estimating a weighted average of stratum specific parameters this article investigates estimators of a weighted average of stratum specific univariate parameters and compares them in terms of a design based estimate of mean squared error mse the research is motivated by a stratified survey sample of florida medicaid beneficiaries in which the parameters are population stratum means and the weights are known and determined by the population sampling frame assuming heterogeneous parameters it is common to estimate the weighted average with the weighted sum of sample stratum means under homogeneity one ignores the known weights in favor of precision weighting adaptive estimators arise from random effects models for the parameters we propose adaptive estimators motivated from these random effects models but we compare their design based performance we further propose selecting the tuning parameter to minimize a design based estimate of mean squared error this differs from the model based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means our design based approach effectively downweights strata with small weights in the assessment of homogeneity which can lead to a smaller mse we compare the standard random effects model with identically distributed parameters to a novel alternative which models the variances of the parameters as inversely proportional to the known weights we also present theoretical and computational details for estimators based on a general class of random effects models the methods are applied to estimate average satisfaction with health plan and care among florida beneficiaries just prior to medicaid reform

bit error probability of trellis coded quadrature amplitude modulation over cross coupled multidimensional channels convolutionally encoded m ary quadrature amplitude modulation m qam systems operated over multidimensional channels for example dual polarized radio systems are considered in this paper we have derived upper bounds on the average bit error probability for 4qam qpsk with conventional convolutional coding by means of a truncated union bound technique and averaging over the cross polarization interference by means of the method of moments by modifying this technique we have found approximate upper bounds on the average biterror probability for bandwidth efficient trellis coded qam systems this is an extension of our previous work 1 that was based on one dominating error event probability as a performance measure our evaluations seem to indicate that bandwidth efficient trellis coded m qam schemes offer much larger coding gains in an interference environment e g a cross coupled interference channel than in a gaussian noise channel in general our findings point out that optimum codes for a gaussian channel are not optimum when applied in an interference environment we note that a rate 1 2 convolutional code for example with a code memory greater than two if applied to two of the bits in each signal point representation can be utilized with a simple decoder to greatly improve the performance of a qam signal in interference also we have introduced a new concept referred to as dualchannel polarization hopping in this paper which can improve the system performance significantly for systems with nonsymmetrical interference

using sample survey weights in multiple regression analyses of stratified samples abstract the rationale for the use of sample survey weights in a least squares regression analysis is examined with respect to four increasingly general specifications of the population regression model the appropriateness of the weighted regression estimate depends on which model is chosen a proposal is made to use the difference between the weighted and unweighted estimates as an aid in choosing the appropriate model and hence the appropriate estimator when applied to an analysis of the familial and environmental determinants of the educational level attained by a sample of young adults the methods lead to a revision of the initial additive model in which interaction terms between county unemployment and race as well as between sex and mother s education are included

parabolic projective functors in type a abstract we classify projective functors on the regular block of rocha caridi s parabolic version of the bgg category o in type a in fact we show that in type a the restriction of an indecomposable projective functor from o to the parabolic category is either indecomposable or zero as a consequence we obtain that projective functors on the parabolic category o in type a are completely determined up to isomorphism by the linear transformations they induce on the level of the grothendieck group which was conjectured by stroppel in 39

asymptotic properties of weighted m estimators for variable probability samples i provide a systematic treatment of the asymptotic properties of weighted m estimators under variable probability stratified sampling the characterization of the sampling scheme and representation of the objective function allow for a straightforward analysis simple consistent asymptotic variance matrix estimators are proposed for a large class of problems when stratification is based on exogenous variables i show that the unweighted m estimator is more efficient than the weighted estimator under a generalized conditional information matrix equality when population frequencies are known a more efficient weighting is possible i also show how the results carry over to multinomial sampling

a type d structure in khovanov homology abstract we describe the first part of a gluing theory for the bigraded khovanov homology with z coefficients this part associates a type d structure to a tangle properly embedded in a half space and proves that the homotopy class of the type d structure is an invariant of the isotopy class of the tangle the construction is modeled off bordered heegaard floer homology but uses only combinatorial diagrammatic methods

