation coefficient

We propose a new time varying correlation coefficient, which is a local correlation measure of a pair of time series. The time varying correlation coefficient is locally estimated using a nonparametric kernel method. Asymptotic normality of the estimated time varying correlation is established, which allows us to construct statistical methods of confidence interval and hypothesis tests. Finite sample validity of the proposed methods are demonstrated by a Monte–Carlo study. The proposed time varying correlation coefficient method is well illustrated by an analysis of five sets of world major stock price index returns.