Partially efficiency-balanced designs-II

efficiency balanced (£R) and partially efficiency balanced (PEB) designs were studied hy Calinski (1971) and Puri and Higam (1971, 1977a). In tais paper we have studied the dual desinas of two classes of PEB designs. It is shown that the dual of any symmetrical PCS design with HN'=N'H is again a PEB design. Also the dual of a PEB(S) with μ₁ = 0 μ₂ = 0and is shown to the again a PEB(S). The relations between PEB designs and linked and partially linked blocks have heen established. As a conseguence, the analysis of linked Mock and partially linkei block designs can he sinrlififid. Sore useful classes of supplencntcd block designs having simple analysis have also been discussed.     

On the optimalizes of the mbgdd's under mixed effects model

In the present paper, under the assumption of a mixed effects model with random block effects, the type 1 optimality of the most balanced group divisible designs of type 1 has been established within the general class of all proper and connected block designs with k<v.     

Inequality for equireplicated n-ary block designs with unequal block sizes

It is shown that certain inequalities known for binary, equireplicated, equiblock-sized block designs remain valid for equireplicated n-ary block designs with unequal block sizes. The approach used here is based on the spectral expansion of the C-matrix of the block design. The main theorems include some useful and combinatorially interesting results.     

Optimal k-circulant supersaturated designs

Optimal k-circulant supersaturated designs have been constructed in literature using computer intensive methods. A systematic method of construction for multi-level experiments based on balanced incomplete block designs is presented in this paper. The method is also applicable to two-level experiments. Illustrative examples are also given.     

A new lower bound to A2-optimality measure for multi-level and mixed-level column balanced designs and its applications

In this paper, a new lower bound to A₂-optimality measure is derived and is applied to multi-level and mixed-level column balanced designs. A₂-optimal multi-level and mixed-level designs are obtained by the application of the new lower bound.     

Proper generalized neighbor designs in circular blocks

Generalized neighbor designs relax the condition of constancy on the number of times two treatments occur as neighbors in a design. In this paper, we constructed generalized neighbor designs in circular blocks of equal size. Catalogs of these designs for block size 5, 7 and 9 are also compiled. All the designs given here are binary.     

Admissibility in factorial designs

The notion of admissibility in factorial designs has been introduced. It has been shown that factorial designs which are binary and have a C-matrix with property A are admissible.     

DT-optimum designs for model discrimination and parameter estimation

The paper introduces DT-optimum designs that provide a specified balance between model discrimination and parameter estimation. An equivalence theorem is presented for the case of two models and extended to an arbitrary number of models and of combinations of parameters. A numerical example shows the properties of the procedure. The relationship with other design procedures for parameter estimation and model discrimination is discussed.     

A Small Sample Test for the Equality of Intraclass Correlation Coefficients Under Unequal Family Sizes for Several Populations

The set of all distinct blocks of a BIBD(v,b,r,k,λ) is referred to as the support of the design. In this paper, the family of BIB designs with v=9 and k=3 is studied from the view of possible support sizes, b*'s. A table is constructed of designs with support sizes belonging to {12,18,20,21,…,84}, for minimum possible b in each case and for any larger admissible b. In constructing this table the methods of trade-off and composition of designs are utilized     

A lower bound for the centred L 2-discrepancy on combined designs under the asymmetric factorials

The foldover is a useful technique in the construction of two-level factorial designs for follow-up experiments. To search an optimal foldover plans is an important issue. In this paper, for a set of asymmetric fractional factorials such as the original designs, a lower bound for centred L ₂-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. All of our results are the extended ones of Ou et al. [Lower bounds of various discrepancies on combined designs, Metrika 74 (2011), pp. 109–119] for symmetric designs to asymmetric designs. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.     

Characterization of certain incomplete block designs

It is shown that certain inequalities known for partially balanced incomplete block (PBIB) designs remain valid for general incomplete block designs. Some conditions for attaining their bounds are also given. Furthermore, the various types of PBIB designs are characterized by relating blocks of designs with association schemes. The approach here is based on the spectral expansion of NN' for the incidence matrix N of an incomplete block design.     

Some series of proper generalized neighbor designs

Neighbor balanced designs are used to remove the neighbor effects but most of these designs require a large number of blocks. To neutralize the neighbor effects in such situations, GN₂-designs are most desirable. This article deals with the (i) refinement of some series of GN₂-designs constructed by Zafaryab et al. (2010) and (ii) construction of some new series of GN₂-designs in circular blocks of equal size.     