efficient estimation and stratified sampling abstract in this paper we investigate estimation of a class of semi parametric models the part of the model that is not specified is the marginal distribution of the explanatory variables the sampling is stratified on the dependent variables implying that the explanatory variables are no longer exogenous or ancillary we develop a new estimator for this estimation problem and show that it achieves the semi parametric efficiency bound for this case in addition we show that the estimator applies to a number of sampling schemes that have previously been treated separately

an sln stable homotopy type for matched diagrams abstract there exists a simplified bar natan khovanov complex for open 2 braids the khovanov cohomology of a knot diagram made by gluing tangles of this type is therefore often amenable to calculation we lift this idea to the level of the lipshitz sarkar stable homotopy type and use it to make new computations similarly there exists a simplified khovanov rozansky sl n complex for open 2 braids with oppositely oriented strands and an even number of crossings diagrams made by gluing tangles of this type are called matched diagrams and knots admitting matched diagrams are called bipartite knots to a pair consisting of a matched diagram and a choice of integer n 2 we associate a stable homotopy type in the case n 2 this agrees with the lipshitz sarkar stable homotopy type of the underlying knot in the case n 3 the cohomology of the stable homotopy type agrees with the sl n khovanov rozansky cohomology of the underlying knot we make some consistency checks of this sl n stable homotopy type and show that it exhibits interesting behaviour for example we find a c p 2 in the sl 3 type for some diagram and show that the sl 4 type can be interesting for a diagram for which the lipshitz sarkar type is a wedge of moore spaces

improving survey weighted least squares regression the weighted least squares wls estimator is often employed in linear regression using complex survey data to deal with the bias in ordinary least squares ols arising from informative sampling in this paper a quasi aitken wls qwls estimator is proposed qwls modifies wls in the same way that cragg s quasi aitken estimator modifies ols it weights by the usual inverse sample inclusion probability weights multiplied by a parameterized function of covariates where the parameters are chosen to minimize a variance criterion the resulting estimator is consistent for the superpopulation regression coefficient under fairly mild conditions and has a smaller asymptotic variance than wls

on the performance of combined quadrature amplitude modulation and convolutional codes for cross coupled multidimensional channels the performance of cross coupled m ary quadrature amplitude modulation qam systems is determined when bandwidth efficient trellis codes are used to combat interference performance with and without compensation for cross coupled interference is presented it is found that simple trellis codes can maintain the error probability at an acceptable level for cross coupling parameters that render uncoded systems unusable up to two dimensional trellis codes are considered for four dimensional qam signals and possibilities of obtaining diversity advantages in the form of higher total system throughput by prolonged availability of the two signals are explored this is accomplished through joint coding over two different constellations the probability of the most likely error events is calculated by using the method of moments the results are applicable to any digital communication system using multidimensional quadrature amplitude modulation e g voiceband modems cross polarized radio systems and to some extent optical systems in the paper the analysis is restricted to nondispersive cross coupling models in most cases the coding gain is larger than in the absence of cross coupling interference specifically it is found that simple codes have coding gains increased by at least 2 db with cross coupling interference relative to that obtained on the additive white gaussian noise channel

a new approach to weighting and inference in sample surveys the validity of design based inference is not dependent on any model assumption however it is well known that estimators derived through design based theory may be inefficient for the estimation of population totals when the design weights are weakly related to the variables of interest and have widely dispersed values we propose estimators that have the potential to improve the efficiency of any estimator derived under the design based theory our main focus is limited to the improvement of the horvitz thompson estimator but we also discuss the extension to calibration estimators the new estimators are obtained by smoothing design or calibration weights using an appropriate model our approach to inference requires the modelling of only one variable the weight and it leads to a single set of smoothed weights in multipurpose surveys this is to be contrasted with other model based approaches such as the prediction approach in which it is necessary to postulate and validate a model for each variable of interest leading potentially to variable specific sets of weights our proposed approach is first justified theoretically and then evaluated through a simulation study

estimating marginal causal effects in a secondary analysis of case control data when an initial case control study is performed data can be used in a secondary analysis to evaluate the effect of the case defining event on later outcomes in this paper we study the example in

