Minimum variance unbiased estimators of the ratio of means of two lognormal variates

The minimum variance unbiased estimators from independent samples of the ratio of the means of two lognormal distributions with equal and unequal shape parameters are derived using a method due to Finney (1941). The like estimator for two gamma distributions of known shape is given. A numerical example from a recent cloud-seeding experiment is also given.     

Best linear unbiased quantile estimators of the logistic distribution using order statistics

This paper deals with the problem of estimating the Quantiles Q(ξ), with ξ=0.01, 0.05(0.05)0.95, 0.99 of the logistic distribution by using order statistics in small samples. Linear unbiased estimators with minimum variance BLUE based on ordered observations are constructed for sample size n = 2(1)10, 15 and 20.     

Range-preserving unbiased estimators in the poisson case

Abstract

The Kruskal–Wallis test is a popular nonparametric test for comparing k independent samples. In this article we propose a new algorithm to compute the exact null distribution of the Kruskal–Wallis test. Generating the exact null distribution of the Kruskal–Wallis test is needed to compare several approximation methods. The 5% cut-off points of the exact null distribution which StatXact cannot produce are obtained as by-products. We also investigate graphically a reason that the exact and approximate distributions differ, and hope that it will be a useful tutorial tool to teach about the Kruskal–Wallis test in undergraduate course.     

Existence of unbiased covariance components estimators

The condition of PINCUS (1974) for the estimability of covariance components in normal models is extended to the case of singular covariance matrices     

Improved unbiased estimators in adaptive cluster sampling

Summary.  The usual design-unbiased estimators in adaptive cluster sampling are easy to compute but are not functions of the minimal sufficient statistic and hence can be improved. Improved unbiased estimators obtained by conditioning on sufficient statistics—not necessarily minimal—are described. First, estimators that are as easy to compute as the usual design-unbiased estimators are given. Estimators obtained by conditioning on the minimal sufficient statistic which are more difficult to compute are also discussed. Estimators are compared in examples.     

On the restricted almost unbiased estimators in linear regression

In this paper, the restricted almost unbiased ridge regression estimator and restricted almost unbiased Liu estimator are introduced for the vector of parameters in a multiple linear regression model with linear restrictions. The bias, variance matrices and mean square error (MSE) of the proposed estimators are derived and compared. It is shown that the proposed estimators will have smaller quadratic bias but larger variance than the corresponding competitors in literatures. However, they will respectively outperform the latter according to the MSE criterion under certain conditions. Finally, a simulation study and a numerical example are given to illustrate some of the theoretical results.     

Calibrated linear unbiased estimators in finite population sampling

Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38] and Rao [2002. Discussion of “Exact linear unbiased estimation in survey sampling”. J. Stat. Plann. Inf. 102, 39–40] suggested some useful techniques of deriving a linear unbiased estimator of a finite population total by modifying a given linear estimator. In this paper we suggest various generalizations of their results. In particular, we search for estimators satisfying the calibration property with respect to a related auxiliary variable and obtain some new calibrated unbiased ratio-type estimators for arbitrary sampling designs. We also explore a few properties of one of the estimators suggested in Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38].     

Symmetrically distributed and unbiased estimators in linear models

Let Y be distributed symmetrically about Xβ. Natural generalizations of odd location statistics, say T‘Y’, and even location-free statistics, say W‘Y’, that were used by Hogg ‘1960, 1967)’ are introduced. We show that T‘Y’ is distributed symmetrically about β and thus E[T‘Y’] = β and that each element of T‘Y’ is uncorrelated with each element of W‘Y’. Applications of this result are made to R-estiraators and the result is extended to a multivariate linear model situation.     

Limit distributions of unbiased estimators in natural exponential families

We obtain the possible limit distributions of unbiased estimators of functions of the parameter of a natural exponential family. The limit distribution depends on <$>j<$>, the order of the first non-zero derivative at the true (but usually unknown) value of the parameter. We show that if <$>j \geq 2<$> then the umvu and the maximum likelihood estimators are not asymptotically equivalent.     

Wavelet threshold based on Stein's unbiased risk estimators of restricted location parameter in multivariate normal

In this paper, the problem of estimating the mean vector under non-negative constraints on location vector of the multivariate normal distribution is investigated. The value of the wavelet threshold based on Stein''s unbiased risk estimators is calculated for the shrinkage estimator in restricted parameter space. We suppose that covariance matrix is unknown and we find the dominant class of shrinkage estimators under Balance loss function. The performance evaluation of the proposed class of estimators is checked through a simulation study by using risk and average mean square error values.     

On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals

Empirical Bayes (EB) methodology is now widely used in statistics. However, construction of EB confidence intervals is still very limited. Following Cox (1975 ), Hill (1990 ) and Carlin & Gelfand (1990 , 1991 ), we consider EB confidence intervals, which are adjusted so that the actual coverage probabilities asymptotically meet the target coverage probabilities up to the second order. We consider both unconditional and conditional coverage, conditioning being done with respect to an ancillary statistic.     

