editing and imputation for quantitative survey data abstract this article develops a three stage strategy for cleaning survey data with missing and outlying values a detection of outlying cases b detection of outlying values within outlying cases and c imputation of likely values for missing and or outlying and edited values methodological tools include distance measures graphical procedures and maximum likelihood and robust estimation for incomplete multivariate normal data data from the annual survey of manufactures asm are used to illustrate the method

the exact number of squares in fibonacci words all our words sequences are binary a square is a subword of the form uu concatenation two squares are distinct if they are of different shape not just translates of each other otherwise they are repeated fibonacci words are defined by f sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub sub j 0 7962

on the number of frames in binary words abstract a frame is a square u u where u is an unbordered word let f n denote the maximum number of distinct frames in a binary word of length n we count this number for small values of n and show that f n is at most n 2 8 for all n and greater than 7 n 30 for any positive and infinitely many n we also show that fibonacci words which are known to contain plenty of distinct squares have only a few frames moreover by modifying the thue morse word we prove that the minimum number of occurrences of frames in a word of length n is n 2 2

optimality of some algorithms to detect quasiperiodicities improving a 1993 algorithm of apostolico and ehrenfeucht independently iliopoulos and mouchard in 1999 and brodal and pedersen in 2000 provided o nlog n algorithms to determine all maximal quasiperiodicities of a word of length n we show here the optimality of this bound providing an infinite family of words w containing o w log w maximal quasiperiodicities we also show that this bound is not reached for the celebrated family of fibonacci words

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

powers in a class of a strict standard episturmian words this paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic sturmian words in particular we explicitly determine all integer powers occurring in such infinite words extending recent results of damanik and lenz d damanik d lenz powers in sturmian sequences european j combin 24 2003 377 390 doi 10 1016 s0195 6698 03 00026 x who studied powers in sturmian words the key tools in our analysis are canonical decompositions and a generalization of singular words which were originally defined for the ubiquitous fibonacci word our main results are demonstrated via some examples including the k bonacci word a generalization of the fibonacci word to a k letter alphabet k 2

high breakdown inference for mixed linear models mixed linear models are used to analyze data in many settings these models have a multivariate normal formulation in most cases the maximum likelihood estimator mle or the residual mle reml is usually chosen to estimate the parameters however the latter are based on the strong assumption of exact multivariate normality welsh and richardson have shown that these estimators are not robust to small deviations from multivariate normality this means that in practice a small proportion of data even only one can drive the value of the estimates on their own because the model is multivariate we propose a high breakdown robust estimator for very general mixed linear models that include for example covariates this robust estimator belongs to the class of s estimators from which we can derive asymptotic properties for inference we also use it as a diagnostic tool to detect outlying subjects we discuss the advantages of this estimator compared with other robust estimators proposed previously and i

models for nonresponse in sample surveys abstract the literature on the analysis of incomplete data using models is reviewed in the context of nonresponse in sample surveys the modeling approach provides a large body of methods for handling unit and item nonresponse some of which cannot be derived from the randomization theory of inference for surveys key concepts from the literature on incomplete data such as factorizations of the likelihood for special data patterns the em algorithm for general data patterns and ignorability of the response mechanism are discussed within the survey context model based procedures are related to common methods for handling nonresponse in surveys such as weighting or imputation of means within subclasses of the population

more properties of the fibonacci word on an infinite alphabet abstract recently the fibonacci word w on an infinite alphabet was introduced by zhang et al 2017 13 as a fixed point of the morphism 2 i 2 i 2 i 1 2 i 1 2 i 2 over all i n in this paper we investigate the occurrence of squares palindromes and lyndon factors in this infinite word

the cost of drilling for oil and gas an application of constrained robust regression abstract the robust regression method of huber 1973 is used to fit a model to the cost of drilling for petroleum because the model includes a categorical variable well type a linear constraint is imposed on the parameter estimates because the model was fit to the logarithm of cost and because it will be used to make repeated predictions of cost an adjustment that approximately unbiases the predictions is imposed the numerical values of the estimates are discussed and a comparison is made with ordinary least squares

