maximum likelihood estimation of functionals of discrete distributions we consider the problem of estimating functionals of discrete distributions and focus on a tight up to universal multiplicative constants for each specific functional nonasymptotic analysis of the worst case squared error risk of widely used estimators we apply concentration inequalities to analyze the random fluctuation of these estimators around their expectations and the theory of approximation using positive linear operators to analyze the deviation of their expectations from the true functional namely their bias we explicitly characterize the worst case squared error risk incurred by the maximum likelihood estimator mle in estimating the shannon entropy h p sum i 1 s p i ln p i and the power sum f alpha p sum i 1 s p i alpha alpha 0 up to universal multiplicative constants for each fixed functional for any alphabet size s leq infty and sample size n for which the risk may vanish as a corollary for shannon entropy estimation we show that it is necessary and sufficient to have n gg s observations for the mle to be consistent in addition we establish that it is necessary and sufficient to consider n gg s 1 alpha samples for the mle to consistently estimate f alpha p 0 the minimax rate optimal estimators for both problems require s ln s and s 1 alpha ln s samples which implies that the mle has a strictly sub optimal sample complexity when 1 we show that the worst case squared error rate of convergence for the mle is n 2 alpha 1 for infinite alphabet size while the minimax squared error rate is n ln n 2 alpha 1 when alpha geq 3 2 the mle achieves the minimax optimal rate n 1 regardless of the alphabet size as an application of the general theory we analyze the dirichlet prior smoothing techniques for shannon entropy estimation in this context one approach is to plug in the dirichlet prior smoothed distribution into the entropy functional while the other one is to calculate the bayes estimator for entropy under the dirichlet prior for squared error which is the conditional expectation we show that in general such estimators do not improve over the maximum likelihood estimator no matter how we tune the parameters in the dirichlet prior this approach cannot achieve the minimax rates in entropy estimation the performance of the minimax rate optimal estimator with n samples is essentially at least as good as that of dirichlet smoothed entropy estimators with n ln n samples

uniform estimates for the finite time ruin probability in the dependent renewal risk model abstract this paper investigates the finite time ruin probability in the dependent renewal risk model where the claim sizes are independent and identically distributed random variables with strongly subexponential tails and the interarrival times are negatively dependent we establish an asymptotic estimate which holds uniformly for the time horizon varying in the positive half line

bootstrap inference in partially identified models defined by moment inequalities coverage of the identified set this paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identi ed econometric models we consider econometric models de ned by nitely many weak moment inequalities y which encompass many applications of economic interest the objective of our inferential procedure is to cover the identi ed set with a prespeci ed probability z we compare our bootstrap procedure a competing asymptotic approximation and subsampling proce dures in terms of the rate at which they achieve the desired coverage level also known as the error in the coverage probability under certain conditions we show that our bootstrap procedure and the asymp totic approximation have the same order of error in the coverage probability which is smaller than the one obtained by using subsampling this implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling a monte carlo study con rms this nding in a small sample simulation

precise rates in the law of the logarithm for negatively associated random variables let x n n 1 be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance set s email protected k 1 nx k m n max k n s k n 1 suppose s 2 ex 1 email protected k 2 ex 1x k we study the precise rates of a kind of weighted infinite series of p m n email protected snlogn and p s n email protected snlogn as email protected 0 and p m email protected email protected email protected 2n8logn as email protected the results are related to the convergence rates of the law of the logarithm and the chung type law of the logarithm

diffusion equation techniques in stochastic monotonicity and positive correlations a diffusion equation approach is investigated for the study of stochastic monotonicity positive correlations and the preservation of lipschitz functions necessary and sufficient conditions are given for diffusion semigroups to be stochastically monotonic and to preserve the class of positively correlated measures applications are given which discuss the shape of the ground state for schrodinger operators v with fkg potentialsv

