robust model based and model assisted predictors of the finite population total the prediction approach to finite population inference has received considerable attention in recent years under this approach the finite population is assumed to be a realization from a superpopulation described by a known probability model usually a linear model the prediction approach is often criticized for its lack of robustness against model misspecification in this article we revisit this important issue and introduce a new robust prediction approach in which the superpopulation model is chosen adaptively from the well known box cox class of probability distributions the richness of the box cox class ensures robustness in our model based prediction approach we explain how our robust model based predictor can be adjusted to handle zero observations for the study variable and to achieve the design unbiasedness and benchmarking properties we demonstrate the robustness of our proposed predictors using a monte carlo simulation study and a real life example

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

minimum aberration construction results for nonregular two level fractional factorial designs summary nonregular two level fractional factorial designs are designs which cannot be specified in terms of a set of defining contrasts the aliasing properties of nonregular designs can be compared by using a generalisation of the minimum aberration criterion called minimum g2 aberration until now the only nontrivial designs that are known to have minimum g2 aberration are designs for n runs and m n 5 factors in this paper a number of construction results are presented which allow minimum g2 aberration designs to be found for many of the cases with n 16 24 32 48 64 and 96 runs and m n 2 2 factors

algorithmic construction of efficient fractional factorial designs with large run sizes fractional factorial ff designs are widely used in practice and typically are chosen according to the minimum aberration criterion a sequential algorithm is developed for constructing efficient ff designs a construction procedure is proposed that allows a design to be constructed only from its minimum aberration projection in the sequential buildup process to efficiently identify nonisomorphic designs designs are categorized according to moment projection pattern a fast isomorphism checking procedure is developed by matching the factors using their delete one factor projections this algorithm is used to completely enumerate all 128 run designs of resolution 4 all 256 run designs of resolution 4 up to 17 factors all 512 run designs of resolution 5 all 1024 run designs of resolution 6 and all 2048 and 4 096 run designs of resolution 7 a method is proposed for constructing minimum aberration ma designs using only a partial catalog of some good designs three approaches to constructing good de

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

relative efficiencies of two stage sampling schemes for mean estimation in multilevel populations when cluster size is informative in multilevel populations there are two types of population means of an outcome variable ie the average of all individual outcomes ignoring cluster membership and the average of cluster specific means to estimate the first mean individuals can be sampled directly with simple random sampling or with two stage sampling tss that is sampling clusters first and then individuals within the sampled clusters when cluster size varies in the population three tss schemes can be considered ie sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster sampling clusters with equal probability and then sampling the same percentage of individuals per cluster and sampling clusters with equal probability and then sampling the same number of individuals per cluster unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative furthermore the three tss schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size the relative efficiency of the sampling schemes is shown to vary across different cluster size distributions however sampling clusters with probability proportional to size is the most efficient tss scheme for many cluster size distributions model based and design based inference are compared and are shown to give similar results the results are applied to the distribution of high school size in italy and the distribution of patient list size for general practices in england

p adic l functions and trivial zeroes the following is adapted from the notes for the lecture it announces results and conjectures about values of the p adic l function of the symmetric square of an elliptic curve

modelling complex survey data with population level information an empirical likelihood approach survey data are often collected with unequal probabilities from a stratified population in many modelling situations the parameter of interest is a subset of a set of parameters with the others treated as nuisance parameters we show that in this situation the empirical likelihood ratio statistic follows a chi squared distribution asymptotically under stratified single and multi stage unequal probability sampling with negligible sampling fractions simulation studies show that the empirical likelihood confidence interval may achieve better coverages and has more balanced tail error rates than standard approaches involving variance estimation linearization or resampling

improved imputation of non responses to mailback questionnaires poor response rates perhaps as low as 10 to 30 per cent certainly bring into question the validity of any survey suffering such a malady repeated mailouts are capable of providing information on those persons who are resistant to responding if one is willing to assume an exponential drop off in response rates then imputation is possible for the entire group of non responders furthermore a second exponential drop off in favourable or non favourable responses to particular items within the questionnaire leads to closed form estimates of population parameters and their associated standard errors three or more mailouts also provide a test of validity of the model assumed