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

some heteroskedasticity consistent covariance matrix estimators with improved finite sample properties abstract we examine several modified versions of the heteroskedasticity consistent covariance matrix estimator of hinkley 1977 and white 1980 on the basis of sampling experiments which compare the performance of quasi t statistics we find that one estimator based on the jackknife performs better in small samples than the rest we also examine the finite sample properties of using modified critical values based on edgeworth approximations as proposed by rothenberg 1984 in addition we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity consistent covariance matrix even in the absence of detected heteroskedasticity

the student s t approximation in a stationary first order autoregressive model the basic model is a gaussian ar 1 model with an intercept but no additional exogenous variables the paper studies the distribution of the t statistic for testing the value of the autoregressive parameter when the model is estimated by least squares the monte carlo estimates of the quantiles of the t statistic show that student s t is not a satisfactory approximation for sample sizes typical in economic applications the main problem is not the shape of the distribution of the t statistic but its location adjusting the t statistic so that it has the same mean and standard deviation as student s t the distribution of this adjusted t statistic is accurately approximated by student s t techniques are presented for accurately approximating the mean and standard deviation of the t statistic such that the adjusted t statistic can be readily calculated in practice the analysis is extended in two directions the first is to examine the effect of introducing an exogenous variable into the basic model in the expanded model student s t also accurately approximates the distribution of the t statistic for testing the autoregressive parameter and for testing the coefficient of the exogenous variable after these t statistics are adjusted for mean and standard deviation the problem of obtaining a feasible adjustment procedure is that the moments of these t statistics now depend on nuisance parameters the second is to examine the robustness of the results in the basic model to several nonnormal error distributions for each nonnormal distribution the t statistic is adjusted using the mean and standard deviation appropriate for the case of normal errors and then the distribution of the modified t statistic is compared with that of student s t

cochannel interference cancelling effects of mse processing and viterbi decoding in on board processing satellites this paper presents cochannel interference cancelling techniques in on board processing satellite systems using orthogonal polarizations the techniques based on mean square error mse criterion and convolutional coding soft decision viterbi decoding sdvd are introduced on board the bit error rate ber is derived for the mixed detection of a desired signal and an undesired cochannel interference when the techniques are applied to binary phase shift keying bpsk and is compared to that of no compensation for the interference performance results obtained theoretically show that the techniques of both the mse and sdvd processings realize excellent improvements of the ber and the improvements become significant in a large interference environment

inner products of 2 representations abstract we define and calculate inner products of 2 representations along the way we prove that the categorical trace t r of 24 sec 3 is multiplicative with respect to various notions of categorical tensor product and we identify the center of the category of equivariant objects we discuss applications ranging from schur s result about the number of irreducible projective representations to a formula for the hochschild cohomology of a global quotient orbifold

regression based methods for using control variates in monte carlo experiments abstract methods based on linear regression provide an easy way to use the information in control variates to improve the efficiency with which certain features of the distributions of estimators and test statistics are estimated in monte carlo experiments we propose a new technique that allows these methods to be used when the quantities of interest are quantiles we also propose new ways to obtain approximately optimal control variates in many cases of interest these methods seem to work well in practice and can greatly reduce the number of replications required to obtain a given level of accuracy

regression analysis of data from a cluster sample abstract for the case of different regression relationships in different subgroups of a finite population only part of which are sampled the extended least squares estimator of any weighted average of the distinct coefficients is derived under assumptions relating only to the first two moments of the distribution of the coefficients under these assumptions the estimator is shown to be the best linear unbiased estimator while under further distributional assumptions it is also the bayesian estimator for a quadratic loss function for the case of unknown variances a method for estimating them from the sample is proposed the empirical estimator thus obtained is shown to perform well by a simulation comparison with the optimal estimator and with other proposed empirical estimators

a link splitting spectral sequence in khovanov homology we construct a new spectral sequence beginning at the khovanov homology of a link and converging to the khovanov homology of the disjoint union of its components the page at which the sequence collapses gives a lower bound on the splitting number of the link the minimum number of times its components must be passed through one another in order to completely separate them in addition we build on work of kronheimer and mrowka and hedden and ni to show that khovanov homology detects the unlink

