Communications in Statistics: Theory and Methods

Chandrasekar, B.; Leo Alexander, T.; Balakrishnan, N.

doi: 10.1081/STA-120014907pmid: N/A

In this paper, we consider exponential models and obtain minimum risk equivariant estimators of the parameters based on Type-II progressively censored samples under standardized quadratic loss function. These generalize the corresponding results for Type-II censored samples.

Shao, Quanxi

doi: 10.1081/STA-120014908pmid: N/A

Maximum likelihood estimation for the type I generalised logistic distributions is investigated. We show that the maximum likelihood estimation usually exists, except when the so-called embedded model problem occurs. A full set of embedded distributions is derived, including Gumbel distribution and a two-parameter reciprocal exponential distribution. Properties relating the embedded distributions are given. We also provide criteria to determine when the embedded distribution occurs. Examples are given for illustration.

Cook, R. J.; Godambe, V. P.; Thompson, M. E.

doi: 10.1081/STA-120014909pmid: N/A

The purpose of this article is to propose a simple semiparametric method for the construction of approximate confidence intervals for the mean of a distribution. The approach is motivated by the theory of estimating functions and is of particular value for problems involving small samples. Results from simulation studies suggest that in small samples this approach is somewhat more robust to non-normality than methods based on the Student's T-pivotal, and hence it compares favourably with standard methods in this context.

Cysneiros, Audrey Helen M. A.; Cordeiro, Gauss M.

doi: 10.1081/STA-120014910pmid: N/A

This paper considers the issue of testing parameters based on score tests in location-scale nonlinear models assuming known scale parameter, which encompasses the elliptical family of distributions and also asymmetric distributions such as the extreme value distributions. Significance levels derived from the score statistic can be misleading, particularly in small samples. We obtain, in matrix notation, a Bartlett-type correction formula to improve score tests in this class of models, thus generalizing results by Ferrari and Cordeiro (Ferrari, S.L.P.; Cordeiro, G.M. Corrected Score Tests for Exponential Family Nonlinear Models. Statist. Probab. Lett. 1996, 26, 7–12) and Ferrari and Arellano-Valle (Ferrari, S.L.P.; Arellano-Valle, R.B. Modified Likelihood Ratio and Score Tests in Linear Regression Models Using the t Distribution. Braz. J. Probab. Statist. 1996, 10, 15–33.). Our results are used to obtain a corrected score statistic for testing that a subset of the nonlinear regression coefficients equals a given vector of constants. The corrected score statistic is distributed as chi-squared with an error of order , n being the sample size, whereas the original score statistic has a chi-squared distribution with error of order . We show that the formulae derived for the Bartlett-type corrections generalize a number of previously published results. We present simulation results comparing the sizes of the usual score tests and their modified versions for linear and nonlinear regression models when the scale parameter is known or it is replaced by a consistent estimate. The paper also provides a numerical comparison of the sizes of analytical corrections for score and likelihood ratio tests and bootstrap tests.

Ali, M. A.; Ashkar, M. Y.

doi: 10.1081/STA-120014911pmid: N/A

This article examines the impact of correlation coefficient on the problem of calibration. An estimator based on a 100(1 − α)%, 0<α<1, calibration confidence interval is obtained. This estimator dominates, in some sense, the available estimators.

Ekström, Magnus

doi: 10.1081/STA-120014912pmid: N/A

In Politis and Romano (Politis, D.N.; Romano, J.P. Nonparametric Resampling for Homogeneous Strong Mixing Random Fields. Journal of Multivariate Analysis 1993, 47, 301–328.), different block resampling estimators of variance of general linear statistics, e.g., a sample mean, were proposed under the assumption of stationarity. In the present paper such estimators of variance of sample means, computed from nonstationary spatially indexed data , where 𝒜 is a finite subset of the integer lattice , are studied. Consistency of estimators of variance will be shown for the following kind of data: Observations taken from different lattice points are allowed to come from different distributions, and the dependence structure is allowed to differ over the lattice. We assume that all observed values are from distributions with the same expected value, or with expected values that decompose additively into directional components. Furthermore, it will be assumed that observations separated by a certain distance are independent.

Chitturi, Pallavi; John, Peter W. M.

doi: 10.1081/STA-120014913pmid: N/A

Optimal main effects plans (MEPs) and optimal foldover designs can often be performed as a series of nested optimal designs. Then, if the experiment cannot be completed due to time or budget constraints, the fraction already performed may still be an optimal design. We show that the optimal MEP for 4t factors in 4t + 4 points does not contain the optimal MEP for 4t factors in 4t + 2 points nested within it. In general, the optimal MEP for 4t factors in 4t + 4 points does not contain the optimal MEPs for 4t factors in 4t + 1, 4t + 2, or 4t + 3 points and the optimal MEP for 4t + 1 factors in 4t + 4 points does not contain the optimal MEPs for 4t + 1 factors in 4t + 2 or 4t + 3 points. We also show that the runs in an orthogonal design for 4t factors in 4t + 4 points, and the optimal foldover designs obtained by folding, should be performed in a certain sequence in order to avoid the possibility of a singular X'X matrix.

Bhaumik, Dulal K.; Khattree, Ravindra; Bagui, Subhash C.

doi: 10.1081/STA-120014914pmid: N/A

In this article, we derive locally optimum tests and Rao's score tests for a two-stage nested design under a certain partial balance. Specifically, it is assumed that for any given level of leading factor, the number of observations at every error stage below it are equal. Formulas are provided so as to efficiently compute the test statistics.

Kovacevic, Milorad S.; Rai, Shesh N.

doi: 10.1081/STA-120014915pmid: N/A

The total variance that accounts for both sources of variability, the assumed superpopulation and the sampling design, is proposed for log-linear modelling and applied to analysis of longitudinal survey data. It is shown that the share of variability attributed to the assumed multinomial model is negligible for large populations and for small sampling rates. The studied approach via the total variance is then applied to a log-linear model reparametrized to model symmetry, persistence, and independence in longitudinal populations. An illustration using data obtained from the Canadian Survey of Labour and Income Dynamics is given.

Sadek, Amr; Limnios, Nikolaos

doi: 10.1081/STA-120014916pmid: N/A

In this paper, we shall study a homogeneous ergodic, finite state, Markov chain with unknown transition probability matrix. Starting from the well known maximum likelihood estimator of transition probability matrix, we define estimators of reliability and its measurements. Our aim is to show that these estimators are uniformly strongly consistent and converge in distribution to normal random variables. The construction of the confidence intervals for availability, reliability, and failure rates are also given. Finally we shall give a numerical example for illustration and comparing our results with the usual empirical estimator results.