doubling and projection a method of constructing two level designs of resolution iv given a two level regular fractional factorial design of resolution iv the method of doubling produces another design of resolution iv which doubles both the run size and the number of factors of the initial design on the other hand the projection of a design of resolution iv onto a subset of factors is of resolution iv or higher recent work in the literature of projective geometry essentially determines the structures of all regular designs of resolution iv with n n 4 1 in terms of doubling and projection where n is the run size and n is the number of factors these results imply that for instance all regular designs of resolution iv with 5n 16 n n 2 must be projections of the regular design of resolution iv with n 2 factors we show that for 9n 32 n 5 n 16 all minimum aberration designs are projections of the design with 5n 16 factors which is constructed by repeatedly doubling the 2 5 1 design defined by i abcde to prove this result we also derive some properties of doubling including an identity that relates the wordlength pattern of a design to that of its double and a result that does the same for the alias patterns of two factor interactions

constructing tables of minimum aberration pn m designs fries and hunter 1980 presented a practical algorithm for selecting standard 2 n m fractional factorial designs based on a criterion they called minimum aberration in this article some simple results are presented that enable the fries hunter algorithm to be used for a wider range of n and m and for designs with factors at p levels where p 2 is prime examples of minimum aberration 2 n m designs with resolution r 4 are given for m n m 9 a matrix is given for generating 3 n m designs with m n m 6 which have or nearly have minimum aberration

doubly robust inference with nonprobability survey samples we establish a general framework for statistical inferences with nonprobability survey samples when relevant auxiliary information is available from a probability survey sample we develop a rigoro

regular fractional factorial designs with minimum aberration and maximum estimation capacity using the approach of finite projective geometry we make a systematic study of estimation capacity a criterion of model robustness under the absence of interactions involving three or more factors some general results providing designs with maximum estimation capacity are obtained in particular for two level factorials it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible we also explore the connection with minimum aberration designs under which the sizes of the alias sets of two factor interactions which are not aliased with main effects are the most uniform possible

complete enumeration of two level orthogonal arrays of strength d with d 2 constraints enumerating nonisomorphic orthogonal arrays is an important yet very difficult problem although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases general results are extremely rare in this paper we provide a complete solution to enumerating nonisomorphic two level orthogonal arrays of strength d with d 2 constraints for any d and any run size n 2 d our results not only give the number of nonisomorphic orthogonal arrays for given d and n but also provide a systematic way of explicitly constructing these arrays our approach to the problem is to make use of the recently developed theory of j characteristics for fractional factorial designs besides the general theoretical results the paper presents some results from applications of the theory to orthogonal arrays of strength two three and four

robust team decision theory this technical note considers linear quadratic team decision problems it shows that linear decisions are optimal and can be found by solving a linear matrix inequality

a model calibration approach to using complete auxiliary information from survey data suppose that the finite population consists of n identifiable units associated with the ith unit are the study variable yi and a vector of auxiliary variables xi the values x1 x2 xn are known for the entire population i e complete but yi is known only if the ith unit is selected in the sample one of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage in this article a unified model assisted framework has been attempted using a proposed model calibration technique the proposed model calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of deville and sarndal and or the generalized regression estimators in the linear model case the pseudoempirical maximum likelihood estimator of chen and sitter when used in this setting gives an estimator that is asymptotically equivalent to the model calibration estimator but with positive weights some existing estimators

empirical likelihood estimation for finite populations and the effective usage of auxiliary information summary in finite population inference problems auxiliary population information is often available we show in this paper that the empirical likelihood method can be naturally applied to such problems to make effective use of the auxiliary information we prove that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information a bahadur type representation for empirical likelihood sample quantiles is given simulation results show that the empirical likelihood estimates perform well among a number of competitors and are model robust