exterior algebra structure on relative invariants of reflection groups let g be a reflection group acting on a vector space v over a field with zero characteristic we denote by s v the coordinate ring of v by m a finite dimensional g module and by a one dimensional character of g in this article we define an algebra structure on the isotypic component associated to of the algebra s v otimes lambda m this structure is then used to obtain various generalizations of usual criterions on regularity of integers

temporal integration and compression near absolute threshold in normal and impaired ears the decrease in absolute threshold with increasing stimulus duration often referred to as temporal integration is greater for listeners with normal hearing than for listeners with sensorineural hearing loss it has been suggested that the difference is related to reduced basilar membrane bm compression in the impaired group the present experiment tested this hypothesis by comparing temporal integration and bm compression in normal and impaired ears at low levels absolute thresholds were measured for 4 24 and 44 ms pure tone signals with frequencies f s of 2 and 4 khz the difference between the absolute thresholds for the 4 and 24 ms signals was used as a measure of temporal integration compression near threshold was estimated by measuring the level of a 100 ms off frequency 0 45f s pure tone forward masker required to mask a 44 ms pure tone signal presented at sensation levels of 5 and 10 db there was a significant negative correlation between amount of temporal integration and absolute threshold however there was no correlation between absolute threshold and compression at low levels both normal and impaired ears showed a nearly linear response the results suggest that the differences in integration between normal and impaired ears cannot be explained by differences in bm compression

reduced feedback schemes using random beamforming in mimo broadcast channels a random beamforming scheme for the gaussian mimo broadcast channel with channel quality feedback is investigated and extended considering the case where the n receivers each have n receive antennas the effects of feeding back various amounts of signal to interference plus noise ratio sinr information are analyzed using the results from order statistics of the ratio of a linear combination of exponential random variables the distribution function of the maximum order statistic of the sinr observed at the receiver is found the analysis from viewing each antenna as an individual user is extended to allow combining at the receivers where it is known that the linear mmse combiner is the optimal linear receiver and the cdf for the sinr after optimal combining is derived analytically using the delta method the asymptotic distribution of the maximum order statistic of the sinr with and without combining is shown to be in the nomenclature of extreme order statistics of type 3 the throughput of the feedback schemes are shown to exhibit optimal scaling asymptotically in the number of users finally to further reduce the amount of feedback a hard threshold is applied to the sinr feedback the amount of feedback saved by implementing a hard threshold is determined and the effect on the system throughput is analyzed and bounded

directional dependence of random vectors in this paper we define and study several properties of the concept of multivariate directional dependence and study the new concept in terms of copulas and provide new measures of multivariate association based on directional dependence finally we show the relationships of directional dependence with other dependence concepts such as association and conditional dependence

invariants of polynomials mod frobenius powers abstract lewis reiner and stanton conjectured a hilbert series for a space of invariants under an action of finite general linear groups using q t binomial coefficients this work gives an analog in positive characteristic of theorems relating various catalan numbers to the representation theory of rational cherednik algebras they consider a finite general linear group as a reflection group acting on the quotient of a polynomial ring by iterated powers of the irrelevant ideal under the frobenius map we prove a variant of their conjecture in the local case when the group acting fixes a reflecting hyperplane

some concepts of negative dependence abstract the theory of positive dependence notions cannot yield useful results for some widely used distributions such as the multinomial dirichlet and the multivariate hypergeometric some conditions of negative dependence that are satisfied by these distributions and which have practical meaning are introduced preservation results for some of these concepts are derived useful inequalities for some widely used distributions are obtained results of mallows 1969 that apply to the multinomial distributions are extended to more distributions examples are listed author

tail behavior of random sums of negatively associated increments abstract let x x k k 1 be a sequence of negatively associated random variables with a common distribution function and finite expectation and let be a nonnegative integer valued random variable independent of x k k 1 in this paper we give unified form for the asymptotic behavior of the random sums s k 1 x k in the case of lim x p x x p x c 0 the results extend the earlier results of aleskeviciene et al 2008 2