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

weighting in survey analysis under informative sampling sampling related to the outcome variable of a regression analysis conditional on covariates is called informative sampling and may lead to bias in ordinary least squares estimation weighting by the reciprocal of the inclusion probability approximately removes such bias but may inflate variance this paper investigates two ways of modifying such weights to improve efficiency while retaining consistency one approach is to multiply the inverse probability weights by functions of the covariates the second is to smooth the weights given values of the outcome variable and covariates optimal ways of constructing weights by these two approaches are explored both approaches require the fitting of auxiliary weight models the asymptotic properties of the resulting estimators are investigated and linearization variance estimators are obtained the approach is extended to pseudo maximum likelihood estimation for generalized linear models the properties of the different weighted estimators are compared in a limited simulation study the robustness of the estimators to misspecification of the auxiliary weight model or of the regression model of interest is discussed

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

control variates for probability and quantile estimation in stochastic systems quantiles indicate the level of system performance that can be delivered with a specified probability while probabilities indicate the likelihood that a specified level of system performance can be achieved we present new estimators for use in simulation experiments designed to estimate such quantiles or probabilities of system performance all of the estimators exploit control variates to increase their precision which is especially important when extreme quantiles in the tails of the distribution of system performance or extreme probabilities near zero or one are of interest control variates are auxiliary random variables with known properties in this case known quantiles and a strong stochastic association with the performance measure of interest since transforming a control variate can increase its effectiveness we propose both continuous and discrete approximations to the optimal variance minimizing transformation for estimating probabilities and then invert the probability estimators to obtain corresponding quantile estimators we also propose a direct control variate quantile estimator that is not based on inverting a probability estimator an empirical study using queueing inventory and project planning examples shows that substantial reductions in mean squared error can be obtained when estimating the 0 9 0 95 and 0 99 quantiles

optimal probability weights for inference with constrained precision abstractprobability weights are used in many areas of research including complex survey designs missing data analysis and adjustment for confounding factors they are useful analytic tools but can lead to statistical inefficiencies when they contain outlying values this issue is frequently tackled by replacing large weights with smaller ones or by normalizing them through smoothing functions while these approaches are practical they are also prone to yield biased inferences this article introduces a method for obtaining optimal weights defined as those with smallest euclidean distance from target weights among all sets of weights that satisfy a constraint on the variance of the resulting weighted estimator the optimal weights yield minimum bias estimators among all estimators with specified precision the method is based on solving a constrained nonlinear optimization problem whose lagrange multipliers and objective function can help assess the trade off between bias and precision of the resulting

a simplified approach to m estimation with application to two stage estimators abstract this paper presents a simple version of the theory of m estimation it is argued that the theory is immediately applicable to almost all estimation schemes employed by econometricians it is further argued that the great overlooked benefit of the theory is that is provides almost automatic asymptotic results e g probability limits and asymptotic covariances thus one need not be a theoretical econometrician to invent and use specially tailored estimators to illustrate its use the theory is applied to a variety of theoretical and applied problems particular attention is paid to two stage estimators

on the use of sampling weights when estimating regression models with survey data abstract in this paper it is argued that when the population regression coefficient is of interest the use of sampling weights can be desirable in regression models with complex survey data a two step ml estimator is proposed as an alternative to ols and weighted least squares specification tests are given the ml estimator does well in simulations including several cases where it is based on a misspecified model the specification tests are effective in selecting the best estimator as an example the methods are used to estimate the returns to education using data from the canadian survey of consumer finances

