• Journal of IKEEE
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• v.28 no.1
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• pp.6-13
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• 2024

This paper proposes an approach to detect abnormal data in automotive controller area network (CAN) using an unsupervised learning model, i.e. autoencoder and Gaussian kernel density estimation function. The proposed autoencoder model is trained with only message ID of CAN data frames. Afterwards, by employing the Gaussian kernel density estimation function, it effectively detects abnormal data based on the trained model characterized by the optimally determined number of frames and a loss threshold. It was verified and evaluated using four types of attack data, i.e. DoS attacks, gear spoofing attacks, RPM spoofing attacks, and fuzzy attacks. Compared with conventional unsupervised learning-based models, it has achieved over 99% detection performance across all evaluation metrics.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.361-368
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• 1993

In recent years, kernel type estimates are abundant. In this paper, we propose a bandwidth selection method for kernel regression of fixed design based on bootstrap procedure. Mathematical properties of proposed bootstrap-based bandwidth selection method are discussed. Performance of the proposed method for small sample case is compared with that of cross-validation method via a simulation study.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1049-1058
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• 2012

Nonparametric methods are often used as an alternative to parametric methods to estimate density function and regression function. In this paper we consider improved methods to select the Bezier points in Bezier curve smoothing that is shown to have the same asymptotic properties as the kernel methods. We show that the proposed methods are better than the existing methods through numerical studies.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.3
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• pp.627-632
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• 2021

ITL (information-theoretic learning) has been applied successfully to adaptive signal processing and machine learning applications, but there are difficulties in deciding the kernel size, which has a great impact on the system performance. The correntropy algorithm, one of the ITL methods, has superior properties of impulsive-noise robustness and channel-distortion compensation. On the other hand, it is also sensitive to the kernel sizes that can lead to system instability. In this paper, considering the sensitivity of the kernel size cubed in the denominator of the cost function slope, a new adaptive kernel estimation method using the rate of change in error power in respect to the kernel size variation is proposed for the correntropy algorithm. In a distortion-compensation experiment for impulsive-noise and multipath-distorted channel, the performance of the proposed kernel-adjusted correntropy algorithm was examined. The proposed method shows a two times faster convergence speed than the conventional algorithm with a fixed kernel size. In addition, the proposed algorithm converged appropriately for kernel sizes ranging from 2.0 to 6.0. Hence, the proposed method has a wide acceptable margin of initial kernel sizes.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.125-136
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• 2020

In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's H-function kernel. We employ a known differentiation formula of Fox's H-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.503-512
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• 2006

In this paper, the Inverse Weibull distribution parameters have been estimated using a new estimation technique based on the non-parametric kernel density function that introduced as an alternative and reliable technique for estimation in life testing models. This technique will require bootstrapping from a set of sample observations for constructing the density functions of pivotal quantities and thus the confidence intervals for the distribution parameters. The performances of this technique have been studied comparing to the conditional inference on the basis of the mean lengths and the covering percentage of the confidence intervals, via Monte Carlo simulations. The simulation results indicated the robustness of the proposed method that yield reasonably accurate inferences even with fewer bootstrap replications and it is easy to be used than the conditional approach. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.905-912
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• 2009

We propose a doubly penalized kernel machine (DPKM) which uses heteroscedastic location-scale model as basic model and estimates both mean and volatility functions simultaneously by kernel machines. We also present the model selection method which employs the generalized approximate cross validation techniques for choosing the hyperparameters which affect the performance of DPKM. Artificial examples are provided to indicate the usefulness of DPKM for the mean and volatility functions estimation.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.193-211
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• 2012

This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we consider $Z_i=(X_i,Y_i)$, $i{\in}\mathbb{N}^N$ be a $\mathcal{F}{\times}\mathbb{R}$-valued measurable strictly stationary spatial process, where $\mathcal{F}$ is a semi-metric space and we study the spatial interaction of $X_i$ and $Y_i$ via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.327-336
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• 2001

This work concerns estimating a regression function, which is not linear, using aggregate data. In much of the empirical research, data are aggregated for various reasons before statistical analysis. In a traditional parametric approach, a linear estimation of the non-linear function with aggregate data can result in unstable estimators of the parameters. More serious consequence is the bias in the estimation of the non-linear function. The approach we employ is the kernel regression smoothing. We describe the conditions when the aggregate data can be used to estimate the regression function efficiently. Numerical examples will illustrate our findings.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.59-78
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• 2004

A regression function in generalized linear model may have a discontinuity/change point at unknown location. In order to estimate the location of the discontinuity point and its jump size, the strategy is to use a nonparametric approach based on one-sided kernel weighted local-likelihood functions. Weak convergences of the proposed estimators are established. The finite-sample performances of the proposed estimators with practical aspects are illustrated by simulated examples.