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

p adic l functions and p adic periods of modular forms let e be an elliptic curve which is defined over q and has stable reduction modulo a given prime p assuming that e is modular one can associate to e a p adic l function lp e s see mz swd a v vi mz t t for its construction in various cases this function is defined by a certain interpolation property and is analytic for sezp in this paper we will assume that e has split multiplicative reduction at p under this assumption the interpolation property implies that lp e 1 0 we will prove a formula for ep e 1 which was discovered experimentally by mazur tate and teitelbaum mz t t by tate s p adic urfiformization theory there is a p adic integer q epzp which we refer to as the tate period for e and a p adic analytic isomorphism

blocked nonregular two level factorial designs this article discusses the optimal blocking criteria for nonregular two level designs we extend the optimal blocking criteria of cheng and wu to nonregular designs by adapting the g and g2 minimum aberration criteria discussed by tang and deng to define word length pattern for nonregular designs we extend the notion of word to nonregular designs through a polynomial representation of factorial designs we define treatment resolution and block resolution for evaluating the degrees of aliasing and confounding we propose four new criteria which we use to search for optimal blocking schemes of 12 run 16 run and 20 run two level orthogonal arrays

some results on 2n m designs of resolution iv with weak minimum aberration it is known that all resolution iv regular 2 n m designs of run size n 2 n m where 5n 16 n n 2 must be projections of the maximal even design with n 2 factors and therefore are even designs this paper derives a general and explicit relationship between the wordlength pattern of any even 2 n m design and that of its complement in the maximal even design using these identities we identify some weak minimum aberration 2 n m designs of resolution iv and the structures of their complementary designs based on these results several families of minimum aberration 2 n m designs of resolution iv are constructed

a note on variance estimation for the regression estimator in double sampling abstract double sampling of a finite population occurs when a sample from the population is itself sampled with the intent of measuring varites in the subsample not already available in the sample an important example is the regression estimator for means or totals which uses values of an auxiliary variable from the full sample to estimate the mean of a variable of interest that is available only on the subsample this article concerns estimation of the variance of the regression estimator the estimators of variance recommended by cochran rely solely on the subsample data at least to first order this article note proposes variance estimators that make better use of the entire sample

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

optimal blocking of two level factorial designs summary blocking of two level factorial designs is considered for block sizes 2 and 4 using the method of fractional partial confounding a d and e optimal designs are obtained for block size 2 within the class of orthogonal designs for which main effects and two factor interactions are all orthogonal to each other before allowing for blocking a d and e optimal designs are obtained for block size 4 within the class of orthogonal designs with main effects orthogonal to blocks the designs obtained also have other favourable properties including orthogonal estimation of effects and orthogonality to superblocks

a graph aided method for planning two level experiments when certain interactions are important in planning a fractional factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects in this article we propose a graph aided method to solve this problem for two level experiments first we choose the defining relations for a 2 n k design according to a goodness criterion such as the minimum aberration criterion then we construct all of the nonisomorphic graphs that represent the solutions to the problem of simultaneous estimation of main effects and two factor interactions for the given defining relations in each graph a vertex represents a factor and an edge represents the interaction between the two factors for the experiment planner the job is simple draw a graph representing the specified interactions and compare it with the list of graphs obtained previously our approach is a substantial improvement over taguchi s linear graphs

theory of j characteristics for fractional factorial designs and projection justification of minimum g2 aberration deng tang 1999 introduced the generalised resolution and minimum g aberration criteria for assessing nonregular fractional factorials in tang deng 1999 a relaxed variant of minimum g aberration called minimum g 2 aberration is proposed and studied these criteria are defined using a set of j values called j characteristics in this paper we show that a factorial design is uniquely determined by its j characteristics just as a regular factorial design is uniquely determined by its defining relation the theorem is given through an explicit formula that relates the set of design points to that of j characteristics through this formula projection justification of minimum g 2 aberration is established

an evaluation of model dependent and probability sampling inferences in sample surveys abstract in this paper we are concerned with inferences from a sample survey to a finite population we contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling a numerical example is examined to illustrate the dangers in the use of model dependent estimators even when the model is apparently consonant with the sample data the paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations

some theory for constructing minimum aberration fractional factorial designs summary minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution minimum aberration designs for n runs and n 2 m n factors have previously been constructed using the novel idea of complementary designs in this paper an alternative method of construction is developed by relating the wordlength pattern of designs to the so called confounding between experimental runs this allows minimum aberration designs to be constructed for n runs and 5n 16 m n 2 factors as well as for n 2 m n