Optimal designs for both model discrimination and parameter estimation

The KL-optimality criterion has been recently proposed to discriminate between any two statistical models. However, designs which are optimal for model discrimination may be inadequate for parameter estimation. In this paper, the DKL-optimality criterion is proposed which is useful for the dual problem of model discrimination and parameter estimation. An equivalence theorem and a stopping rule for the corresponding iterative algorithms are provided. A pharmacokinetics application and a bioassay example are given to show the good properties of a DKL-optimum design.     

A Note on Criterion-Robust Optimal Designs for Model Discrimination and Parameter Estimation in Polynomial Regression Models

Consider the problem of discriminating between the polynomial regression models on [?1, 1] and estimating parameters in the models. Zen and Tsai (2002 Zen , M. M. , Tsai , M. H. ( 2002 ). Some criterion-robust optimal designs for the dual problem of model discrimination and parameter estimation . Sankhya Ind. J. Statist. 64 : (Series B, Pt. 3) : 322 – 338 . [Google Scholar]) proposed a multiple-objective optimality criterion, M _γ-criterion, which uses weight γ (0 ≤ γ ≤ 1) for model discrimination and α = β = (1 ? γ)/2 for parameter estimation in each model. In this article, we generalize it to a wider setup with different values of α and β. For instance, α = 2 β suggests that the “smaller” model is more likely to be the true model. Using similar techniques, the corresponding criterion-robust optimal design is investigated. A study for the original criterion-robust optimal design with α = β, through M-efficiency, shows that it is good enough for any wider setup.     

A new special class of peb designs

A new class of partially efficiency-balanced designs is introduced from a practical point of view. This new design includes all equireplicated incomplete block designs available in literature as special cases. The fundamental properties of the design are clarified with relation to other block designs.     

Lower bound of average centered L2-discrepancy for U-type designs

Uniform designs are widely used in various scientific investigations and industrial applications. By considering all possible level permutation of the factors, a connection between average centered L₂-discrepancy and generalized wordlength pattern for asymmetrical fractional factorial designs is derived. Moreover, we present new lower bounds to the average centered L₂-discrepancy for symmetrical and asymmetrical U-type designs. For illustration of the theoretical results, the lower bounds for symmetrical and asymmetrical U-type designs are tabulated, and numerical results indicate that our lower bounds behave well and can be recommended for use in practice.     

On perturbations of Stein operator

In this article, we obtain a Stein operator for the sum of n independent random variables (rvs) which is shown as the perturbation of the negative binomial (NB) operator. Comparing the operator with NB operator, we derive the error bounds for total variation distance by matching parameters. Also, three-parameter approximation for such a sum is considered and is shown to improve the existing bounds in the literature. Finally, an application of our results to a function of waiting time for (k₁, k₂)-events is given.     

D s -optimal designs for Kozak's tree taper model

In this work, we study D _s -optimal design for Kozak's tree taper model. The approximate D _s -optimal designs are found invariant to tree size and hence create a ground to construct a general replication-free D _s -optimal design. Even though the designs are found not to be dependent on the parameter value p of the Kozak's model, they are sensitive to the s×1 subset parameter vector values of the model. The 12 points replication-free design (with 91% efficiency) suggested in this study is believed to reduce cost and time for data collection and more importantly to precisely estimate the subset parameters of interest.     

Lower Bounds on the Symmetric L 2-Discrepancy and Their Application

The role of uniformity measured by the symmetric L ₂-discrepancy given in Hickernell (1998 Hickernell , F. J. (1998). A generalized discrepancy and quadrature error bound. Math. Computat. 67:299–322.[Crossref], [Web of Science ®] , [Google Scholar]) has been studied in fractional factorial designs. The issue of lower bounds on the symmetric L ₂-discrepancy is crucial in the construction of uniform designs. This article reports some new lower bounds on the symmetric L ₂-discrepancy for symmetric fractional factorials and for a set of asymmetric fractional factorials. It is valuable to use these lower bounds to measure uniformity of given designs.     

Pseudo-empirical Bayes estimation of small area means under a nested error linear regression model with functional measurement errors

Small area estimation is studied under a nested error linear regression model with area level covariate subject to measurement error. Ghosh and Sinha (2007) obtained a pseudo-Bayes (PB) predictor of a small area mean and a corresponding pseudo-empirical Bayes (PEB) predictor, using the sample means of the observed covariate values to estimate the true covariate values. In this paper, we first derive an efficient PB predictor by using all the available data to estimate true covariate values. We then obtain a corresponding PEB predictor and show that it is asymptotically “optimal”. In addition, we employ a jackknife method to estimate the mean squared prediction error (MSPE) of the PEB predictor. Finally, we report the results of a simulation study on the performance of our PEB predictor and associated jackknife MSPE estimator. Our results show that the proposed PEB predictor can lead to significant gain in efficiency over the previously proposed PEB predictor. Area level models are also studied.