efficient estimation of quadratic finite population functions in the presence of auxiliary information by viewing quadratic and other second order finite population functions as totals or means over a derived synthetic finite population we show that the recently proposed model calibration and pseudoempirical likelihood methods for effective use of auxiliary information from survey data can be readily extended to obtain efficient estimators of quadratic and other second order finite population functions in particular estimation of a finite population variance covariance or variance of a linear estimator can be greatly improved when auxiliary information is available the proposed methods are model assisted in that the resulting estimators are asymptotically design unbiased irrespective of the correctness of a working model but very efficient if the working model is nearly correct they have a number of attractive features which include applicability to a general sampling design incorporation of information on possibly multivariate auxiliary variables and the ability to entertain linear or nonlinear

on estimating distribution functions and quantiles from survey data using auxiliary information summary ratio and difference estimators of a population distribution function under a general sampling design are obtained using auxiliary population information the relative mean errors and relative mean square errors of these estimators and a model based estimator of chambers dunstan 1986 are compared through a simulation study the advantages of the design based estimators over the model based estimator under model misspecifications especially for large samples are demonstrated ratio and difference estimators of a population quantile are also studied

a connection between uniformity and aberration in regular fractions of two level factorials summary we show a link between the two apparently unrelated areas of uniformity and minimum aberration with reference to regular fractions of two level factorials we derive an expression for the centred l2 discrepancy measure for uniformity in terms of the word length pattern this result indicates in particular excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration

semiparametric inference for the dominance index under the density ratio model summary an important and often discussed research problem in statistics is how to compare several populations examples arise in medical science engineering finance and other fields often population means or medians are compared however one population may have a higher mean income for example because of a small number of super rich individuals the mean therefore may not reflect the wealth of the general population instead an index of the degree of stochastic dominance of one population over another would better reflect their relative wealth currently we can estimate such an index under restrictive conditions but there is no generic estimator with a known asymptotic distribution in this paper we suggest linking the populations via the density ratio model under this model we develop an empirical likelihood estimator and establish its asymptotic normality in addition we improve the estimation efficiency by examining the similarities between the populations furthermore we provide a valid bootstrap method for hypothesis testing and the construction of confidence intervals simulation experiments show that the proposed estimator substantially improves the estimation efficiency and power of the test and leads to confidence intervals with satisfactorily precise coverage probabilities it is also robust with respect to mild model misspecification two examples are given to demonstrate the usefulness of both the method and the concept

2n l designs with weak minimum aberration since not all 2 n l fractional factorial designs with maximum resolution are equally good fries and hunter introduced the minimum aberration criterion for selecting good 2 n l fractional factorial designs with the same resolution we modify the concept of minimum aberration and define weak minimum aberration and show the usefulness of this new design concept using some techniques from finite geometry we construct 2 n l fractional factorial designs of resolution iii with weak minimum aberration further several families of 2 n l fractional factorial designs of resolution iii and iv with minimum aberration are obtained

quantile estimation with a complex survey design estimation of the finite population distribution function and related statistics such as the median and interquartile range is considered large sample properties of estimators constructed from stratified cluster samples and properties of large sample confidence intervals are established the results are obtained within the context of a sequence of finite populations generated from a superpopulation

minimum aberration and model robustness for two level fractional factorial designs summary the performance of minimum aberration two level fractional factorial designs is studied under two criteria of model robustness simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived it is also shown that a minimum aberration design of resolution ilil or higher maximizes the number of two factor interactions which are not aliases of main effects and subject to that condition minimizes the sum of squares of the sizes of alias sets of two factor interactions this roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform it follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here examples are given to show that minimum aberration designs are indeed highly efficient

generalized minimum aberration for asymmetrical fractional factorial designs by studying treatment contrasts and anova models we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs the criterion is independent of the choice of treatment contrasts and thus model free it works for symmetrical and asymmetrical designs regular and nonregular designs in particular it reduces to the minimum aberration criterion for regular designs and the minimum g 2 aberration criterion for two level nonregular designs in addition by exploring the connection between factorial design theory and coding theory we develop a complementary design theory for general symmetrical designs which covers many existing results as special cases