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

the sorted effects method discovering heterogeneous effects beyond their averages the partial ceteris paribus effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates despite the apparent importance of heterogeneity a common practice in modern empirical work is to largely ignore it by reporting average partial effects or at best average effects for some groups while average effects provide very convenient scalar summaries of typical effects by definition they fail to reflect the entire variety of the heterogeneous effects in order to discover these effects much more fully we propose to estimate and report sorted effects a collection of estimated partial effects sorted in increasing order and indexed by percentiles by construction the sorted effect curves completely represent and help visualize the range of the heterogeneous effects in one plot they are as convenient and easy to report in practice as the conventional average partial effects they also serve as a basis for classification analysis where we divide the observational units into most or least affected groups and summarize their characteristics we provide a quantification of uncertainty standard errors and confidence bands for the estimated sorted effects and related classification analysis and provide confidence sets for the most and least affected groups the derived statistical results rely on establishing key new mathematical results on hadamard differentiability of a multivariate sorting operator and a related classification operator which are of independent interest we apply the sorted effects method and classification analysis to demonstrate several striking patterns in the gender wage gap we find that this gap is particularly strong for married women ranging from 60 to 0 between the 2 and 98 percentiles as a function of observed and unobserved characteristics while the gap for never married women ranges from 40 to 20 the most adversely affected women tend to be married do not have college degrees work in sales and have high levels of potential experience

reliability properties under a stopping time shift abstract considering a series representation of a coherent system using a shift transform of the components lifetime t i at its critical level y i we study two problems first under such a shift transform we analyse the preservation properties of the non parametric distribution classes and secondly the association preserving property of the components lifetime under such transformations

solving optimization problems with diseconomies of scale via decoupling we present a new framework for solving optimization problems with a diseconomy of scale in such problems our goal is to minimize the cost of resources used to perform a certain task the cost of resources grows superlinearly as xq q 1 with the amount x of resources used we define a novel linear programming relaxation for such problems and then show that the integrality gap of the relaxation is aq where aq is the q th moment of the poisson random variable with parameter 1 using our framework we obtain approximation algorithms for the minimum energy efficient routing minimum degree balanced spanning tree load balancing on unrelated parallel machines and unrelated parallel machine scheduling with nonlinear functions of completion times problems our analysis relies on the decoupling inequality for nonnegative random variables the inequality states that ie1nxi q cq ie1nyi q where xi are independent nonnegative random variables yi are possibly dependent nonnegative random variables and each yi has the same distribution as xi the inequality was proved by de la pena in 1990 de la pena ibragimov and sharakhmetov showed that cq 2 for qi 1 2 and cq aq1 q for q 2 we show that the optimal constant is cqe aq1 q for any q 1 we then prove a more general inequality for every convex function v elv ie1nxi r elv p ie1n yi r and for every concave function el ie1n xi r el p ie1n yi r where p is a poisson random variable with parameter 1 independent of the random variables yi

restricted isometry property for general p norms the restricted isometry property rip is a fundamental property of a matrix which enables sparse recovery informally an m times n matrix satisfies rip of order k for the ell p norm if ax p approx x p for every vector x with at most k non zero coordinates for every 1 leq p we obtain almost tight bounds on the minimum number of rows m necessary for the rip property to hold prior to this paper only the cases p 1 1 1 log n and 2 were studied interestingly our results show that the case p 2 is a singularity point the optimal number of rows m is widetilde theta k p for all p in 1 infty setminus 2 as opposed to widetilde theta k for p 2 we also obtain almost tight bounds for the column sparsity of rip matrices and discuss the implications of our results for the stable sparse recovery problem as defined by candes et al

convergence of series of dependent φ subgaussian random variables the almost sure convergence of weighted sums of subgaussian m acceptable random variables is investigated as corollaries the main results are applied to the case of negatively dependent and m dependent subgaussian random variables finally an application to random fourier series is presented