to model or not to model competing modes of inference for finite population sampling finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution rather than on statistical models for the measured variables this article reviews the debate between design based and model based inference the basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples strengths and weakness of design based and model based inference for surveys are discussed it is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings these ideas are illustrated using the problem of inference from unequal probability samples a model based regression analysis that leads to a combination of design based and model based weighting is described

optimal blocking schemes for 2n and 2n p designs systematic sources of variations in factorial experiments can be effectively reduced without biasing the estimates of the treatment effects by grouping the runs into blocks for full factorial designs optimal blocking schemes are obtained by applying the minimum aberration criterion to the block defining contrast subgroup a related concept of order of estimability is proposed for fractional factorial designs because of the intrinsic difference between treatment factors and block variables the minimum aberration approach has to be modified a concept of admissible blocking schemes is proposed for selecting block designs based on multiple criteria the resulting 2 n and 2 n p designs are shown to have better overall properties for practical experiments than those in the literature

construction of two level split lot fractional factorial designs for multistage processes split lot designs also known as multiway split unit designs are useful in factorial experiments where there are multiple processing stages such experiments occur for example in the fabrication of integrated circuits in the semiconductor industry and in product assembly the designs have a split plot structure at each stage so that settings of the factors are applied to sublots of experimental runs rather than to individual runs this allows experimental runs to be processed at much less expense than if the runs were completely randomized in this article split lot designs are constructed for two three and four processing stages the designs have minimum aberration under the split lot structure and minimize in various senses the confounding of main effects and two factor interactions with the sublots at each stage

optimal sampling and estimation strategies under the linear model in some cases model based and model assisted inferences can lead to very different estimators these two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator a strategy being a pair composed of a sampling design and an estimator we show that under a linear model the optimal model assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the horvitz thompson estimator if the heteroscedasticity of the model is fully explainable by the auxiliary variables then this strategy is also optimal in a model based sense moreover under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model the best linear unbiased estimator and the horvitz thompson estimator are equal finally it is possible to construct a single estimator for both the design and model variance the inference can thus be valid under the sampling design and under the model

a note on the definition of resolution for blocked 2 k p designs when two level fractional factorial designs are blocked the application of the standard definition of resolution requires careful consideration sometimes linear contrasts that superficially appear to be estimates of higher order interaction effects are in reality estimates of first order effects experimenters may therefore inadvertently choose designs that are of lower resolution than intended or unknowingly confound important effects in this note i discuss this subtle problem and propose an additional rule to the usual definition of resolution that provides a conservative but more realistic assessment of the resolution with this more realistic characterization experimenters are provided with a warning about possible confounding i also show that my amendment to the definition of resolution may be useful when characterizing designs in which several two level contrasts are combined to accommodate factors with four or more levels

a marginal model for analyzing discrete outcomes from longitudinal surveys with outcomes subject to multiple cause nonresponse techniques for analyzing categorical outcomes obtained from longitudinal survey samples with outcomes subject to multiple cause nonresponse are developed within the framework of weighted generalized estimating equations development of these techniques was motivated by disability data obtained from the longitudinal study of aging lsoa a longitudinal survey sample containing missing follow up for many elderly participants we posit a model that combines different multivariate link functions to permit fitting markov models to an outcome with categories represented by a mixture of ordinal success states and multiple failure states extending the missing data approach of robins rotnitzky and zhao to longitudinal survey sample settings we use multiple logit models to model the probability of multiple reasons for missing success or failure outcomes given the assumption that the probability of nonresponse depends only on observed responses and covariates specified in the missing data model weighted est

design selection and classification for hadamard matrices using generalized minimum aberration criteria deng and tang 1999 and tang and deng 1999 proposed and justified two criteria of generalized minimum aberration for general two level fractional factorial designs the criteria are defined using a set of values called j characteristics in this article we examine the practical use of the criteria in design selection specifically we consider the problem of classifying and ranking designs that are based on hadamard matrices a theoretical result on j characteristics is developed to facilitate the computation the issue of design selection is further studied by linking generalized aberration with the criteria of efficiency and estimation capacity our studies reveal that generalized aberration performs quite well under these familiar criteria

