A note on nonparametric density deconvolution by weighted kernel estimators

Lee, Sungho The Korean Data and Information Science Society 2014 한국데이터정보과학회지 Vol.25 No.4

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

A note on nonparametric density deconvolution by weighted kernel estimators

이성호 한국데이터정보과학회 2014 한국데이터정보과학회지 Vol.25 No.4

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

A note on nonparametric density deconvolution by weighted kernel estimators

Sung Ho Lee 한국데이터정보과학회 2014 한국데이터정보과학회지 Vol.25 No.4

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement er-ror, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double expo-nentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density es-timator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

A gamma kernel density estimation for insurance loss data

Jeon, Y.,Kim, J.H.T. North-Holland, Pub. Co ; Elsevier Science Ltd 2013 Insurance, mathematics & economics Vol.53 No.3

Fitting insurance loss data can be challenging because of their non-negativity, asymmetry, skewness, and possible multi-modality. Though many parametric models have been used in the actuarial literature, these difficulties call for more flexible models for actuarial applications. In this paper, we propose a new class of gamma kernel density estimators (GKDEs) based on the gamma density. We prove that the density of the proposed model converges to that of any loss random variable which is non-negative and continuous, and establish its rate of convergence, under some technical conditions. The proposed model has several advantages over the existing gamma kernel class by Chen (2000) in that it is a valid density for any finite sample and has standard distributional quantities, such as the moments, the conditional tail moments, and the compound distribution with GKDE claim amounts, in analytic form. The model is also a competing model of the Erlang mixture by Lee and Lin (2010) in its flexibility, but with a straightforward implementation and optimization. As numerical examples, we fit the gamma kernel density estimator to actual insurance data and find that the proposed model gives adequate results compared to the Erlang mixture and the Phase-type models.

Effects of Physical Factors on Computed Tomography Image Quality

Min-Cheol Jeon,Man-Seok Han,Jae-Uk Jang,Dong-Young Kim 한국자기학회 2017 Journal of Magnetics Vol.22 No.2

The purpose of this study was to evaluate the effects of X-ray photon energy, tissue density, and the kernel essential for image reconstruction on the image quality by measuring HU and noise. Images were obtained by scanning the RMI density phantom within the CT device, and HU and noise were measured as follows: images were obtained by varying the tube voltages, the tube currents and eight different kernels. The greater the voltage-dependent change in the HU value but the noise was decreased. At all densities, changes in the tube current did not exert any significant influence on the HU value, whereas the noise value gradually decreased as the tube current increased. At all densities, changes in the kernel did not exert any significant influence on the HU value. The noise value gradually increased in the lower kernel range, but rapidly increased in the higher kernel range. HU is influenced by voltage and density, and noise is influenced by voltage, current, kernel, and density. This affects contrast resolution and spatial resolution.

Nonparametric Discontinuity Point Estimation in Density or Density Derivatives

Huh, Jib The Korean Statistical Society 2002 Journal of the Korean Statistical Society Vol.31 No.2

Probability density or its derivatives may have a discontinuity/change point at an unknown location. We propose a method of estimating the location and the jump size of the discontinuity point based on kernel type density or density derivatives estimators with one-sided equivalent kernels. The rates of convergence of the proposed estimators are derived, and the finite-sample performances of the methods are illustrated by simulated examples.

오차 영-확률 최대화 학습법을 위한 적응 커널-폭 추정

김남용(Namyong Kim),권기현(Kihyeon Kwon) 대한전자공학회 2021 전자공학회논문지 Vol.58 No.10

An adaptive importance sampling method with a Kriging metamodel to calculate failure probability

이승규,김재훈 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.12

A Markov chain simulation was performed to extract points in a failure region. A Kriging metamodel was constructed to approximate a limit state based on the points extracted by the Markov chain simulation. A kernel sampling density was constructed to approximate the optimal importance sampling density. The points extracted in the failure region by the Markov chain simulation were assumed as a mean of each kernel. An importance sampling method was applied to calculate the failure probability. In the importance sampling method, points are extracted from the kernel in the vicinity of a limit state. Considering the statistical distance as well as the learning function, additional experimental points were selected for the kriging metamodel. A stable numerical calculation method was applied to find the parameters of the kernel sampling density. The completeness of the Kriging metamodel was evaluated on the basis of possible changes in failure probability.

Testing for Trend Stationarity Using Spectral Density Estimators

Jin Lee 한국계량경제학회 2008 한국계량경제학회 학술대회 논문집 Vol.2008 No.2

We propose a new test statistic for trend stationarity against di¤erence stationarity using spectral density estimators. The spectral density of the …rst di¤erenced process equals to zero at the zero frequency under the null of trend stationarity, whereas di¤erence stationarity yields positive spectrum near zero frequency. With this one-sided nature of the spectrum, we construct valid testing procedures based on kernel-based spectral density estimators. Note that the spectral density estimator becomes degenerate under the null, where one do not simply apply standard results in the literature of heteroskedasticity and autocorrelation consistent (HAC) estimation. We provide new results on asymptotic distribution of the spectral density estimator under degeneracy. It is found that the convergence rates ensuring nondegenerating asymptotic variance of the estimator are much faster than the rate required for conventional HAC estimators. Consistency of the proposed test is also discussed. Simulation studies show that our spectrum-based test is competitive in terms of power in comparison with well-known KPSS test. Applications to some US macroeconomic series are presented.

크리깅 근사모델 기반의 중요도 추출법을 이용한 고장확률 계산 방안

이승규(Seunggyu Lee),김재훈(Jae Hoon Kim) 대한기계학회 2017 大韓機械學會論文集A Vol.41 No.5

마르코프체인 시뮬레이션으로 추출한 점을 기반으로 커널 밀도함수를 구성하고 중요도 추출함수로 가정하였다. 크리깅 근사모델은 한계상태식 근방에서 상세히 구성되었다. 고장확률은 크리깅 근사모델에 대해 중요도 추출법을 수행하여 계산하였다. 커널 밀도함수가 한계상태식의 근방에서 더 많은 점을 추출할 수 있도록 기존의 방법을 개선하였다. 커널 밀도함수의 파라메터를 찾기 위한 안정적인 수치계산 방안이 제시된다. 크리깅 근사모델의 불확실성으로 인해 계산된 고장확률이 변경될 가능성을 계산하여, 크리깅 근사모델의 완성도를 평가하였다. The kernel density was determined based on sampling points obtained in a Markov chain simulation and was assumed to be an important sampling function. A Kriging metamodel was constructed in more detail in the vicinity of a limit state. The failure probability was calculated based on importance sampling, which was performed for the Kriging metamodel. A pre-existing method was modified to obtain more sampling points for a kernel density in the vicinity of a limit state. A stable numerical method was proposed to find a parameter of the kernel density. To assess the completeness of the Kriging metamodel, the possibility of changes in the calculated failure probability due to the uncertainty of the Kriging metamodel was calculated.