approximations for finite time ruin probability in a dependent discrete time risk model with cmc simulations consider a discrete time risk model in which the insurer is allowed to invest its wealth into a risk free or a risky portfolio under a certain regulation then the insurer is said to be exposed to a stochastic economic environment that contains two kinds of risks the insurance risk and financial risk within period i the net insurance loss is denoted by xi and the stochastic discount factor from time i to zero is denoted by i for any integer n assume that x1 xn form a sequence of pairwise asymptotically independent but not necessarily identically distributed real valued random variables with distributions f1 fn respectively 1 2 n are another sequence of arbitrarily dependent positive random variables and the two sequences are mutually independent under the assumption that the average distribution n1i 1nfi is dominatedly varying tailed and some moment conditions on i i 1 n we derive a weakly equivalent formula for the finite time ruin probability we demonstrate our obtained results through a crude monte carlo simulation with asymptotics

precise asymptotics for the linear processes generated by associated random variables in hilbert spaces let e k k z be a strictly stationary associated sequence of random variables taking values in a real separable hilbert space and a k k z be a sequence of bounded linear operators for a linear process x k i a i e k i the precise probability and moment convergence rates of i 1 nx i in some limit theorems are discussed

independence via uncorrelatedness under certain dependence structures a characterization of independence via uncorrelatedness is shown to hold for the families satisfying positive and negative dependence conditions for the associated random variables the bounds on covariance functions obtained by lebowitz comm math phys 28 1972 313 321 readily yield such a characterization an elementary proof for the same characterization is also given for a condition weaker than association labeled as strong positive negative orthant dependence this condition is compared with the linear positive dependence under which newman and wright ann probab 9 1981 671 675 obtained the characterization

nonparametric identification in panels using quantiles abstract this paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity the effects of interest are derivatives of the average and quantile structural functions of the model we find that these derivatives are identified with two time periods for stayers i e for individuals with the same regressor values in two time periods we show that the identification results carry over to models that allow location and scale time effects we propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects the bootstrap proposed allows inference for function valued parameters such as quantile effects uniformly over a region of quantile indices and or regressor values an empirical application to engel curve estimation with panel data illustrates the results

negative association of random variables with applications random variables x 1 cdots x k are said to be negatively associated na if for every pair of disjoint subsets a 1 a 2 of 1 2 cdots k operatorname cov lbrack f x 1 i in a 1 g x j j in a 2 rbrack leq 0 for all nondecreasing functions f g the basic properties of negative association are derived especially useful is the property that nondecreasing functions of mutually exclusive subsets of na random variables are na this property is shown not to hold for several other types of negative dependence recently proposed one consequence is the inequality p x i leq x i i 1 cdots k leq prod k 1p x i leq x i for na random variables x 1 cdots x k and the dual inequality resulting from reversing the inequalities inside the square brackets in another application it is shown that negatively correlated normal random variables are na other na distributions are the a multinomial b convolution of unlike multinomials c multivariate hypergeometric d dirichlet and e dirichlet compound multinomial negative association is shown to arise in situations where the probability measure is permutation invariant applications of this are considered for sampling without replacement as well as for certain multiple ranking and selection procedures in a somewhat striking example na and positive association representing quite strong opposing types of dependence are shown to exist side by side in models of categorical data analysis

deconvolving multivariate kernel density estimates from contaminated associated observations we consider the estimation of the multivariate probability density function f x sub 1 x sub p of x sub 1 x sub p of a stationary positively or negatively associated pa or na random process x sub i sub i 1 sup spl infin from noisy observations both ordinary smooth and super smooth noise are considered quadratic mean and asymptotic normality results are established

association of normal random variables and slepian s inequality abstract a simple extension of slepian s inequality is given which implies the original inequality and the result that positively correlated normal variables are associated author