a characterization of the squares in a fibonacci string a finite fibonacci stringfn is defined as follows f0 b f1 a for every integer n 2 fn fn 1fn 2 for n 1 the length of fn is denoted by the infinite fibonacci stringf is the string which contains every fn n 1 as a prefix apart from their general theoretical importance fibonacci strings are often cited as worst case examples for algorithms which compute all the repetitions or all the abelian squares in a given string in this paper we provide a characterization of all the squares in f hence in every prefix fn this characterization naturally gives rise to a algorithm which specifies all the squares of fn in an appropriate encoding this encoding is made possible by the fact that the squares of fn occur consecutively in runs the number of which is by contrast the known general algorithms for the computation of the repetitions in an arbitrary string require time and produce outputs when applied to a fibonacci string fn

assessing influence in multiple linear regression with incomplete data the problem of assessing influence and detecting influential cases in multiple linear regression with incomplete data is considered a case is said to be influential if appreciable changes in fitted regression coefficients occur when it is removed from the data a one step influence measure is derived based on the em algorithm for detecting cases that are influential in the maximum likelihood estimation of the regression coefficients results are compared with the complete data cook s distance measure techniques are demonstrated by examples

multiple edit multiple imputation for multivariate continuous data multiple imputation replaces an incomplete dataset with m 1 simulated complete versions that are analyzed separately by standard methods we present a natural extension of multiple imputation for handling the dual problems of nonresponse and response error this extension which we call multiple edit multiple imputation memi replaces an observed dataset containing missing values and errors with m 1 simulated versions of the ideal dataset that is complete and error free these ideal data sets are analyzed separately and the results are combined using the same rules as for multiple imputation the resulting inferences simultaneously reflect uncertainty due to nonresponse and response error memi may be an attractive alternative to deterministic or quasi statistical edit and imputation procedures used by many data collecting agencies producing memi s requires assumptions about the distribution of the ideal data the nature of nonresponse and a model for the response error mechanism however fittin

repetitive perhaps but certainly not boring in this paper some of the work done on repetitions in strings is surveyed especially that of an algorithmic nature several open problems are described and conjectures formulated about some of them

kazhdan lusztig cells and the frobenius schur indicator abstract let w be a finite coxeter group it is well known that the number of involutions in w is equal to the sum of the degrees of the irreducible characters of w following a suggestion of lusztig we show that this equality is compatible with the decomposition of w into kazhdan lusztig cells the proof uses a generalisation of the frobenius schur indicator to symmetric algebras which may be of independent interest

downweighting influential clusters in surveys certain clusters may be extremely influential on survey estimates and consequently contribute disproportionately to their variance we propose a general approach to estimation that downweights highly influential clusters with the amount of downweighting based on m estimation applied to the empirical influence of the clusters the method is motivated by a problem in census coverage estimation and we illustrate it by using data from the 1990 post enumeration survey pes in this context an objective prespecified methodology for handling influential observations is essential to avoid having to justify judgmental post hoc adjustment of weights in 1990 both extreme weights and large errors in the census led to extreme influence we estimated influence by taylor linearization of the survey estimator and we applied m estimators based on the t distribution and the huber function as predicted by theory the robust procedures greatly reduced the estimated variance of estimated coverage rates more so tha

a unified approach to exploratory factor analysis with missing data nonnormal data and in the presence of outliers factor analysis is regularly used for analyzing survey data missing data data with outliers and consequently nonnormal data are very common for data obtained through questionnaires based on covariance matrix estimates for such nonstandard samples a unified approach for factor analysis is developed by generalizing the approach of maximum likelihood under constraints statistical properties of the estimates for factor loadings and error variances are obtained a rescaled bartlett corrected statistic is proposed for evaluating the number of factors equivariance and invariance of parameter estimates and their standard errors for canonical varimax and normalized varimax rotations are discussed numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures

