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.

This paper introduces a method of blockwise empirical Euclidean likelihood for weakly dependent processes. The strong consistency andasymptotic normality of the blockwise empirical Euclidean likelihoodestimation are proved. It is deduced that the blockwise empirical Euclidean likelihood ratio statistic is asymptotically a chi-square statistic. These results show that the blockwise empirical Euclidean likelihood estimation is more asymptotically effcient than the original empirical (Euclidean) likelihood estimation and it is useful for weakly dependent processes.

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.

In this paper formulas for computing the E (s2) values of some kinds of E (s2) optimal super-saturated designs are given, and a general algorithm of constructing E (s2) optimal supersaturated designs from cyclic BIBDs is proposed. Within this class of designs, by further discriminating the pairwise correlations, e cient designs of runs from 6 to 24 are constructed and tabulated. Comparisons with other existing designs are made at last, demonstrating the e ectiveness of our method.

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.