• Communications for Statistical Applications and Methods
• /
• v.18 no.5
• /
• pp.625-636
• /
• 2011

This paper proposes two parametric entropy estimators, the minimum variance unbiased estimator and the maximum likelihood estimator, for the lognormal distribution for a comparison of the properties of the two estimators. The variances of both estimators are derived. The influence of the bias of the maximum likelihood estimator on estimation is analytically revealed. The distributions of the proposed estimators obtained by the delta approximation method are also presented. Performance comparisons are made with the two estimators. The following observations are made from the results. The MSE efficacy of the minimum variance unbiased estimator appears consistently high and increases rapidly as the sample size and variance, n and ${\sigma}^2$, become simultaneously small. To conclude, the minimum variance unbiased estimator outperforms the maximum likelihood estimator.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.4
• /
• pp.799-803
• /
• 2003

We obtained the best linear unbiased estimator for the scale parameter of the generalized Pareto Distribution by the order statistics.

• Asian-Australasian Journal of Animal Sciences
• /
• v.18 no.8
• /
• pp.1066-1070
• /
• 2005

To estimate the cumulative power of discrimination (CPD) existing within Haimen chicken populations in China, we isolated a total of 252 genomic DNAs from four chicken populations (Rugao, Jiangchun, Wan-Nan and Cshiqishi) through a saturated salt procedure. All the genomic DNAs were used in a polymerase chain reaction (PCR) with ten microsatellite markers. Amplified PCR-products with the selected markers were separated on a 12% polyacrylamide gel with pBR322DNA/MspI used as internal standard marker. Genetic diversity indices including mean allele number among loci, unbiased heterozygosity ($h_i$) within locus, effective number of alleles ($N_e$) and polymorphism information content (PIC) as well as the unbiased average heterozygosity (H) among loci in the populations were calculated using the generated allele frequencies by each marker. The mean allele number for all loci ranged between 4.00${\pm}$0.33 (Rugao) to 4.90${\pm}$0.48 (Cshiqishi) and across populations for all loci was 4.60${\pm}$0.20, while (H) ranged from 0.65${\pm}$0.03 (Rugao) to 0.69${\pm}$0.03 (Jiangchun) among loci and across populations, (H) was 0.67${\pm}$0.01. The generated unbiased average heterozygosity among loci in each population was integrated to the global formula of CPD and the result demonstrated that the CPD within the four Haimen chicken populations was 98.75%.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.11
• /
• pp.5365-5380
• /
• 2016

Estimation of signal-to-noise ratio (SNR) is an important problem in wireless communication systems. It has been studied for various constellation types and channels using different estimation techniques. Maximum likelihood estimation is a technique which provides efficient and in most cases unbiased estimators. In this paper, we have applied maximum likelihood estimation for systems employing square or cross QAM signals which are undergoing slow flat Rayleigh fading. The problem has been considered under various scenarios like data-aided (DA), non-data-aided (NDA) and partially data-aided (PDA) and the performance of each type of estimator has been evaluated and compared. It has been observed that the performance of DA estimator is best due to usage of pilot symbols, with the drawback of greater bandwidth consumption. However, this can be catered for by using partially data-aided estimators whose performance is better than NDA systems with some extra bandwidth requirement.

• Journal of the Korean Statistical Society
• /
• v.24 no.1
• /
• pp.45-64
• /
• 1995

When a random sample is taken from a certain class of discrete and continuous distributions whose support depend on two parameters, we could find that there exists the complete and sufficient statistic for parameters which belong to a certain class, and fomulate the uniformly minimum variance unbiased estimator (UMVUE) of any estimable function. Some UMVUE's of parametric functions are illustrated for the class of the distribution. Especially, we find that the UMVUE of some estimable parametric function from the truncated normal distribution could be expressed by the version of the Mill's ratio.

• IE interfaces
• /
• v.22 no.3
• /
• pp.214-222
• /
• 2009

In the early design stage, system reliability must be estimated from life testing data at the component level. Previously, a point estimate of system reliability was obtained from the unbiased estimate of the component reliability after assuming that the number of failed components for a given time followed a binomial distribution. For deriving the confidence interval of system reliability, either the lognormal distribution or the normal approximation of the binomial distribution was assumed for the estimator of system reliability. In this paper, a new estimator is used for the component level reliability, which is biased but has a smaller mean square error than the previous one. We propose to use the beta distribution rather than the lognormal or approximated normal distribution for developing the confidence interval of the system reliability. A numerical example based on Monte Carlo simulation illustrates advantages of the proposed approach over the previous approach.

• Journal of Institute of Control, Robotics and Systems
• /
• v.20 no.2
• /
• pp.170-174
• /
• 2014

In this paper, an unknown input estimation method via the optimal FIR smoother is proposed for linear discrete-time systems. The unknown inputs are represented by random walk processes and treated as auxiliary states in augmented state space models. In order to estimate augmented states which include unknown inputs, the optimal FIR smoother is applied to the augmented state space model. Since the optimal FIR smoother is unbiased and independent of any a priori information of the augmented state, the estimates of each unknown input are independent of the initial state and of other unknown inputs. Moreover, the proposed method can be applied to stochastic singular systems, since the optimal FIR smoother is derived without the assumption that the system matrix is nonsingular. A numerical example is given to show the performance of the proposed estimation method.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.1659-1662
• /
• 1997

The objective of this paper is to estimate the aerodynamic derivatives of a single turbo-prop aircraft at a specified flight condition for the best deduction of the dynamic characteristics using modified maximum likelihood estimation method whcih is known to be unbiased, efficient, and consistent. The flight test data necessary to the estimation of aerodynamic derivatives is obtained by implementing the six degree of freedom nonlinear flight simulation to consider the effects of several control input types, control deflection amplitudes, and intensity of turbulence. The simulated data is added with the measurement noise, which is regarded as the actual flight test data.

• Communications for Statistical Applications and Methods
• /
• v.30 no.4
• /
• pp.403-410
• /
• 2023

Two-Phase sampling, which was first introduced by Neyman (1938), has various applications in different forms. Variance estimation for two-phase sampling has been an important research topic because conventional variance estimators used in most softwares are not working. In this paper, we considered a variance estimation for two-phase sampling in which stratified two-stage cluster sampling designs are used in both phases. By defining a conditionally unbiased estimator of an approximate variance estimator, which is calculable when all elements in the first phase sample are observed, we propose an explicit form of variance estimator of the double expanded estimator for a two-phase sample. A small simulation study shows the proposed variance estimator has a negligible bias with small variance. The suggested variance estimator is also applicable to other linear estimators of the population total or mean if appropriate residuals are defined.

• Structural Engineering and Mechanics
• /
• v.74 no.4
• /
• pp.503-514
• /
• 2020

This study proposes prediction models for the shear strength of steel fiber reinforced concrete (SFRC) and ultra-high-performance fiber reinforced concrete (UHPC) beams using a Bayesian parameter estimation approach and a collected experimental database. Previous researchers had already proposed shear strength prediction models for SFRC and UHPC beams, but their performances were limited in terms of their prediction accuracies and the applicability to UHPC beams. Therefore, this study adopted a statistical approach based on a collected database to develop prediction models. In the database, 89 and 37 experimental data for SFRC and UHPC beams without stirrups were collected, respectively, and the proposed equations were developed using the Bayesian parameter estimation approach. The proposed models have a simplified form with important parameters, and in comparison to the existing prediction models, provide unbiased high prediction accuracy.