• Title/Summary/Keyword: density estimator

Search Result 133, Processing Time 0.027 seconds

Utilizing Order Statistics in Density Estimation

  • Kim, W.C.;Park, B.U.
    • Communications for Statistical Applications and Methods
    • /
    • v.2 no.2
    • /
    • pp.227-230
    • /
    • 1995
  • In this paper, we discuss simple ways of implementing non-basic kernel density estimators which typically ceed extra pilot estimation. The methods utilize order statistics at the pilot estimation stages. We focus mainly on bariable lacation and scale kernel density estimator (Jones, Hu and McKay, 1994), but the same idea can be applied to other methods too.

  • PDF

A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

  • Asghari, P.;Fakoor, V.;Sarmad, M.
    • Communications for Statistical Applications and Methods
    • /
    • v.21 no.2
    • /
    • pp.115-124
    • /
    • 2014
  • In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

Design of New Density Estimator with Entropy Maximization (엔트로피 최대화를 이용한 새로운 밀도추정자의 설계)

  • Kim, Woong-Myung;Lee, Hyon-Soo
    • Proceedings of the Korean Information Science Society Conference
    • /
    • 2005.11b
    • /
    • pp.796-798
    • /
    • 2005
  • 본 연구에서는 엔트로피 이론을 사용하여 ICA(Independent Component Analysis) 점수함수를 생성하는 새로운 밀도추정자(Density Estimator)를 제안한다. 원 신호에 대한 밀도함수의 추정은 적당한 점수함수를 생성하기 위해 필요하고, 미분 가능한 밀도함수인 커널을 이용한 밀도추정법(Kernel Density Estimation)을 이용하여 점수함수를 생성하였다. 보다 빠른 점수함수의 생성을 위해서 식의 형태를 convolution 형태로 표현하였으며, ICA 학습을 위해서 결합엔트로피를 최대화(Joint Entropy Maximization)하는 방향으로 커널의 폭을 학습하였다. 이를 위해서 기울기 강하법(Gradient descent method)를 사용하였으며, 이러한 제약 사항은 새로운 밀도 추정자를 설계하기 위한 기본적인 개념을 나타낸다. 실험결과, 커널의 폭을 담당하는 smoothing parameters들이 일정한 값으로 학습함을 알 수 있었다.

  • PDF

Estimation of the exponentiated half-logistic distribution based on multiply Type-I hybrid censoring

  • Jeon, Young Eun;Kang, Suk-Bok
    • Communications for Statistical Applications and Methods
    • /
    • v.27 no.1
    • /
    • pp.47-64
    • /
    • 2020
  • In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

Classification of Precipitation Data Based on Smoothed Periodogram (평활된 주기도를 이용한 강수량자료의 군집화)

  • Park, Man-Sik;Kim, Hee-Young
    • The Korean Journal of Applied Statistics
    • /
    • v.21 no.3
    • /
    • pp.547-560
    • /
    • 2008
  • It is well known that spectral density function determines auto-covariance function of stationary time-series data and smoothed periodogram is a consistent estimator of spectral density function. Recently, Kim and Park (2007) showed that smoothed- periodogram based distances performs very well for the classification. In this paper, we introduce classification methods with smoothed periodogram and apply the approaches to the monthly precipitation measurements obtained from January, 1987 through December, 2007 at 22 locations in South Korea.

A Blind Hopping Phase Estimator in Hopped FM/BFSK Systems (도약 FM/BFSK 시스템에서 블라인드 도약 위상 추정기)

  • Seong, Jinsuk;Jeong, Min-A;Kim, Kyung-Ho;Lee, Seong Ro
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.39C no.7
    • /
    • pp.573-581
    • /
    • 2014
  • We proposed a hopping phase estimator to demodulate the received signals without any hopping information in frequency hopping spread spectrum systems. The demodulation process in this paper is as follows: hopped frequency tracking is accomplished by choosing a frequency component with maximum amplitude after taking discrete Fourier transform and a hopping frequency estimator which estimates the phase generated by hopped frequency is established through difference product and down-sampling. We obtained the probability density function and variance performance of the proposed estimator and confirmed that the analysis and the simulation results were agreed with each other.

THE STUDY OF PARAMETRIC AND NONPARAMETRIC MIXTURE DENSITY ESTIMATOR FOR FLOOD FREQUENCY ANALYSIS

  • Moon, Young-Il
    • Water Engineering Research
    • /
    • v.1 no.1
    • /
    • pp.49-61
    • /
    • 2000
  • Magnitude-frequency relationships are used in the design of dams, highway bridges, culverts, water supply systems, and flood control structures. In this paper, possible techniques for analyzing flood frequency at a site are presented. A currently used approach to flood frequency analysis is based on the concept of parametric statistical inference. In this analysis, the assumption is make that the distribution function describing flood data in known. However, such an assumption is not always justified. Even though many people have shown that the nonparametric method provides a better fit to the data than the parometric method and gives more reliable flood estimates. the noparpmetric method implies a small probability in extrapolation beyond the highest observed data in the sample. Therefore, a remedy is presented in this paper by introducing an estimator which mixes parametric and nonparametric density estimate.

  • PDF

BERRY-ESSEEN BOUNDS OF RECURSIVE KERNEL ESTIMATOR OF DENSITY UNDER STRONG MIXING ASSUMPTIONS

  • Liu, Yu-Xiao;Niu, Si-Li
    • Bulletin of the Korean Mathematical Society
    • /
    • v.54 no.1
    • /
    • pp.343-358
    • /
    • 2017
  • Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.