intensity discrimination of gaussian windowed tones indications for the shape of the auditory frequency time window the just noticeable difference in intensity jnd i was measured for 1 khz tones with a gaussian shaped envelope as a function of their spectro temporal shape the stimuli with constant energy and a constant product of bandwidth and duration ranged from a long duration narrow band tone to a short duration broadband click the jnd i was measured in three normal hearing listeners at sensation levels of 0 10 20 and 30 db in 35 db a spl pink noise at intermediate sensation levels jnd i depends on the spectro temporal shape at the extreme shapes tones and clicks intensity discrimination performance is best whereas at intermediate shapes the jnd i is larger similar results are observed at a higher overall sound level and at a higher carrier frequency the maximum jnd i is observed for stimuli with an effective bandwidth of about 1 3 octave and an effective duration of 4 ms at 1 khz 1 ms at 4 khz a generalized multiple window model is proposed that assumes that the spectro temporal domain is partitioned into internal auditory frequency time windows the model predicts that intensity discrimination thresholds depend upon the number of windows excited by a signal jnd i is largest for stimuli covering one window

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

towards a theory of negative dependence the fkg theorem says that the positive lattice condition an easily checkable hypothesis which holds for many natural families of events implies positive association a very useful property thus there is a natural and useful theory of positively dependent events there is as yet no corresponding theory of negatively dependent events there is however a need for such a theory this paper unfortunately contains no substantial theorems its purpose is to present examples that motivate a need for such a theory give plausibility arguments for the existence of such a theory outline a few possible directions such a theory might take and state a number of specific conjectures which pertain to the examples and to a wish list of theorems

auditory temporal integration and the power function model the auditory temporal integration function was studied with the objective of improving both its quantitative description and the specification of its principle independent variable stimulus duration in sec i temporal integration data from 20 studies were subjected to uniform analyses using standardized definitions of duration and two models of temporal integration analyses revealed that these data were best described by a power function model used in conjunction with a definition of duration termed assigned duration that de emphasized the rise fall portions of the stimuli there was a strong effect of stimulus frequency and in general the slope of the temporal integration function was less than 10 db per decade of duration i e a power function exponent less than 1 0 in sec ii an experimental study was performed to further evaluate the models and definitions detection thresholds were measured in 11 normal hearing human subjects using a total of 24 single burst and multiple burst acoustic stimuli of 3 125 khz the issues addressed are the quantitative description of the temporal integration function the definition of stimulus duration the similarity of the integration processes for single burst and multiple burst stimuli and the contribution of rise fall time to the integration process a power function in conjunction with the assigned duration definition was again most effective in describing the data single and multiple burst stimuli both seemed to be integrated by the same central mechanism with data for each type of stimulus being described by a power function exponent of approximately 0 6 at 3 125 khz it was concluded that the contribution of the rise fall portions of the stimuli can be factored out from the rest of the temporal integration process in sec iii the conclusions that emerged from the review of published work and the present experimental work suggested that auditory temporal integration is best described by a power function in conjunction with the assigned duration definition the exponent for the power function is typically less than 1 0 and varies with frequency and hearing level second a means of empirically assaying the contribution of the rise fall portions of the stimuli is presented and evaluated finally properties of a central auditory integrator are hypothesized abstract truncated at 250 words

psychometric functions and temporal integration in electric hearing temporal integration functions and psychometric functions for detection were obtained in eight users of the nucleus 22 electrode cochlear implant stimuli were 100 hz 200 microseconds phase trains of biphasic pulses with durations ranging from 0 44 to 630 4 ms 1 to 64 pulses temporal integration functions were measured for 21 electrodes slopes of these functions were considerably shallower than the 2 5 db doubling slopes typically observed in acoustic hearing they varied widely across subjects and for different electrodes in a given subject ranging from 0 06 to 1 94 db doubling of stimulus pulses with a mean standard deviation s d value of 0 42 0 38 psychometric functions were measured for 11 of the same 21 electrodes slopes of psychometric functions also varied across subjects and electrodes and were 2 20 times steeper than those reported by other investigators for normal hearing and cochlear impaired acoustic listeners slopes of individual psychometric functions for 1 2 4 and 8 pulse stimuli ranged from 0 20 to 1 84 log d db with a mean s d value of 0 77 0 45 psychometric function slopes did not vary systematically with stimulus duration in most cases a clear inverse relation between slopes of psychometric functions and slopes of temporal integration functions was observed this relation was reasonably well described by a hyperbolic function predicted by the multiple looks model of temporal integration viemeister and wakefield j acoust soc am 90 858 865 1991 psychometric function slopes tended to increase with absolute threshold and were inversely correlated with dynamic range suggesting that observed differences in psychometric function slopes across subjects and electrodes may reflect underlying differences in neural survival

