tests for deletion it has been suggested in the ecological literature that species may be excluded or deleted from an environment because they do not differ sufficiently from other species in the environment we develop tests of various deletion hypotheses based on the assumption of a random distribution of species sizes the results provide information on the behavior of quantities of interest to ecologists studying this phenomenon namely contiguous ratios and allow us to gauge the extent of deletion required before we can be confident of detecting it the results indicate that this random effects approach leads to tests which have low power for ecological applications but may be more useful in fields which permit larger sample sizes

empirical correction to the likelihood ratio statistic for structural equation modeling with many variables survey data typically contain many variables structural equation modeling sem is commonly used in analyzing such data the most widely used statistic for evaluating the adequacy of a sem model is t ml a slight modification to the likelihood ratio statistic under normality assumption t ml approximately follows a chi square distribution when the number of observations n is large and the number of items or variables p is small however in practice p can be rather large while n is always limited due to not having enough participants even with a relatively large n empirical results show that t ml rejects the correct model too often when p is not too small various corrections to t ml have been proposed but they are mostly heuristic following the principle of the bartlett correction this paper proposes an empirical approach to correct t ml so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi square distribution results show that empirically corrected statistics follow the nominal chi square distribution much more closely than previously proposed corrections to t ml and they control type i errors reasonably well whenever n max 50 2p the formulations of the empirically corrected statistics are further used to predict type i errors of t ml as reported in the literature and they perform well

tests for character displacement character displacement is an important concept in ecology which has been surrounded by controversy due largely to a lack of clearly stated hypotheses and statistical tests existing tests implicity assume random species sizes estimated without error a random effects model we introduce the log uniform distribution for species sizes and show that it has properties of direct relevance to character displacement we present tests which assume uniform and log normal species sizes and have the log uniform distribution as an alternative the tests have low power for sample sizes typically encountered in ecology the effect of estimating species sizes is small the results exemplify the shortcomings of the traditional random effects model for species sizes

space time trade offs for higher radix modular multiplication using repeated addition the value of using a higher radix for modular multiplication in the context of rsa is investigated the main conclusion is that for algorithms which perform the multiplication via repeated addition there is broadly speaking a direct trade off between space and time provided by change of radix thus chip area utilized is roughly proportional to speed however initially as the radix is increased from 2 there is a short lived increase in speed greater than the extra area used

simulation based finite and large sample tests in multivariate regressions abstract in the context of multivariate linear regression mlr models it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection in this paper we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of mlr systems for the case of uniform linear hypotheses we present exact distributional invariance results concerning several standard test criteria these include wilks likelihood ratio lr criterion as well as trace and maximum root criteria the normality assumption is not necessary for most of the results to hold implications for inference are two fold first invariance to nuisance parameters entails that the technique of monte carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses second the invariance property of the latter statistic is exploited to derive general nuisance parameter free bounds on the distribution of the lr statistic for arbitrary hypotheses even though it may be difficult to compute these bounds analytically they can easily be simulated hence yielding exact bounds monte carlo tests illustrative simulation experiments show that the bounds perform well our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation based test methods e g the parametric bootstrap which may be applied when the bounds are not conclusive

area time optimal vlsi integer multiplier with minimum computation time according to vlsi theory logn n is the range of computation times for which there may exist an at2 optimal multiplier of n bit integers such networks were previously known for the time range log2n 0 n in this paper we settle this theoretical question by exhibiting a class of at2 optimal multipliers with computation times logn 0 n1 2 our designs are based on the dft on a fermat ring whose elements are represented in a redundant radix 4 form to ensure 0 1 addition time

optimal rank based tests for homogeneity of scatter we propose a class of locally and asymptotically optimal tests based on multivariate ranks and signs for the homogeneity of scatter matrices in m elliptical populations contrary to the existing parametric procedures these tests remain valid without any moment assumptions and thus are perfectly robust against heavy tailed distributions validity robustness nevertheless they reach semiparametric efficiency bounds at correctly specified elliptical densities and maintain high powers under all efficiency robustness in particular their normal score version outperforms traditional gaussian likelihood ratio tests and their pseudo gaussian robustifications under a very broad range of non gaussian densities including for instance all multivariate student and power exponential distributions

testing hypotheses about the shape parameter of a gamma distribution the purpose of this expository article is to provide greater access to critical values for testing hypotheses about the shape parameter of a gamma distribution among the possible tests we consider tests of exponentiality against gamma increasing failure rate and or decreasing failure rate alternatives extensive tables of critical values are given for individual sample sizes from 2 to 30 and values of the shape parameter in half integer increments from i to 10 median unbiased estimators are also given for the shape parameter to avoid small sample complications with maximum likelihood methods power curves are given for testing exponentiality against gamma alternatives these curves illustrate certain advantages of this parametric test over nonparametric alternatives

