A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions

The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations. We focus attention on one-eighth and one-sixteenth fractions of two-level factorials and show that optimal QC designs often have larger generalized resolution and projectivity than comparable regular designs. Moreover, some of these designs are found to have maximum projectivity among all designs.Comment: Published in at http://dx.doi.org/10.1214/10-AOS815 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Maximal rank minimum aberration and doubling

Chen and Cheng [Chen, H., Cheng, C.-S., 2006. Doubling and projection: A method of constructing two-level designs of resolution IV. Ann. Statist. 34, 546-558] discussed the method of doubling for constructing two-level regular designs of resolution IV. In this paper, we study some further properties of doubling. Relations between the maximal rank minimum aberration and minimum aberration designs and how to construct some maximal rank minimum aberration designs are also considered.

Multistratum fractional factorial split-plot designs with minimum aberration and maximum estimation capacity

This paper introduces minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) criteria for discriminating among rival nonisomorphic regular multistratum fractional factorial split-plot (FFSP) designs. Some general rules for identifying MSA or MSEC multistratum FFSP designs through their consulting designs are also established. It is an improvement and generalization of the related results in (Statist. Sinica 12 (2002) 885). The comparison between the MSEC criterion and that of Mukerjee and Fang (2002) is briefly given.Consulting design Estimation capacity Minimum secondary aberration Multistratum Fractional factorial split-plot design Projective geometry

sn-m Designs containing clear main effects or clear two-factor interactions

For a fixed number of runs, when can designs have clear main effects or clear two-factor interactions (in brief, 2fi's)? This paper gives the maximum value of n in sn-m designs containing clear main effects or clear 2fi's, where s is any prime or prime power. It is a generalization of the related results in Chen and Hedayat (J. Statist. Plann. Inference 75 (1998) 147-158) for two-level designs. It is further concluded that the weak minimum aberration designs have a maximum number of clear main effects for two-level designs. A collection of designs containing most clear main effects or clear 2fi's for 16, 32, 27, and 81 runs is given.Clear Fractional factorial design Minimum aberration Regular Resolution

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.Quasi likelihood Profile quasi-likelihood Efficiency Semiparametric

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.Blockwise Dependent data Empirical Euclidean likelihood

A note on Phillips (1991): "A constrained maximum likelihood approach to estimating switching regressions"

Phillips [Phillips R.F., 1991. A constrained maximum likelihood approach to estimating switching regressions. Journal of Econometrics 48, 241-262] proposed a constrained maximum-likelihood approach to estimating the parameters in a switching regression model. In this note, we propose a new approach which leads to a proof of a more general result than Phillips's. Specifically, we prove that the Constrained MLE (CMLE) is still strongly consistent when the constant c decreases to 0 at the rate of as n increases to [infinity], with [alpha]>1. We also suggest a suitable [alpha], hence cn, for practice based on simulation results.Consistency Constrained maximum likelihood estimator Singularity Switching regression VC class

2006,26A(7):1153–1158 A NOTE ON 2 m−p IV DESIGNS WITH THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS ∗

Abstract: In this article, the authors obtain some theoretical results for 2 m−p IV designs to have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2 m−p IV designs with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration

Empirical likelihood for the two-sample mean problem

We apply empirical likelihood method to constructing confidence regions for the difference of the means of two d-dimensional samples. It is shown that the empirical likelihood ratio test has an asymptotic chi-squared distribution. The Bartlett correction for the univariate case (d=1) has been investigated by Jing [1995. Two-sample empirical likelihood method. Statist. Probab. Lett. 24, 315-319]. Unfortunately, the Bartlett correction obtained in that article was incorrect. In this article the correct Bartlett correction is found and its effectiveness is shown by a simulation study.Empirical likelihood Bartlett correction Coverage accuracy Two-sample problem