• Title/Summary/Keyword: Least squared method

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Estimation for the Half Logistic Distribution Based on Double Hybrid Censored Samples

  • Kang, Suk-Bok;Cho, Young-Seuk;Han, Jun-Tae
    • Communications for Statistical Applications and Methods
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    • v.16 no.6
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    • pp.1055-1066
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    • 2009
  • Many articles have considered a hybrid censoring scheme, which is a mixture of Type-I and Type-II censoring schemes. We introduce a double hybrid censoring scheme and derive some approximate maximum likelihood estimators(AMLEs) of the scale parameter for the half logistic distribution under the proposed double hybrid censored samples. The scale parameter is estimated by approximate maximum likelihood estimation method using two different Taylor series expansion types. We also obtain the maximum likelihood estimator(MLE) and the least square estimator(LSE) of the scale parameter under the proposed double hybrid censored samples. We compare the proposed estimators in the sense of the mean squared error. The simulation procedure is repeated 10,000 times for the sample size n = 20(10)40 and various censored samples. The performances of the AMLEs and MLE are very similar in all aspects but the MLE and LSE have not a closed-form expression, some numerical method must be employed.

Hybrid Closed-Form Solution for Wireless Localization with Range Measurements (거리정보 기반 무선위치추정을 위한 혼합 폐쇄형 해)

  • Cho, Seong Yun
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.7
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    • pp.633-639
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    • 2013
  • Several estimation methods used in the range measurement based wireless localization area have individual problems. These problems may not occur according to certain application areas. However, these problems may give rise to serious problems in particular applications. In this paper, three methods, ILS (Iterative Least Squares), DS (Direct Solution), and DSRM (Difference of Squared Range Measurements) methods are considered. Problems that can occur in these methods are defined and a simple hybrid solution is presented to solve them. The ILS method is the most frequently used method in wireless localization and has local minimum problems and a large computational burden compared with closed-form solutions. The DS method requires less processing time than the ILS method. However, a solution for this method may include a complex number caused by the relations between the location of reference nodes and range measurement errors. In the near-field region of the complex solution, large estimation errors occur. In the DSRM method, large measurement errors occur when the mobile node is far from the reference nodes due to the combination of range measurement error and range data. This creates the problem of large localization errors. In this paper, these problems are defined and a hybrid localization method is presented to avoid them by integrating the DS and DSRM methods. The defined problems are confirmed and the performance of the presented method is verified by a Monte-Carlo simulation.

Effective Reduction of Horizontal Error in Laser Scanning Information by Strip-Wise Least Squares Adjustments

  • Lee, Byoung-Kil;Yu, Ki-Yun;Pyeon, Moo-Wook
    • ETRI Journal
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    • v.25 no.2
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    • pp.109-120
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    • 2003
  • Though the airborne laser scanning (ALS) technique is becoming more popular in many applications, horizontal accuracy of points scanned by the ALS is not yet satisfactory when compared with the accuracy achieved for vertical positions. One of the major reasons is the drift that occurs in the inertial measurement unit (IMU) during the scanning. This paper presents an algorithm that adjusts for the error that is introduced mainly by the drift of the IMU that renders systematic differences between strips on the same area. For this, we set up an observation equation for strip-wise adjustments and completed it with tie point and control point coordinates derived from the scanned strips and information from aerial photos. To effectively capture the tie points, we developed a set of procedures that constructs a digital surface model (DSM) with breaklines and then performed feature-based matching on strips resulting in a set of reliable tie points. Solving the observation equations by the least squares method produced a set of affine transformation equations with 6 parameters that we used to transform the strips for adjusting the horizontal error. Experimental results after evaluation of the accuracy showed a root mean squared error (RMSE) of the adjusted strip points of 0.27 m, which is significant considering the RMSE before adjustment was 0.77 m.

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Time-Varying Parameter Estimation of Passive Telemetry RF Sensor System Using RLS Algorithm (RLS 알고리즘을 이용한 원격 RF 센서 시스템의 시변 파라메타 추정)

  • Kim, Kyung-Yup;Yu, Dong-Gook;Lee, Joon-Tark
    • Proceedings of the KIEE Conference
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    • 2007.04c
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    • pp.29-33
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    • 2007
  • In this paper, time-varying parameter of passive telemetry RF sensor system is estimated using RLS(Rescursive $\leq$* Square) algorithm. In order to overcome the problems such as power limits and complication that general RF sensor system including IC chip has, the principle of inductive coupling is applied to model sensor system The model parameter is rearranged for applying RLS algorithm based on mathematical model to the derived model using inductive coupling principle. Time variant parameter of rearranged model is estimated using forgetting factor, and in case measured data is contaminated by noise and modelling error, the performance of RLS algorithm characterized by the convergence of squared error sum is verified by simulation.

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Autocorrelation in Statistical Analyses of Fisheries Time Series Data (수산 관련 시계열 자료를 이용한 통계학적 분석에서의 자기상관에 대한 고찰)

  • Park Young Cheol;Hiyama Yoshiaki
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.35 no.3
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    • pp.216-222
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    • 2002
  • Autocorrelation in time series data can affect statistical inference in correlation or regression analyses. To improve a regression model from which the residuals are autocorrelated, Yule-Walker method, nonlinear least squares estimation, maximum likelihood method and 'prewhitening' method have been used to estimate the parameters in a regression equation. This study reviewed on the estimation methods of preventing spurious correlation in the presence of autocorrelation and applied the former three methods, Yule-Walker, nonlinear least squares and maximum likelihood method, to a 20-year real data set. Monte carlo simulation was used to compare the three parameter estimation methods. However, the simulation results showed that the mean squared error distributions from the three methods simulated do not differ significantly.