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

bartlett correction of the unit root test in autoregressive models summary the usual conditions for a bartlett correction are not fulfilled when testing for a unit root in a gaussian autoregressive model however by expanding the moments of the likelihood ratio statistic it can be shown that the bartlett correction improves the asymptotic distribution approximation

testing hypotheses concerning unions of linear subspaces abstract the likelihood ratio test lrt for hypotheses concerning unions of linear subspaces is derived for the normal theory linear model a more powerful test an intersection union test is proposed for the case in which the subspaces are not all of the same dimension a theorem is proved that may be used to identify hypotheses that concern unions of linear subspaces some hypotheses about the spacings between normal means are shown to concern unions of linear subspaces and therefore can be tested using the lrt finally the computation of the lrt statistic is discussed

an approach to comparing treatments based on repeated measures summary a mixed effects model is assumed for comparing treatments based on repeated measurements the covariance structure of the data is interpreted as some systematic inhomogeneity of individual profiles along the time axis rather than as serial correlation then a method of comparing treatment effects is proposed as well as that of testing the homogeneity of individual profiles a follow up analysis of residuals for the resulting model is also mentioned

analyzing dispersion effects from replicated factorial experiments recent developments in quality engineering methods have led to considerable interest in the analysis of dispersion effects from designed experiments a commonly used method for identifying important dispersion effects from replicated experiments is based on least squares analysis of the logarithm of the within replication variance bartlett and kendall 1946 box and meyer 1986 introduced a pooling technique for unreplicated two level experiments we extend this to replicated two level experiments and compare its performance with the least squares analysis we show that both of these methods can be obtained as special cases of maximum likelihood estimation under normal theory the pooling technique is generally biased and is not recommended for model identification the least squares analysis performs well as a model identification tool but the estimators can be inefficient in such cases we recommend that the parameters of the identified submodel be estimated by maximum likelihood we derive some prop

a bartlett adjustment to the likelihood ratio test for a system of equations abstract a bartlett adjustment to be applied to the likelihood ratio test statistic when testing parameter restrictions in a system of equations is derived as special cases results are also obtained for testing hypotheses on the mean of a normal variate linear restrictions in the linear model restrictions in a nonlinear model and linear restrictions in the multivariate linear model

improved likelihood ratio statistics for exponential family nonlinear models summary this paper gives a general formula for the expected likelihood ratio statistic for exponential family nonlinear models corrected up to order n 1 where n is the sample size this result generalizes previous work by cordeiro 1983 various general bartlett adjustment formulae are given to some special models and improved likelihood ratio tests are discussed

combinatorial ricci flows on surfaces we show that the analogue of hamilton s ricci flow in the combinatorial setting produces solutions which converge exponentially fast to thurston s circle packing on surfaces as a consequence a new proof of thurston s existence of circle packing theorem is obtained as another consequence ricci flow suggests a new algorithm to find circle packings

bipartite modular multiplication method this paper proposes a new modular multiplication method that uses montgomery residues defined by a modulus m and a montgomery radix r whose value is less than the modulus m this condition enables the operand multiplier to be split into two parts that can be processed separately in parallel increasing the calculation speed the upper part of the split multiplier can be processed by calculating a product modulo m of the multiplicand and this part of the split multiplier the lower part of the split multiplier can be processed by calculating a product modulo m of the multiplicand this part of the split multiplier and the inverse of a constant r two different implementations based on this method are proposed one uses a classical modular multiplier and a montgomery multiplier and the other generates partial products for each part of the split multiplier separately which are added and accumulated in a single pipelined unit a radix 4 version of a multiplier based on a radix 4 classical modular multiplier and a radix 4 montgomery multiplier has been designed and simulated the proposed method is also suitable for software implementation in a multiprocessor environment

inference from grouped data in three parameter weibull models with applications to breakdown voltage experiments an important objective of breakdown voltage experiments is to estimate either the threshold below which no breakdown occurs or other voltage levels below which breakdown occurs with a small probability a commonly used statistical technique in these studies is to fit a three parameter weibull distribution to the experimental data difficulties in applying the method of maximum likelihood to three parameter weibull models due to nonregularity have led to a variety of alternative approaches in the literature in practice however voltage breakdown and other failure time data are usually discretized or rounded off for grouped data from the weibull model there are still difficulties in applying likelihood methods when the sample size is moderate because of the so called embedded model problem after a brief review of this problem and related likelihood theory we show how the difficulties can be resolved and how likelihood based confidence intervals for the weibull parameters and quantiles can be constru