identification of tandem repeats over large alphabet inputs makes use of simple list structure instead of suffix trees algorithm finds all the primitive maximal tandem repeats of all sizes theoretically the algorithm is linear in space in practice the algorithm is linear in time and independent of the size of alphabet application in stringology and bioinformatics a primitive tandem repeat is a substring in string s if it can be expressed as two or more contiguous copies of where the base cannot be expressed in terms of yet a shorter substring substring is maximal if there is no copy of to either its left or right tandem repeats or arrays are known to play an important role in biology e g determining parentage we present a deterministic algorithm that finds all the exact primitive maximal tandem arrays that occur in s where at iteration k it discovers all the repeats with base length k our algorithm uses a simple list structure for all its operations in theory the algorithm scales well with the size of the alphabet for strings over the alphabet it has a complexity of o s in space and o b s b 2 2 in time where b is the length of the longest primitive base of a tandem repeat in s experimental results on real biological sequences randomly generated sequences using large sized alphabets and fibonacci strings show that in practice the algorithm has indeed a linear complexity both in space and time

robust estimation of dispersion matrices and principal components abstract this paper uses monte carlo methods to compare the performances of several robust procedures for estimating a correlation matrix and its principal components the estimators are formed either from separate bivariate analyses or by simultaneous manipulation of all variables by using techniques such as multivariate trimming and m estimation the m estimators stand up exceptionally well they and the multivariate trimming procedure are especially effective at estimating the principal components including a near singularity however the m estimators can break down relatively easily when the dimensionality is large and the outliers are asymmetric with missing data the element wise approach becomes more attractive

robust estimation of multivariate location and scatter in the presence of missing data two main issues regarding data quality are data contamination outliers and data completion missing data these two problems have attracted much attention and research but surprisingly they are seldom considered together popular robust methods such as s estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data except for the obviously inefficient approach of deleting all incomplete cases we generalize the definition of s estimators of multivariate location and scatter to simultaneously deal with missing data and outliers we show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random we derive an algorithm similar to the expectation maximization algorithm for computing the proposed estimators this algorithm is initialized by an extension for missing data of the minimum volume ellipsoid we assess the performance of our proposal by monte carlo simulation and give some real dat

simple and flexible detection of contiguous repeats using a suffix tree we study the problem of detecting all occurrences of primitive tandem repeats and tandem arrays in a string we first give a simple time and space optimal algorithm to find all tandem repeats and then modify it to become a time and space optimal algorithm for finding only the primitive tandem repeats both of these algorithms are then extended to handle tandem arrays the contribution of this paper is both pedagogical and practical giving simple algorithms and implementations based on a suffix tree using only standard tree traversal techniques

on the determination of kazhdan lusztig cells for affine weyl groups with unequal parameters abstract let w be a coxeter group and l be a weight function on w following lusztig we have a corresponding decomposition of w into left cells which have important applications in representation theory we study the case where w is an affine weyl group of type g 2 using explicit computation with coxeter and chevie we show that 1 there are only finitely many possible decompositions into left cells and 2 the number of left cells is finite in each case thus confirming some of lusztig s conjectures in this case a key ingredient of the proof is a general result which shows that the kazhdan lusztig polynomials of affine weyl group are invariant under large enough translations

three overlapping squares the three squares lemma 9 famously explored the consequences of supposing that three squares occur at the same position in a string essentially it showed that this phenomenon could not occur unless the longest of the three squares was at least the sum of the lengths of the other two more recently several papers 10 30 21 13 have greatly extended this result to a new periodicity lemma npl by supposing that only two of the squares occur at the same position with a third occurring in a neighbourhood to the right in these cases also similar restrictions apply in this paper an alternative strategy is proposed the consequences of having only two squares at neighbouring positions are carefully analyzed and then the observation is made that the analysis applies in a straightforward way though perhaps with complicated details to the three neighbouring squares problem in its full generality we then apply these new insights first to proofs of the final two remaining unproved subcases out of a total of 14 of the npl 10 then to an instance of the more general problem

computing kazhdan lusztig cells for unequal parameters abstract following lusztig we consider a coxeter group w together with a weight function l this gives rise to the pre order relation l and the corresponding partition of w into left cells we introduce an equivalence relation on weight functions such that in particular l is constant on equivalent classes we shall work this out explicitly for w of type f 4 and check that several of lusztig s conjectures concerning left cells with unequal parameters hold in this case even for those parameters which do not admit a geometric interpretation the proofs involve some explicit computations using chevie