Best Linear Unbiased Estimators of Location and Scale Ranked Set Parameters under Moving Extremes Sampling Design

In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.

De-correlated unbiased sequential filtering based on best unbiased linear estimation for target tracking in Doppler radar

In target tracking applications,the Doppler measurement contains information of the target range rate,which has the potential capability to improve the tracking performance.However,the nonlinear degree between the measurement and the target state increases with the introduction of the Doppler measurement.Therefore,target tracking in the Doppler radar is a nonlinear filtering problem.In order to handle this problem,the Kalman filter form of best linear unbiased estimation(BLUE)with position measurements is proposed,which is combined with the sequential filtering algorithm to handle the Doppler measurement further,where the statistic characteristic of the converted measurement error is calculated based on the predicted information in the sequential filter.Moreover,the algorithm is extended to the maneuvering target tracking case,where the interacting multiple model(IMM)algorithm is used as the basic framework and the model probabilities are updated according to the BLUE position filter and the sequential filter,and the final estimation is a weighted sum of the outputs from the sequential filters and the model probabilities.Simulation results show that compared with existing approaches,the proposed algorithm can realize target tracking with preferable tracking precision and the extended method can achieve effective maneuvering target tracking.

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.

Estimation of a Linear Model in Terms of Intra-Class Correlations of the Residual Error and the Regressors

Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

Genetic Dissection of Grain Size Traits Through Genome-Wide Association Study Based on Genic Markers in Rice

Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance makes these traits complex to breed on account of several alleles contributing to the complete trait expression.We employed genome-wide association study in an association panel of 88 rice genotypes using 142 new candidate gene based SSR(cgSSR)markers,derived from yield-related candidate genes,with the efficient mixed-model association coupled mixed linear model for dissecting complete genetic control of grain size traits.A total of 10 significant associations were identified for four grain size-related characters(grain weight,grain length,grain width,and length-width ratio).Among the identified associations,seven marker trait associations explain more than 10%of the phenotypic variation,indicating major putative QTLs for respective traits.The allelic variations at genes OsBC1L4,SHO1 and OsD2 showed association between 1000-grain weight and grain width,1000-grain weight and grain length,and grain width and length-width ratio,respectively.The cgSSR markers,associated with corresponding traits,can be utilized for direct allelic selection,while other significantly associated cgSSRs may be utilized for allelic accumulation in the breeding programs or grain size improvement.The new cgSSR markers associated with grain size related characters have a significant impact on practical plant breeding to increase the number of causative alleles for these traits through marker aided rice breeding programs.

Fisher information for generalized Rayleigh distribution in ranked set sampling design with application to parameter estimation

In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.

A Study of the Equivalence of the BLUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models

Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X 1 : X 2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M 2 X 1β1under the model and its best linear unbiased estimators under the reduced linear models of are given, where M 2 = I -X 2 X 2 + . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M 2 X 1β1 under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model.

Checking for normality in linear mixed models

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

Dynamic stress–strength reliability estimation of system with survivalsignature

In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. The stresses, applied repeatedly at random cycle times, will causethe degradation of strength. In addition, the number of cycles in an interval is assumed to followa Poisson distribution. In the case of the strength and stress random variables following exponential distributions, the expression for the reliability of the proposed dynamic stress–strengthmodel is derived based on survival signature. The reliability is estimated by using the best linearunbiased estimation (BLUE). Considering the Type-II censored failure times, the best linear unbiased predictors (BLUP) for the unobserved coherent system failure times are developed basedon the observed failure times. Monte Carlo simulations are performed to compare the BLUE ofparameters with different values and compute the BLUP. A real data set is also analysed for anillustration of the findings.

Application of Generalized Standard Addition Method and Ultraviolet Spectroscopy to Quantify Electrolytic Depolymerization of Lignin

Industrial lignin waste is an important byproduct of bio-refineries and the paper industry.Depolymerization of industrial lignin could generate useful aromatic compounds.This group has focused on electrolytic decomposition of biorefinery lignin.To quantify electrolytic decomposition of the lignin in a highly caustic solution,ultraviolet(UV)spectroscopy provides a useful probe.The conversion of the neat lignin to the oxidized products achieved by the electrolytic reactor may be measured by quantifying the amount of unreacted neat lignin that remains in the effluent.Because the properties of electrolytic decomposition products are largely unknown,a useful approach to quantify decomposition of the neat lignin is to use a multivariate calibration method referred to as the generalized standard addition method(GSAM).In this approach,the electrolytic decomposition products represent a background interference and the neat lignin that remains can be quantified.This approach allows the conversion of the neat lignin to be calculated in a solution that is a complex mixture.

Influence Analysis in Growth Curve Model with Covariate Matrix Disturbance

Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and computational formula which can assess the disturbing influence.