bartlett s cochran s and hartley s tests on variances are liberal when the underlying distribution is long tailed abstract for samples of equal size the p values of bartlett s cochran s and hartley s tests for the equality of several variances obtained under the normality assumption are shown to underestimate the true p values when the parent distribution is a normal or a x 2 1 scale mixture or when there is within sample dependence the proof uses elements of majorization theory when the sample sizes are not equal a partial extension is obtained for the two sample case

a bootstrap comparison of genetic covariance matrices summary an important problem in evolutionary biology is how population bottlenecks affect additive genetic variance va when only additive effects are present a decrease in va is predicted whereas with many forms of nonadditive interactions an increase is predicted we present an analysis of the changes in variance that occur as a result of a bottleneck in a population of the red flour beetle tribolium castaneum in this experiment the additive genetic covariance matrix for four traits in two sexes was measured in the ancestral population the population then went through a bottleneck and the genetic covariance matrix was again measured these data were analyzed by first examining the univariate estimates for va and second examining the covariance matrices for the univariate measures the statistic we used was the change in va for the multivariate comparisons we used three measures the difference in rank the difference in the number of positive eigenvalues to test changes in the number of heritable traits a multivariate equivalent of bartlett s statistic to test changes in the size of the matrices and a modification of mantel s correlation to test for changes in the correlation structure of the matrices because the distribution of all of these measures is complex and dependent on the specifics of the particular matrices being compared we chose to use a bootstrap analysis to test for significance for females we found that following the population bottleneck va was significantly decreased and that the correlation structure of the matrix was significantly changed for males we found that following the population bottleneck va significantly increased but that the correlation structure was unchanged

testing the homogeneity of variances in a two way classification summary approximations have been obtained to the null distribution of bartlett s type of statistic for testing the homogeneity of one way variances in a two way classification simulation studies show that the approximations give satisfactory results even for a very small number of rows and columns

computing surface uniformization using discrete beltrami flow in this paper we propose a novel algorithm for computing surface uniformization for surfaces with arbitrary topology according to the celebrated uniformization theorem all riemann surfaces can be classified as elliptic parabolic or hyperbolic our algorithm is able to work on all these cases by first constructing an initial map onto an appropriate domain such as a sphere or a polygon in the plane mathbb r 2 or the hyperbolic disk d and then morphing the diffeomorphism based on the discrete beltrami flow algorithm for high genus surfaces both the final mapping and the target domain are unknown which presents a challenge in general each such surface can be conformally mapped onto d modulo a discrete subgroup of all fractional linear transforms on d a conformal copy of the surface which is also its uniformization domain can be visualized as a fundamental polygon in d corresponding to the discrete subgroup where the generators of the discrete subgroup map each side of the fundament

bootstrap methods for testing homogeneity of variances this article describes the use of bootstrap methods for the problem of testing homogeneity of variances when means are not assumed equal or known the methods are new in this context and allow the use of normal theory test statistics such as f s 2 1 s 2 2 without the normality assumption that is crucial for validity of critical values obtained from the f distribution both asymptotic analysis and monte carlo sampling show that the new resampling procedures compare favorably with older methods in terms of test validity and power

testing for autocorrelation and equality of covariance matrices repeated measures are frequently taken in clinical trials and animal studies the correlation structure of these measures may follow a pattern such as that of a first order autoregressive process that can be used to provide an improved statistical analysis a combined test for autocorrelation and equality of covariance matrices based on a likelihood ratio statistic is presented a correction factor for the test statistic that allows the chi square distribution to better approximate its distribution is investigated and is evaluated by simulation study two competing estimators of the autocorrelation coefficient are also discussed and these estimators lead to two forms of the test statistic we compare the two test statistics using simulation studies a method for handling missing data is also considered an illustrative example is presented to demonstrate the methods