blocked regular fractional factorial designs with maximum estimation capacity in this paper the problem of constructing optimal blocked regular fractional factorial designs is considered the concept of minimum aberration due to fries and hunter is a well accepted criterion for selecting good unblocked fractional factorial designs cheng steinberg and sun showed that a minimum aberration design of resolution three or higher maximizes the number of two factor interactions which are not aliases of main effects and also tends to distribute these interactions over the alias sets very uniformly we extend this to construct block designs in which i no main effect is aliased with any other main effect not confounded with blocks ii the number of two factor interactions that are neither aliased with main effects nor confounded with blocks is as large as possible and iii these interactions are distributed over the alias sets as uniformly as possible such designs perform well under the criterion of maximum estimation capacity a criterion of model robustness which has a direct statistical meaning some general results on the construction of blocked regular fractional factorial designs with maximum estimation capacity are obtained by using a finite projective geometric approach

calibration estimators in survey sampling abstract this article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information estimation is equivalent to attaching weights to the survey data we focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations we briefly mention an application to the case in which the information consists of known marginal counts in a two or multi way table known as generalized raking the general regression estimator greg was conceived with multivariate auxiliary information in mind ordinarily this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x but we note that the greg can be derived by a different route by focusing instead on the weights the ordinary sampling weights of the kth observation is 1 k where k is the inclusion probabilit

blocked regular fractional factorial designs with minimum aberration this paper considers the construction of minimum aberration ma blocked factorial designs based on coding theory the concept of minimum moment aberration due to xu 2003 for unblocked designs is extended to blocked designs the coding theory approach studies designs in a row wise fashion and therefore links blocked designs with nonregular and supersaturated designs a lower bound on blocked wordlength pattern is established it is shown that a blocked design has ma if it originates from an unblocked ma design and achieves the lower bound it is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros sufficient conditions are given for constructing ma blocked designs from unblocked ma designs the theory is then applied to construct ma blocked designs for all 32 runs 64 runs up to 32 factors and all 81 runs with respect to four combined wordlength patterns

optimal calibration estimators in survey sampling we show that the model calibration estimator for the finite population mean which was proposed by wu sitter 2001 through an intuitive argument is optimal among a class of calibration estimators we also present optimal calibration estimators for the finite population distribution function the population variance the variance of a linear estimator and other quadratic finite population functions under a unified framework the proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified a limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial the question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation

characterization of minimum aberration 2 sp n k designs in terms of their complementary designs a general result is obtained that relates the word length pattern of a 2 n k design to that of its complementary design by applying this result and using group isomorphism we are able to characterize minimum aberration 2 n k designs in terms of properties of their complementary designs the approach is quite powerful for small values of 2 n k n 1 in particular we obtain minimum aberration 2 n k designs with 2 n k n 1 1 to 11 for any n and k

estimation of fish abundance indices based on scientific research trawl surveys summary the fish abundance index over an ocean region is defined here to be the integral of expected catch per unit effort cpue approximated by the sum of expected cpue over grid squares when trawl surveys are done within grid squares selected according to a probability sampling design several other sources of variation such as the fish population dynamics and the catching process are also involved in such situations model assisted methods for estimating abundance assessed under both design and model perspectives have some advantages over purely design based methods such as the horvitz thompson ht estimator or purely model based prediction approaches this article develops model assisted empirical likelihood el methods via loglinear regression and nonparametric smoothing the methods are applied to grid surveys of the grand bank region carried out annually by fishery products international from 1996 through 2002 the ht and el methods produce similar point estimates of abundance indices simulation results however indicate that the el estimator under local linear smoothing is associated with smaller standard errors