hypothesis testing with complex survey data the use of classical quadratic test statistics with particular reference to regression problems abstract sample surveys often have complex sample designs with multistage cluster sampling stratification and differential selection probabilities this article is concerned with testing the null hypothesis h 0 where the p dimensional parameter g and is a q dimensional vector of means the asymptotic framework that consists of a sequence of increasing finite populations is used to define as the limit of finite population means as part of the inference we use replicated estimates of variances that take into account the complex sample design the wald statistic can be used to test h 0 but inference for based on the wald statistic can have low power thus an alternative to using a wald test is pursued in this article first define a classical quadratic test statistic that would be used if one had a simple random sample of the population second treating this quadratic form as a population parameter use design based methods to estimate it from the observed survey data last use

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

computing kernel smoothed conditional quantiles from many observations abstract quantiles of a variable y conditional on another variable x when plotted against x can be a useful descriptive tool these plots give a quick impression of the functional form of the relation between x and the location spread and shape of the conditional distribution of y if several y are observed for each x then sample quantiles could be calculated for each x the resulting quantile plot may be quite noisy however and smoothing across x may be desired this article presents an algorithm that calculates kernel smoothed conditional quantiles with a cross validation choice of bandwidth for x it is computationally feasible for large data sets when x assumes a small number of values since it requires only one pass through the full data set the cross validation does not require a pass through the data because of simplifications arising from the l 1 loss function being based on absolute values the technique is illustrated by plotting the conditional quantiles of the net wealth of a sample of

estimating a finite population mean from unequal probability samples abstract two approaches to estimating a finite population mean from unequal probability samples are contrasted in the prediction approach a model is specified for the population values and is used to predict the nonsampled values in the generalized regression approach the horvitz thompson estimator of the population mean is modified to allow the introduction of covariate information sarndal 1980 generalized regression estimates have the desirable property of asymptotic design consistency which is not always enjoyed by estimates in the prediction class however it is suggested that the prediction approach is the more principled method of estimation if asymptotic design consistency is a desirable property in a given application then only models that yield asymptotically design consistent prediction estimates should be used two classes of models with this property are suggested namely fixed and random effects models that allow a separate intercept for subclasses of the population indexed by the pr

approximate bias correction in econometrics abstract this paper discusses methods for reducing the bias of consistent estimators that are biased in finite samples these methods are available whenever the bias function which relates the bias of the parameter estimates to the values of the parameters can be estimated by computer simulation or by some other method if so bias can be reduced by one full order in the sample size and in some cases that may not be unrealistic virtually eliminated unfortunately reducing bias may increase the variance or even the mean squared error of an estimator whether it does so depends on the shape of the bias function the results of the paper are illustrated by applying them to two problems estimating the autoregressive parameter in an ar 1 model with a constant term and estimating a logic model

on the robustness of weighted methods for fitting models to case control data summary we compare the robustness under model misspecification of two approaches to fitting logistic regression models with unmatched case control data one is the standard survey approach based on weighted versions of population estimating equations the other is the likelihood based approach that is standard in medical applications the conventional view is that the less efficient survey weighted approach leads to greater robustness we conclude that this view is not always justified

asymptotic inference from multi stage samples i develop a gmm based framework for asymptotic inference to analyze data from surveys whose designs involve stratification and clustering i set up the estimation problem derive the appropriate asymptotic distribution theory as the number of clusters per stratum tends to infinity and compute asymptotic standard errors that are robust to sample design effects the analysis is then extended to nonparametric regression and to semiparametric estimation based on u processes empirical illustrations are provided using consumption expenditure data from the complexly designed indian national household survey

a general purpose unequal probability sampling plan summary we present a general purpose unequal probability without replacement sampling plan with fixed sample size in contrast to existing such plans our scheme keeps the sample size fixed and lets the population units enter the sample one at a time through a carefully designed random mechanism consequently all high order inclusion probabilities can be easily computed