higher order semiparametric frequentist inference with the profile sampler we consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution the first order validity of this procedure established by lee kosorok and fine 2005 is extended to second order validity in the setting where the infinite dimensional nuisance parameter achieves the parametric rate specifically we obtain higher order estimates of the maximum profile likelihood estimator and of the efficient fisher information moreover we prove that an e frequentist confidence interval for the parametric component at level alpha can be estimated by the alpha level credible set from the profile sampler with an error of order op n 1 as far as we are aware these results are the first higher order frequentist results obtained for semiparametric estimation a fully bayesian interpretation is established under a certain data dependent prior the theory is verified for three specific examples 1 introduction the focus of this paper is on higher order frequentist inference for the parametric component of a semiparametric model in addition to the d dimensional euclidean parameter semiparametric models also have an infinite dimensional parameter which is sometimes called the nuisance parameter a classic example is the cox proportional hazards model for right censored survival data 7 where interest focuses on the log hazard ratios for the regression covariate vector z the integrated baseline hazard function is the infinite dimensional nuisance parameter the involvement of an infinite dimensional nuisance parameter in semiparametric models generally complicates maximum likelihood inference for in particular estimating the limiting variance of n n 0 where 0 is the true value of usually requires estimating an infinite dimensional operator of course this is not a problem with the cox model since the profile likelihood for does not involve the nuisance parameter but for most semiparametric models this simplification of the profile likelihood does not occur and supported in part by grant ca075142

genus zero surface conformal mapping and its application to brain surface mapping we developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one forms for surfaces with or without boundaries gu and yau 2002 gu and yau 2003 for genus zero surfaces our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map in this paper we apply the algorithm to the cortical surface matching problem we use a mesh structure to represent the brain surface further constraints are added to ensure that the conformal map is unique empirical tests on magnetic resonance imaging mri data show that the mappings preserve angular relationships are stable in mris acquired at different times and are robust to differences in data triangulation and resolution compared with other brain surface conformal mapping algorithms our algorithm is more stable and has good extensibility

frequentist and bayesian bartlett correction of test statistics based on adjusted profile likelihoods summary for inference about a multidimensional parameter b in the presence of nuisance param

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

computing quasiconformal maps using an auxiliary metric and discrete curvature flow surface mapping plays an important role in geometric processing which induces both area and angular distortions if the angular distortion is bounded the mapping is called a quasiconformal mapping qc mapping many surface mappings in our physical world are quasiconformal the angular distortion of a qc mapping can be represented by the beltrami differentials according to qc teichmuller theory there is a one to one correspondence between the set of beltrami differentials and the set of qc surface mappings under normalization conditions therefore every qc surface mapping can be fully determined by the beltrami differential and reconstructed by solving the so called beltrami equation in this work we propose an effective method to solve the beltrami equation on general riemann surfaces the solution is a qc mapping associated with the prescribed beltrami differential the main strategy is to define an auxiliary metric am on the domain surface such that the original qc mapping becomes conformal under the auxiliary metric the desired qc mapping can then be obtained by using the conventional conformal mapping method in this paper we first formulate a discrete analogue of qc mappings on triangular meshes then we propose an algorithm to compute discrete qc mappings using the discrete yamabe flow method to the best of our knowledge it is the first work to compute the discrete qc mappings for general riemann surfaces especially with different topologies numerically the discrete qc mapping converges to the continuous solution as the mesh grid size approaches to 0 we tested our algorithm on surfaces scanned from real life with different topologies experimental results demonstrate the generality and accuracy of our auxiliary metric method

highly accurate likelihood analysis for the seemingly unrelated regression problem the linear and nonlinear seemingly unrelated regression problem with general error distribution is analyzed using recent likelihood theory that arguably provides the definitive distribution for assessing a scalar parameter this involves implicit but well defined conditioning and marginalization for determining intrinsic measures of departure highly accurate p values are obtained for the key difference between two regression coefficients of central interest the p value gives the statistical position of the data with respect to the key parameter the theory and the results indicate that this methodology provides substantial improvement on first order likelihood procedures both in distributional accuracy and in precise measurement of the key parameter

the modified signed likelihood statistic and saddlepoint approximations summary for a number of tests in exponential families we show that the use of a normal approximation to the modified signed likelihood ratio statistic r is equivalent to the use of a saddlepoint approximation this is also true in a large deviation region where the signed likelihood ratio statistic r is of order in

exponentiation using division chains exponentiation may be performed faster than the traditional square and multiply method by iteratively reducing the exponent module numbers which as exponents themselves require few multiplications this mainly includes those with few nonzero bits for a suitable choice of such divisors the resulting mixed basis representation of the exponent reduces the expected number of nonsquaring multiplications by over half at the cost of a single extra register preprocessing effort depends entirely on the exponent and can be kept down to the work saved in a single exponentiation moreover no precomputed look up tables are required so the method is especially applicable where space is at a premium in particular it outperforms the instance of the m ary method which uses the same space however for 512 bit exponents it beats every instance of the m ary method achieving well under 635 multiplications on average both hardware and software implementations of the rsa crypto system can benefit from this algorithm

