This paper extends the 4m2n minimum aberration designs (MA designs) of Wu and Zhang (1993) to the case of (S2)Sn−k, where S is any prime or prime power. Some basic properties of (S2)Sn−k MA designs, including the relations with Sn−k MA designs, are discussed. The (9)3n−k MA designs with 27 runs and (16)4n−k MA designs with 64 runs are tabulated, and some (4)2n−k MA designs are constructed using the above relations.

this paper, the only assumptions on the distribution of data are those concerning rst two moments. Our purpose is to estimate the parameter of interest in the presence of nuisance parameter under these weak assumptions on the distribution. We de ne a quasi-least favorable curve andconstruct its estimator, andthen yielda pro le quasi-score function of the parameter of interest. The estimator of parameter of interest obtainedfrom this score function is asymptotically e1cient. On the other hand, we employ this method to estimate the parameter in the semiparametric model. In this model the nonparametric component plays the role of nuisance parameter andit takes values in a in nite-dimensional space. The methodis also available for semiparametric model andthe estimator obtainedby the extension is asymptotically e1cient.

Supersaturated design is a form of fractional factorial design and has recently received much interest because of its potential in factor screening experiments. This paper mainly concerns the existing criteria for mixed-level designs, i.e. the w2ðDÞ criterion (for design D) proposed by Yamada and Matsui (J. Statist. Plann. Inference 104 (2002) 459), the EðfNODÞ criterion proposed by Fang et al. (Metrika 58 (2003b) 279) and the minimum moment aberration (MMA) proposed by Xu (Statist. Sinica 13 (2003) 691). A lower bound of χ2 (D) is obtained along with the sufficient and necessary condition for achieving it. The connections between χ2 (D) and other criteria are discussed. Especially, it is shown that χ2 (D) and the second power moment χ2 (D) are in fact equivalent to each other and hence the two criteria, χ2 (D) and MMA, share the same optimal supersaturated designs, which can be constructed from saturated orthogonal arrays and other supersaturated designs.

The authors introduce the notion of split generalized wordlength pattern (GWP), i.e., treatment GWP and block GWP, for a blocked nonregular factorial design. They generalize the minimum aberration criterion to suit this type of design. Connections between factorial design theory and coding theory allow them to obtain combinatorial identities that govern the relationship between the split GWP of a blocked factorial design and that of its blocked consulting design. These identities work for regular and nonregular designs. Furthermore, the authors establish general rules for identifying generalized minimum aberration (GMA) blocked designs through their blocked consulting designs. Finally they tabulate and compare some GMA blocked designs from Hall' s orthogonal array OA (16; 215; 2) of type III.

In this paper, the minimum aberration criterion is extended for choosing blocked fractional factorial designs. Ideally, one should seek a design that has minimum aberration with respect to both treatments and blocks. We prove the nonexistence of such a design. For this reason, it is needed to compromise between the wordlength pattern of blocks and that of treatments. By exploring the wordlength patterns of a two-level fractional factorial design, we introduce a concept of alias pattern and give accurate formulas for calculating the number of alias relations for any pair of orders of treatment effects as well as of treatment and block e ects. According to the structure of alias pattern and the hierarchical principles on treatment and block e ects, a minimum aberration criterion for selecting blocked fractional factorial designs is studied. Some optimal blocked fractional factorial designs are given and comparisons with other approaches are made.