knot homology via derived categories of coherent sheaves i the mathfrak sl 2 case using derived categories of equivariant coherent sheaves we construct a knot homology theory which categorifies the quantum mathfrak sl m knot polynomial our knot homology naturally satisfies the categorified moy relations and is conjecturally isomorphic to khovanov rozansky homology our construction is motivated by the geometric satake correspondence and is related to manolescu s by homological mirror symmetry

the chromatic polynomial of fatgraphs and its categorification abstract motivated by khovanov homology and relations between the jones polynomial and graph polynomials we construct a homology theory for embedded graphs from which the chromatic polynomial can be recovered as the euler characteristic for plane graphs we show that our chromatic homology can be recovered from the khovanov homology of an associated link we apply this connection with khovanov homology to show that the torsion free part of our chromatic homology is independent of the choice of planar embedding of a graph we extend our construction and categorify the bollobas riordan polynomial a generalization of the tutte polynomial to embedded graphs we prove that both our chromatic homology and the khovanov homology of an associated link can be recovered from this categorification

knot homology via derived categories of coherent sheaves ii mathfrak sl _ m case using derived categories of equivariant coherent sheaves we construct a knot homology theory which categorifies the quantum mathfrak sl m knot polynomial our knot homology naturally satisfies the categorified moy relations and is conjecturally isomorphic to khovanov rozansky homology our construction is motivated by the geometric satake correspondence and is related to manolescu s by homological mirror symmetry

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

a categorification of the jones polynomial author s khovanov mikhail abstract we construct a bigraded cohomology theory of links whose euler characteristic is the jones polynomial

khovanov homology and the symmetry group of a knot we introduce an invariant of tangles in khovanov homology by considering a natural inverse system of khovanov homology groups as application we derive an invariant of strongly invertible knots this invariant takes the form of a graded vector space that vanishes if and only if the strongly invertible knot is trivial while closely tied to khovanov homology and hence the jones polynomial we observe that this new invariant detects non amphicheirality in subtle cases where khovanov homology fails to do so in fact we exhibit examples of knots that are not distinguished by khovanov homology but owing to the presence of a strong inversion may be distinguished using our invariant this work suggests a strengthened relationship between khovanov homology and heegaard floer homology by way of two fold branched covers that we formulate in a series of conjectures

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

quantum link homology via trace functor i motivated by topology we develop a general theory of traces and shadows for an endobicategory which is a pair bicategory and endobifunctor for a graded linear bicategory and a fixed invertible parameter q we quantize this theory by using the endofunctor sigma q such that sigma q alpha q deg alpha sigma alpha for any 2 morphism alpha and coincides with sigma otherwise applying the quantized trace to the bicategory of chen khovanov bimodules we get a new triply graded link homology theory called quantum annular link homology if q 1 we reproduce asaeda przytycki sikora homology for links in a thickened annulus we prove that our homology carries an action of which intertwines the action of cobordisms in particular the quantum annular homology of an n cable admits an action of the braid group which commutes with the quantum group action and factors through the jones skein relation this produces a nontrivial invariant for surfaces knotted in four dimensions moreover a direct computation for torus links shows that the rank of quantum annular homology groups depend on the quantum parameter q

robust estimators for simultaneous equations models this paper presents a class of robust estimators for linear and non linear simultaneous equations models which are a direct generalization of the maximum likelihood estimator the new estimators are obtained as solutions of a generalized likelihood equation they are resistant to deviations from the model distribution to outlying observations and to some model misspecifications an optimality principle leads to the construction of an optimal robust estimator which is the best trade off between efficiency at the model and robustness

robust inference in sample selection models the problem of non random sample selectivity often occurs in practice in many fields the classical estimators introduced by heckman are the backbone of the standard statistical analysis of these models however these estimators are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice we develop a general framework to study the robustness properties of estimators and tests in sample selection models we derive the influence function and the change of variance function of heckman s two stage estimator and we demonstrate the non robustness of this estimator and its estimated variance to small deviations from the model assumed we propose a procedure for robustifying the estimator prove its asymptotic normality and give its asymptotic variance both cases with and without an exclusion restriction are covered this allows us to construct a simple robust alternative to the sample selection bias test we illustrate the use of our new methodology in an analysis of ambulatory expenditures and we compare the performance of the classical and robust methods in a monte carlo simulation study