A Parameter Estimation Method using Nonlinear Least Squares (비선형 최소제곱법을 이용한 모수추정 방법론)

  • Oh, Suna;Song, Jongwoo
    • The Korean Journal of Applied Statistics
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    • v.26 no.3
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    • pp.431-440
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    • 2013
  • We consider the problem of estimating the parameters of heavy tailed distributions. In general, maximum likelihood estimation(MLE) is the most preferred method of parameter estimation because it has good properties such as asymptotic consistency, normality and efficiency. However, MLE is not always the best solution because MLE is unstable or does not exist in some cases. This paper proposes another parameter estimation method, non-linear least squares(NLS) and compares its performance to MLE. The NLS estimator is achieved by minimizing sum of squared difference between empirical cumulative distribution function(CDF) and a theoretical distribution function. In this article, we compare the NLS method to MLE using simulated data from heavy tailed distributions. The NLS method is shown to perform better than MLE in Burr distribution when the sample size is small; in addition, it performs well in a Frechet distribution.

Sparse Representation Learning of Kernel Space Using the Kernel Relaxation Procedure (커널 이완절차에 의한 커널 공간의 저밀도 표현 학습)

  • 류재홍;정종철
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2001.12a
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    • pp.60-64
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    • 2001
  • In this paper, a new learning methodology for Kernel Methods is suggested that results in a sparse representation of kernel space from the training patterns for classification problems. Among the traditional algorithms of linear discriminant function(perceptron, relaxation, LMS(least mean squared), pseudoinverse), this paper shows that the relaxation procedure can obtain the maximum margin separating hyperplane of linearly separable pattern classification problem as SVM(Support Vector Machine) classifier does. The original relaxation method gives only the necessary condition of SV patterns. We suggest the sufficient condition to identify the SV patterns in the learning epochs. Experiment results show the new methods have the higher or equivalent performance compared to the conventional approach.

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The Development of Accurate GPS Module Using Discrete-Time $H_{\infty}$ Filter (이산형 $H_{\infty}$ 필터를 이용한 고정밀 GPS 모듈의 개발)

  • Hieu, Nguyen Hoang;Long, Nguyen Phi;Lee, Sang-Hoon;Park, Ok-Deuk;Kim, Hyun-Su;Kim, Han-Sil
    • Proceedings of the KIEE Conference
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    • 2006.10c
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    • pp.351-353
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    • 2006
  • In this paper, we present the traditional GPS Position- Velocity (PV) model to apply for both Discrete-Time Kalman Filter and Discrete-Time $H_{\infty}$ Filter. The positioning algorithms of both filters are proposed for a stand-alone low-cost GPS module to increase its accuracy. For disturbance cancellation, the Kalman Filter requires the statistical information about process and measurement noises while the $H_{\infty}$ Filter only requires that these noises are bounded. Experiments show that with the same measurement data, $H_{\infty}$ Filter gives us better positioning results compared with Least-Squared method and Kalman Filter.

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Small-Sample Inference in the Errors-in-Variables Model (소표본 errors-in-vairalbes 모형에서의 통계 추론)

  • 소병수
    • Journal of Korean Society for Quality Management
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    • v.25 no.1
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    • pp.69-79
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    • 1997
  • We consider the semiparametric linear errors-in-variables model: yi=(${\alpha}+{\beta}ui+{\varepsilon}i$, xi=ui+${\varepsilon}i$ i=1, …, n where (xi, yi) stands for an observation vector, (ui) denotes a set of incidental nuisance parameters, (${\alpha}$ , ${\beta}$) is a vector of regression parameters and (${\varepsilon}i$, ${\delta}i$) are mutually uncorrelated measurement errors with zero mean and finite variances but otherwise unknown distributions. On the basis of a simple small-sample low-noise a, pp.oximation, we propose a new method of comparing the mean squared errors(MSE) of the various competing estimators of the true regression parameters ((${\alpha}$ , ${\beta}$). Then we show that a class of estimators including the classical least squares estimator and the maximum likelihood estimator are consistent and first-order efficient within the class of all regular consistent estimators irrespective of type of measurement errors.

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An Image Steganography Scheme based on LSB++ and RHTF for Resisting Statistical Steganalysis

  • Nag, Amitava;Choudhary, Soni;Basu, Suryadip;Dawn, Subham
    • IEIE Transactions on Smart Processing and Computing
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    • v.5 no.4
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    • pp.250-255
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    • 2016
  • Steganography is the art and science of secure communication. It focuses on both security and camouflage. Steganographic techniques must produce the resultant stego-image with less distortion and high resistance to steganalysis attack. This paper is mainly concerned with two steganographic techniques-least significant bit (LSB)++ and the reversible histogram transformation function (RHTF). LSB++ is likely to produce less distortion in the output image to avoid suspicion, but it is vulnerable to steganalysis attacks. RHTF using a mod function technique is capable of resisting the most popular and efficient steganalysis attacks, such as the regular-singular pair attack and chi-squared detection steganalysis, but it produces a lot of distortion in the output image. In this paper, we propose a new steganographic technique by combining both methods. The experimental results show that the proposed technique overcomes the respective drawbacks of each method.