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Considering the presence of first order residual effects of treatments, a family of variance balanced changeover designs has been presented and universal optimality of the designs is established. The designs use only v experimental units and (v − 1)/2 periods for v = 4t + 3 prime or prime power number of treatments; t being a positive integer. A special feature of the proposed designs is that ‘in...
In this paper, we discuss interval estimation for the common mean of several heterogeneous log-normal (LN) populations. The proposed procedure is based on a higher order likelihood method. The merits of our proposed method are numerically compared with other three methods with respect to their expected lengths and coverage probabilities. Numerical studies have shown that the coverage probabilities...
In this work the ranked set sampling technique has been applied to estimate the scale parameter $$\alpha $$ of a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in the order statistics arising from this distribution and observed that median of a random sample contains...
For longitudinal data, the within-subject covariance matrix plays an important role in statistical inference and it is of great interest to investigate this. In the paper, two kinds of estimators are investigated for the random effect covariance matrix D1 and the error variance σ2 in linear mixed models. One is to estimate D1 first and then to estimate σ2; the other kind is to estimate σ2 first...
Theoretical results are derived for finding D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions. The upper bounds of the determinant of the related matrix for D-optimality are obtained. For run sizes 12 and 20, D-optimal orthogonal arrays are found for all requirement sets with three or less two-factor interactions, and all the D-optimal orthogonal...
The main result of the paper is the following characterization of the generalized arcsine density pγ(t) = tγ−1(1 − t)γ−1/B(γ, γ) with $${t \in (0, 1)}$$ and $${\gamma \in(0,\frac12) \cup (\frac12,1)}$$ : a r.v. ξ supported on [0, 1] has the generalized arcsine density pγ(t) if and only if $${ {\mathbb E} |\xi- x|^{1-2 \gamma}}$$ has the same value for almost all $${x...
In this paper, the estimation of order-restricted means of two normal distributions is studied under the LINEX loss function, when the variances are unknown and possibly unequal. Under certain sufficient conditions to be described in this paper, the proposed plug-in estimators uniformly perform better than the existing unrestricted maximum likelihood estimators. Further, the restricted maximum likelihood...
In this paper, we consider the estimation problem of individual weights of three objects. For the estimation we use the chemical balance weighing design and the criterion of D-optimality. We assume that the error terms $${\varepsilon_{i},\ i=1,2,\dots,n,}$$ are a first-order autoregressive process. This assumption implies that the covariance matrix of errors depends on the known parameter ρ....
Two methods are given for adapting a kernel density estimate to obtain an estimate of a density function with bias O(hp) for any given p, where h = h(n) is the bandwidth and n is the sample size. The first method is standard. The second method is new and involves use of Bell polynomials. The second method is shown to yield smaller biases and smaller mean squared...
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