a complementary design theory for doubling a complementary design theory for doubling by hongquan xu 1 and ching shui cheng 2 university of california los angeles and university of california berkeley august 11 2006 chen and cheng 2006a discussed the method of doubling for con structing two level fractional factorial designs they showed that for 9n 32 n 5n 16 all minimum aberration designs with n runs and n factors are projections of the maximal design with 5n 16 factors which is constructed by repeatedly doubling the 2 5 1 design de ned by i abcde this paper develops a general complementary design the ory for doubling for any design obtained by repeated doubling general identities are established to link the wordlength patterns of each pair of complementary projection designs a rule is developed for choosing minimum aberration projection designs from the maximal design with 5n 16 factors it is further shown that for 17n 64 n 5n 16 all minimum aberration designs with n runs and n factors are projections of the maximal design with n runs and 5n 16 factors ams 2000 subject classi cations primary 62k15 key words and phrases maximal design minimum aberration pless power moment identity wordlength pattern running title doubling and complementary designs supported in part by nsf grant dms 0505728 supported in part by nsf grant dms 0505556

theory of optimal blocking of 2 n m designs in this paper we define the blocking wordlength pattern of a blocked fractional factorial design by combining the wordlength patterns of treatment defining words and block defining words the concept of minimum aberration can be defined in terms of the blocking wordlength pattern and provides a good measure of the estimation capacity of a blocked fractional factorial design by blending techniques of coding theory and finite projective geometry we obtain combinatorial identities that govern the relationship between the blocking wordlength pattern of a blocked 2 n m design and the split wordlength pattern of its blocked residual design based on these identities we establish general rules for identifying minimum aberration blocked 2 n m designs in terms of their blocked residual designs using these rules we study the structures of some blocked 2 n m designs with minimum aberration

multiply robust imputation procedures for the treatment of item nonresponse in surveys summaryitem nonresponse in surveys is often treated through some form of imputation we introduce multiply robust imputation in finite population sampling this is closely related to multiple robustness which extends double robustness in practice multiple nonresponse models and multiple imputation models may be fitted each involving different subsets of covariates and possibly different link functions an imputation procedure is said to be multiply robust if the resulting estimator is consistent when all models but one are misspecified a jackknife variance estimator is proposed and shown to be consistent random and fractional imputation procedures are discussed a simulation study suggests that the proposed estimation procedures have low bias and high efficiency

estimation with missing data beyond double robustness summary we propose an estimator that is more robust than doubly robust estimators based on weighting completecasesusingweightsotherthaninverseprobabilitywhenestimatingthepopulationmean of a response variable subject to ignorable missingness we allow multiple models for both the propensity score and the outcome regression our estimator is consistent if any of the multiple models is correctly specified such multiple robustness against model misspecification is a significant improvement over double robustness which allows only one propensity score model and one outcome regression model our estimator attains the semiparametric efficiency bound when one propensity score model and one outcome regression model are correctly specified without requiring knowledge of which models are correct

some identities on q sp n m designs with application to minimum aberration designs chen and hedayat and tang and wu studied and characterized minimum aberration 2 n m designs in terms of their complemetary designs based on a new and more powerful approach we extend the study to identify minimum aberration q n m designs through their complementary designs by using macwilliams identities and krawtchouk polynomials in coding theory we obtain some general and explicit relationships between the wordlength pattern of a q n m design and that of its complementary design these identities provide a powerful tool for characterizing minimum aberration q n m designs the case of q 3 is studied in more details

constrained maximum likelihood estimation for model calibration using summary level information from external big data sources information from various public and private data sources of extremely large sample sizes are now increasingly available for research purposes statistical methods are needed for using information from such big data sources while analyzing data from individual studies that may collect more detailed information required for addressing specific hypotheses of interest in this article we consider the problem of building regression models based on individual level data from an internal study while using summary level information such as information on parameters for reduced models from an external big data source we identify a set of very general constraints that link internal and external models these constraints are used to develop a framework for semiparametric maximum likelihood inference that allows the distribution of covariates to be estimated using either the internal sample or an external reference sample we develop extensions for handling complex stratified sampling designs such as case co

empirical likelihood inference under stratified random sampling using auxiliary population information summary the empirical likelihood method under stratified random sampling is used for making inferences on finite population parameters our results show that it can lead to efficient estimators by making effective use of auxiliary population information in the form of overall population totals or means ascertained from external sources empirical likelihood ratio confidence intervals for the population mean are also studied and adjusted intervals with asymptotically correct coverage rates are obtained