a resampling procedure for complex survey data abstract in complex survey data often the sampling design induces a non iid structure to the data e g without replacement sampling stratification multistage or unequal probability of selection though techniques for variance estimation and confidence intervals do exist they often are cumbersome to implement or do not extend to complex designs it would be desirable to have resampling methods that reuse the existing estimation system repeatedly using computing power to avoid theoretical work and that can be applied to such data in recognition of this need various resampling procedures for variance estimation and confidence intervals in sample survey data where the sampling is without replacement have been proposed in the literature these include the jackknife the with replacement bootstrap bwr the without replacement bootstrap bwo and the rescaling bootstrap the bwr and bwo are applicable only to simple sampling designs others have shown the asymptotic consistency of jackknife vari

a noninformative bayesian approach to interval estimation in finite population sampling abstract a noninformative bayesian approach to interval estimation in finite population sampling is discussed given the sample this method introduces the polya distribution as a pseudo posterior distribution over the unobserved members of the population in many cases this distribution yields interval estimates similar to those of standard frequentist theory in addition it can be used in situations where the standard methods are difficult to apply for example in producing an interval estimate for the ratio of two medians we also consider related point estimation problems and observe that estimators derived from the pseudo posterior often perform better than classical alternatives

robust estimation for finite populations based on a working model a common scenario in finite population inference is that it is possible to find a working superpopulation model which explains the main features of the population but which may not capture all the fine details in addition there are often outliers in the population which do not follow the assumed superpopulation model in situations like these it is still advantageous to make use of the working model to estimate finite population quantities provided that we do it in a robust manner the approach that we suggest is first to fit the working model to the sample and then to fine tune for departures from the model assumed by estimating the conditional distribution of the residuals as a function of the auxiliary variable this is a more direct approach to handling outliers and model misspecification than the huber approach that is currently being used two simple methods stratification and nearest neighbour smoothing are used to estimate the conditional distributions of the residuals which result in two modifications to the standard model based estimator of the population distribution function the estimators suggested perform very well in simulation studies involving two types of model departure and have small variances due to their model based construction as well as acceptable bias the potential advantage of the proposed robustified model based approach over direct nonparametric regression is also demonstrated

a bayesian approach to the design and analysis of fractionated experiments specifying a prior distribution for the large number of parameters in the statistical model is a critical step in a bayesian approach to the design and analysis of experiments this article shows that the prior distribution can be induced from a functional prior on the underlying transfer function the functional prior requires specification of only a few hyperparameters and thus can be easily implemented in practice the usefulness of the approach is demonstrated through the analysis of some experiments the article also proposes a new class of design criteria and establishes their connections with the minimum aberration criterion

existence and construction of randomization defining contrast subspaces for regular factorial designs regular factorial designs with randomization restrictions are widely used in practice this paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of randomization restrictions we use finite projective geometry to determine the existence of designs with the required structure and develop a systematic approach for their construction an attractive feature is that commonly used factorial designs with randomization restrictions are special cases of this general representation issues related to the use of these designs for particular factorial experiments are also addressed

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

conditional properties of some estimators in stratified sampling abstract the prediction properties of the stratified expansion estimator the separate and combined ratio estimators and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable several estimators of variance for each total estimator are considered including standard ones from probability sampling theory alternative choices derived from a superpopulation model and the jackknife the theory is tested in an empirical study using a real population earlier studies of the ratio and regression estimators under simple random sampling plans have illustrated that conditional properties of those estimators and of the linearization variance estimators that are often used with them can be much different and less desirable than unconditional properties whether similar results hold for stratified samples and estimators has been the subject of some debate this article illustrates both theoretically and empirically that the use of stratifi

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

structure function for aliasing patterns in boldsymbol 2 l n design with multiple groups of factors a general approach to studying fractional factorial designs with multiple groups of factors is proposed a structure function is generated by the defining contrasts among different groups of factors and the remaining columns the structure function satisfies a first order partial differential equation by solving this equation general results about the structures and properties of the designs are obtained as an important application practical rules for the selection of optimal single arrays for robust parameter design experiments are derived

estimation in survey sampling robustness and optimality abstract it is shown how the criteria of efficiency and robustness can be integrated fruitfully in a single optimality criterion within the framework of the unified theory godambe 1955 this is achieved by extending the scope of the usual model based estimation using appropriate sampling designs some situations of common occurrence in survey practice are discussed with a numerical study

the prediction approach to robust variance estimation in two stage cluster sampling abstract robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two stage cluster sample in which the first stage sampling fraction is small the analysis is based on prediction superpopulation models that allow for very general correlation structure within clusters results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters ratio regression and mean of ratios statistics are in the class of population total estimators considered

