Runchu Zhang

Construction of E(s2) optimal supersaturated designs using cyclic BIBDs

Abstract In this paper formulas for computing the E(s2) values of some kinds of E(s2) optimal supersaturated 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, efficient designs of runs from 6 to 24 are constructed and tabulated. Comparisons with other existing designs are made at last, demonstrating the effectiveness of our method.

Optimal blocking of two-level fractional factorial designs

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 effects. According to the structure of alias pattern and the hierarchical principles on treatment and block effects, 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.

Blockwise empirical Euclidean likelihood for weakly dependent processes

This paper introduces a method of blockwise empirical Euclidean likelihood for weakly dependent processes. The strong consistency and asymptotic normality of the blockwise empirical Euclidean likelihood estimation 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 efficient than the original empirical (Euclidean) likelihood estimation and it is useful for weakly dependent processes.

Empirical Likelihood Ratio Test for a Change-Point in Linear Regression Model

A nonparametric method based on the empirical likelihood is proposed to detect the change-point in the coefficient of linear regression models. The empirical likelihood ratio test statistic is proved to have the same asymptotic null distribution as that with classical parametric likelihood. Under some mild conditions, the maximum empirical likelihood change-point estimator is also shown to be consistent. The simulation results show the sensitivity and robustness of the proposed approach. The method is applied to some real datasets to illustrate the effectiveness.

Adaptive Nonparametric Comparison of Regression Curves

We propose a new test for comparison of two regression curves, which integrates generalized likelihood ratio (GLR) statistics (Fan et al., 2001) with the data-driven criterion of selecting the smoothing parameter proposed by Guerre and Lavergne (2005). The local linear nonparametric estimator is used to construct the GLR statistic. We prove that the corresponding test statistic is asymptotically normal and free of nuisance parameters and covariate designs under the null hypothesis. The test adapts to the unknown smoothness of the difference between two regression functions and can detect local alternatives converging to the null hypothesis at rate . The wild bootstrap technique is used to approximate the critical values of the test for small samples. A simulation study is conducted to investigate the finite sample properties of the new adaptive test and to compare it with some other available procedures in the literature. The simulation results demonstrate the sensitivity and robustness of the proposed approach.

Construction of Optimal Blocking Schemes for Robust Parameter Designs

Robust parameter design (RPD) is an important issue in experimental designs. If all experimental runs cannot be performed under homogeneous conditions, blocking the units is effective. In this paper, we obtain the correspondence relation between fractional factorial RPDs and the blocking schemes for full factorial RPDs. In addition, we provide a construction of optimal blocking schemes that make all main effects and control-by-noise two-factor interactions estimable.

Some Results on Fractional Factorial Split-Plot Designs with Multi-Level Factors

Fractional factorial split-plot (FFSP) designs have received much attention in recent years. In this article, the matrix representation for FFSP designs with multi-level factors is first developed, which is an extension of the one proposed by Bingham and Sitter (1999b) for the two-level case. Based on this representation, periodicity results of maximum resolution and minimum aberration for such designs are derived. Differences between FFSP designs with multi-level factors and those with two-level factors are highlighted.

Profile quasi-likelihood

In this paper, the only assumptions on the distribution of data are those concerning first 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 define a quasi-least favorable curve and construct its estimator, and then yield a profile quasi-score function of the parameter of interest. The estimator of parameter of interest obtained from this score function is asymptotically efficient. 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 and it takes values in a infinite-dimensional space. The method is also available for semiparametric model and the estimator obtained by the extension is asymptotically efficient.

On optimal two-level nonregular factorial split-plot designs

This article studies two-level nonregular factorial split-plot designs. The concepts of indicator function and aliasing are introduced to study such designs. The minimum G-aberration criterion proposed by Deng and Tang (1999) [4] for two-level nonregular factorial designs is extended to the split-plot case. A method to construct the whole-plot and sub-plot parts is proposed for nonregular designs. Furthermore, the optimal split-plot schemes for 12-, 16-, 20- and 24-run two-level nonregular factorial designs are searched, and many such schemes are tabulated for practical use.

The asymptotic distributions of empirical likelihood ratio statistics in the presence of measurement error

Abstract Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.