Estimation of the parameter in the problem of the nile

Estimation of the parameter in the problem of the Nile is treated as a decision problem with squared error loss, It is shown that the minimum risk scale equivariant estimator dominates the incomplete sufficient unbiased estimators considered by Iwase and Seto, Sharper bounds for the equivariant estimator are derived which may be used to obtain the values of the same from the sample with sufficient accuracy.     

On the sufficient statistics for multivariate ARMA models: approximate approach

This paper is an investigation on the sufficient statistic for the parameters of the vector-valued (multivariate) ARMA models, when a finite sample is available. In the simplest case ARMA(1,1), by using the factorization theorem, we present a sufficient statistic whose dimension depends on the sample size and this dimension is even larger than the sample size. In this case and under some restrictions, we have solved this problem and have presented a sufficient statistic whose dimension does not depend on the sample size. In the general case, due to the complexity of the problem, we will use the modified versions of the likelihood function to find an approximate sufficient statistic in terms of the periodogram. The dimension of this sufficient statistic depends on the sample size; however, this dimension is much lower than the sample size.     

On constructing almost unbiased estimators of finite population mean using transformed auxiliary variable

${\overline y}$ , ratio _R and Tracy et al. (1999) estimators. Received: October 12, 1999; revised version: April 25, 2000     

Some unbiased estimators versus mean per unit and ratio estimators in finite population sample surveys

We present some unbiased estimators at the population mean in a finite population sample surveys with simple random sampling design where information on an auxiliary variance x positively correlated with the main variate y is available. Exact variance and unbiased estimate of the variance are computed for any sample size. These estimators are compared for their precision with the mean per unit and the ratio estimators. Modifications of the estimators are suggested to make them more precise than the mean per unit estimator or the ratio estimator regardless of the value of the population correlation coefficient between the variates x and y. Asymptotic distribution of our estimators and confidnece intervals for the population mean are also obtained.     

An admissibility condition in the class of unbiased estimators of finite population parameters

Summary A general sufficient condition is found for estimators of a finite population parameter to be admissible in the class of its unbiased estimators. The solution extends a result given by Godambe and Joshi and appears as a unified condition which applies indistinctly to those unbiased estimators of the most usual parameters (linear and quadratic forms of the population values) for which the previous admissibility proofs were worked out separately. A further more restrictive condition proves the admissibility of estimators concerning some parameters which are non polinominal functions of the population values.     

Tests of fit for the Laplace distribution based on correcting moments of entropy estimators

ABSTRACT

In this paper, we first consider the entropy estimators introduced by Vasicek [A test for normality based on sample entropy. J R Statist Soc, Ser B. 1976;38:54–59], Ebrahimi et al. [Two measures of sample entropy. Stat Probab Lett. 1994;20:225–234], Yousefzadeh and Arghami [Testing exponentiality based on type II censored data and a new cdf estimator. Commun Stat – Simul Comput. 2008;37:1479–1499], Alizadeh Noughabi and Arghami [A new estimator of entropy. J Iran Statist Soc. 2010;9:53–64], and Zamanzade and Arghami [Goodness-of-fit test based on correcting moments of modified entropy estimator. J Statist Comput Simul. 2011;81:2077–2093], and the nonparametric distribution functions corresponding to them. We next introduce goodness-of-fit test statistics for the Laplace distribution based on the moments of nonparametric distribution functions of the aforementioned estimators. We obtain power estimates of the proposed test statistics with Monte Carlo simulation and compare them with the competing test statistics against various alternatives. Performance of the proposed new test statistics is illustrated in real cases.     

Some conditions for optimality of the almost unbiased estimators of regression coefficients

The purpose of this paper is to examine the asymptotic properties of the operational almost unbiased estimator of regression coefficients which includes almost unbiased ordinary ridge estimator a s a special case. The small distrubance approximations for the bias and mean square error matrix of the estimator are derived. As a consequence, it is proved that, under certain conditions, the estimator is more efficient than a general class of estimators given by Vinod and Ullah (1981). Also it is shown that, if the ordinary ridge estimator (ORE) dominates the ordinary least squares estimator then the almost unbiased ordinary ridge estimator does not dominate ORE under the mean square error criterion.     

A note on the efficiencies of two almost unbiased predictive ratio estimators

Using the predictive approach advocated by Basu (1971), we consider two almost unbiased ratio estimators of the population mean and study their efficiencies under a linear model.     

Unbiased asymptotically optimal estimates for the problem of the nile

We obtain a class of unbiased estimates with asymptotically minimal variance for a function of the parameter in Fisher's problem of the Nile.