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

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

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

does simple random sampling provide adequate balance une etude empirique montre que sous un echantillonnage aleatoire simple les intervalles de confiance du total peuvent avoir des probabilites de recouvrement conditionnelles qui sont imposantes de facon persistante lorsque la taille de l echantillon croit

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

construction of row column factorial designs the arrangement of 2 n factorials in row column designs to estimate main effects and two factor interactions is investigated single replicate constructions are given which enable estimation of all main effects and maximise the number of estimable two factor interactions constructions and guidance are given for multi replicate designs in single arrays and in multiple arrays consideration is given to constructions for 2 n t fractional factorials

model based multiplicity estimation of population size a survey is conducted at w of k selection units or lists e g health care institutions or weeks in a year to estimate n the total number of individuals with particular characteristics our estimator utilizes two items determined for each survey participant the number u among the w lists in s and the number j among all k lists on which each survey participant appears in its traditional form selection units are chosen using probability sampling and the statistical properties of the estimator derive from the sampling mechanism here selection units are purposively chosen to maximize the chance that they are typical and a model based analysis is used for inference if the sample is typical the ml estimators of n and e j are unbiased if a condition on the second moment of u j is satisfied the model based variance of the estimator of n based on a purposively chosen typical sample is smaller than one based on a randomly chosen sample methods to test whether the typical assumption is valid using data from the survey are not yet available the importance of proper selection of the sample to maximize the chance that it is typical and model breakdown does not occur must be emphasized

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

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

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

minimum aberration two level split plot designs the treatment design portion of fractionated two level split plot designs is associated with a subset of the 2 n k fractional factorial designs the concept of aberration is then extended to these splitplot designs to compare designs two methods are presented for constructing two level minimumaberration split plot designs along with examples an extensive catalog of such designs is tabulated extensions to prime level designs and relations to inner outer arrays are also presented

fractional resolution and minimum aberration in blocked 2 n k designs systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks this is accomplished through the use of blocking factors the concepts of resolution and minimum aberration design optimization criteria ordinarily used to rank unblocked fractional factorial designs are extended to such blocked fractional factorial designs by treating the treatment and blocking factors differently in terms of their contribution to word length in the defining contrast subgroup some limited theoretical results are derived and tables of minimumaberration blocked two level fractional factorial designs are presented and considered the relationship between clear effects effects that are estimable when higher order effects are assumed negligible and minimum aberration in the presence of blocking is discussed

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

the effect of sampling design and response mechanism on multivariate regression based predictors abstract a general regression procedure for the prediction of a vector of population means in situations of nonresponse is proposed the multivariate treatment of the prediction problem is not computationally complicated and allows the borrowing of information from one target variable to the other even when both variables are subject to nonresponse the predictors are optimal under a general model that specifies the first and second moments of the joint distribution of the survey variables the effects of the sampling design and response mechanism on the properties of the predictors are investigated and appropriate modifications and bias corrections that use the sample inclusion probabilities are proposed the performance of the predictors is illustrated empirically and compared with that of other predictors using simulated and real data data collected in governmental and other large scale surveys is almost always incomplete typical causes for the incompleteness of the data are delays in attaining part

a kernel method for estimating finite population distribution functions using auxiliary information summary this paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population a method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable the resulting estimator compares favourably with existing estimators in terms of efficiency conditional behaviour and robustness the proposed method also has the advantage of producing estimates which are bona fide distribution functions this is not the case for many calibration type estimators suggested in the literature finally the proposed method is applicable under any probability sampling scheme

fractional factorial designs with admissible sets of clear two factor interactions we consider the problem of selecting two level fractional factorial designs that allow joint estimation of all main effects and some specified two factor interactions 2fi s without aliasing from other 2fi s this problem is to find among all 2 m p designs with given m and p those resolution iv designs whose sets of clear 2fi s contain the specified 2fi s as subsets we use a linear graph to represent the set of clear 2fi s for a resolution iv design where each line connecting two vertexes represents a clear 2fi between the factors represented by the two vertexes we call a 2 m p resolution iv design admissible if its graph is not isomorphic to any proper subgraph of the graph of any other 2 m p resolution iv design we show that all even resolution iv designs are inadmissible we then use a classical subgraph isomorphism algorithm to determine all admissible designs of 32 64 and 128 runs this leads to a concise catalog of all admissible designs of 32 and 64 runs and a lengthy but substantially re