a spanning tree cohomology theory for links abstract in their recent preprint baldwin ozsvath and szabo defined a twisted version with coefficients in a novikov ring of a spectral sequence previously defined by ozsvath and szabo from khovanov homology to heegaard floer homology of the branched double cover along a link in their preprint they give a combinatorial interpretation of the e 3 term of their spectral sequence the main purpose of the present paper is to prove directly that this e 3 term is a link invariant we also give some concrete examples of computation of the invariant

link homologies and the refined topological vertex we establish a direct map between refined topological vertex and sl n homological invariants of the of hopf link which include khovanov rozansky homol ogy as a special case this relation provides an exact answer for homological invariants of the hopf link whose components are colored by arbitrary representations of sl n at present the mathematical formulation of such homological invariants is available only for the fundamental representation the khovanov rozansky theory and the rela tion with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations r1 r2 our result is a first direct veri fication of a series of conjectures which identifies link homologies with the hilbert space of bps states in the presence of branes where the physical interpretation of gradings is in terms of charges of the branes ending on lagrangian branes

a propensity score adjustment for multiple group structural equation modeling in the behavioral and social sciences quasi experimental and observational studies are used due to the difficulty achieving a random assignment however the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates to estimate average treatment effects when the treatment variable is binary rosenbaum and rubin 1983a proposed adjustment methods for pretreatment variables using the propensity score

khovanov homology and the slice genus we use lee s work on the khovanov homology to define a knot invariant s we show that s k is a concordance invariant and that it provides a lower bound for the smooth slice genus of k as a corollary we give a purely combinatorial proof of the milnor conjecture

khovanov homology open books and tight contact structures abstract we define the reduced khovanov homology of an open book s and identify a distinguished contact element in this group which may be used to establish the tightness or non fillability of contact structures compatible with s our construction generalizes the relationship between the reduced khovanov homology of a link and the heegaard floer homology of its branched double cover as an application we give combinatorial proofs of tightness for several contact structures which are not stein fillable lastly we investigate a comultiplication structure on the reduced khovanov homology of an open book which parallels the comultiplication on heegaard floer homology defined in baldwin 2008 4

inference on inequality from household survey data abstract i develop a theory of asymptotic inference for the lorenz curve and the gini coefficient for testing economic inequality when the data come from stratified and clustered household surveys with large number of clusters per stratum using the asymptotic framework of bhattacharya asymptotic inference from multi stage surveys journal of econometrics 126 1 145 171 i derive a weak convergence result for the continuously indexed lorenz process even when the underlying density is not uniformly bounded away from zero i provide analytical formulae for the asymptotic covariance functions that are corrected for both stratification and clustering and develop consistent tests for lorenz dominance inference on the gini coefficient follows as a corollary the methods are applied to per capita household expenditure data from the complexly designed indian national sample survey to test for changes in inequality before and after the reforms of the early 1990s ignoring the survey design is seen to produce qualitatively different results especially in the urban sector where the population sorts more completely into rich and poor neighborhoods

khovanov seidel quiver algebras and ozsvath szabo s bordered theory abstract in the 2016 preprint kauffman states bordered algebras and a bigraded knot invariant ozsvath and szabo introduced a set of algebraic constructions in the spirit of bordered heegaard floer homology their constructions can be used to compute knot floer homology algebraically for knots in the 3 sphere in this paper we investigate a relationship between ozsvath szabo s bordered theory and the algebras and bimodules constructed by khovanov and seidel in quivers floer cohomology and braid group actions 2002 specifically we show that the khovanov seidel quiver algebras are isomorphic to quotients of idempotent truncations of some of ozsvath szabo s algebras furthermore we show that the dg bimodule associated to a braid generator by khovanov seidel with the right action restricted using the quotient map is homotopy equivalent to ozsvath szabo s da bimodule with the left action induced using the quotient map