the removal method for estimating natural populations incorporating auxiliary information the removal method was originally designed to estimate the size of a pest population the technique involves monitoring the decline in the success rate in catching animals as the population is reduced if for example after removing 25 rats from a population the success rate in catching further rats were to drop by a factor of 2 one might guess that the population had declined to half its original size this is the reasoning behind the basic removal estimate in this instance the population size would be estimated at 50 individuals of course it is also possible that the rat population is substantially larger and that the large decline in numbers captured is attributable to another factor the remaining rats for example could be better at avoiding capture thus the removal method like most other techniques for estimating parameters of natural populations is plagued by assumptions that are at best highly questionable furthermore these methods often ignore potentially valuable auxiliary evidence signs of activity such as scats etc can also provide clues as to the size of the remaining population methodology intended to combat simultaneously both these deficiencies is proposed here the basic notion is that when the input for an estimation scheme is extended to include information of more than one type the dependence on the restrictive assumptions associated with the use of any single component will be reduced the statistical methodology involves a standard computer calculation of a maximum likelihood estimate and a slight modification to a common scheme for generating confidence limits the chi squared approximation to the distribution of the maximum likelihood ratio test statistic monte carlo simulations are used to demonstrate that with the inclusion of information on signs of activity the estimation scheme becomes more robust to departures from the assumptions of the removal method

modular multiplication without trial division let n 1 we present a method for multiplying two integers called n residues modulo n while avoiding division by n n residues are represented in a nonstandard way so this method is useful only if several computations are done modulo one n the addition and subtraction algorithms are unchanged 1 description some algorithms 1 2 4 5 require extensive modular arith metic we propose a representation of residue classes so as to speed modular multiplication without affecting the modular addition and subtraction algorithms other recent algorithms for modular arithmetic appear in 3 6 fix n 1 define an a residue to be a residue class modulo n select a radix r coprime to n possibly the machine word size or a power thereof such that r n and such that computations modulo r are inexpensive to process let r l and n be integers satisfying 0 n then return t n else return t to validate redc observe mn tn n tmod r so t is an integer also tr tmod n so t tr x mod n thirdly 0 t mn rn rn so 0 t 2n if r and n are large then t mn may exceed the largest double precision value one can circumvent this by adjusting m so r m 0 given two numbers x and y between 0 and n 1 inclusive let z redc xy then z xy r x mod n so xr l yr x zrx mod n also 0 z n so z is the product of x and y in this representation other algorithms for operating on n residues in this representation can be derived from the algorithms normally used the addition algorithm is unchanged since xr x yr x zr x mod n if and only if x y z mod n also unchanged are

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

accurate directional inference for vector parameters in linear exponential families we consider inference on a vector valued parameter of interest in a linear exponential family in the presence of a finite dimensional nuisance parameter based on higher order asymptotic theory for likelihood we propose a directional test whose p value is computed using one dimensional integration the work simplifies and develops earlier research on directional tests for continuous models and on higher order inference for discrete models and the examples include contingency tables and logistic regression examples and simulations illustrate the high accuracy of the method which we compare with the usual likelihood ratio test and with an adjusted version due to skovgaard in high dimensional settings such as covariance selection the approach works essentially perfectly whereas its competitors can fail catastrophically

let s fix it fixed b asymptotics versus small b asymptotics in heteroskedasticity and autocorrelation robust inference in the presence of heteroscedasticity and autocorrelation of unknown forms the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter depending on whether this lag truncation parameter is speci ed to grow at a slower rate than or the same rate as the sample size we obtain two types of asymptotic approximations the small b asymptotics and the xed b asymptotics using techniques for probability distribution approximation and high order expansions this paper shows that the xed b asymptotic approximation provides a higher order re nement to the rst order small b asymptotics this result provides a theoretical justi cation on the use of the xed b asymptotics in empirical applications on the basis of the xed b asymptotics and higher order small b asymptotics the paper introduces a new and easy to use asymptotic f test that employs a nite sample corrected wald statistic and uses an f distribution as the reference distribution finally the paper develops a bandwidth selection rule that is testing optimal in that the bandwidth minimizes the type ii error of the asymptotic f test while controlling for its type i error monte carlo simulations show that the asymptoticf test with the testing optimal bandwidth works very well in nite samples