posterior convergence given the mean for various applications one wants to know the asymptotic behavior of x the posterior density of a parameter given the mean x of the data rather than the full data set here we show that x is asymptotically normal in an l 1 sense and we identify the mean of the limiting normal and its asymptotic variance the main results are first proved assuming that x 1 x n are independent and identical suitable modifications to obtain results for the nonidentical case are given separately our results may be used to construct approximate hpd highest posterior density sets for the parameter which is of use in the statistical theory of standardized educational tests they may also be used to show the covariance between two test items conditioned on the mean is asymptotically nonpositive this has implications for constructing tests of item independence

weighted likelihood estimation under two phase sampling we develop asymptotic theory for weighted likelihood esti mators wle under two phase stratied sampling without replacement we also consider several variants of wle s involving estimated weights and calibration a set of empirical process tools are developed including a glivenko cantelli theorem a theorem for rates of convergence of z estimators and a donsker theorem for the inverse probability weighted em pirical processes under two phase sampling and sampling without replace ment at the second phase using these general results we derive asymptotic distributions of the wle of a nite dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is es timable either at regular or non regular rates we illustrate these results and methods in the cox model with right censoring and interval censor ing we compare the methods via their asymptotic variances under both sampling without replacement and the more usual and easier to analyze assumption of bernoulli sampling at the second phase ams 2000 subject classications primary 62e20 secondary 62g20 62d99 62n01

temporal integration at 6 khz as a function of masker bandwidth thresholds were measured for a 6 khz sinusoidal signal presented within a 500 ms masker the masker was either a bandpass gaussian noise of varying bandwidth or a sinusoid of the same frequency as the signal the spectrum level of the noise masker was kept constant at 20 db spl and the level of the sinusoidal masker was 40 db spl thresholds for signal durations between 2 and 300 ms were measured for masker bandwidths ranging from 60 to 12 000 hz the masker was spectrally centered around 6 khz for masker bandwidths less than 600 hz the slope of the temporal integration function decreased with decreasing masker bandwidth the results are not consistent with current models of temporal integration or temporal resolution it is suggested that the results at narrow bandwidths can be understood in terms of changes in the power spectrum of the stimulus envelope or modulation spectrum according to this view the onset and offset ramps of the signal introduce detectable high frequency components into the modulation spectrum which provide a salient cue in narrowband maskers for broadband maskers these high frequency components are masked by the inherent rapid fluctuations in the masker envelope additionally for signal durations between 7 and 80 ms signal thresholds decreased by up to 5 db as the masker bandwidth increased from 1200 to 12 000 hz the mechanisms underlying this effect are not yet fully understood

intentionally biased bootstrap methods summary a class of weighted bootstrap techniques called biased bootstrap or b bootstrap methods is introduced it is motivated by the need to adjust empirical methods such as the uniform bootstrap in a surgical way to alter some of their features while leaving others unchanged depending on the nature of the adjustment the b bootstrap can be used to reduce bias or to reduce variance or to render some characteristic equal to a predetermined quantity examples of the last application include a b bootstrap approach to hypothesis testing in nonparametric contexts where the b bootstrap enables simulation under the null hypothesis even when the hypothesis is false and a b bootstrap competitor to tibshirani s variance stabilization method an example of the bias reduction application is adjustment of nadaraya watson kernel estimators to make them competitive with local linear smoothing other applications include density estimation under constraints outlier trimming sensitivity analysis skewness or kurtosis reduction and shrinkage

a large sample study of the bayesian bootstrap on donne une justification asymptotique du bootstrap bayesien on obtient des resultats lies a l article de rubin 1981 dans le meme sens que bickel et freedman 1981 et singh 1981 se rapportant a l article d efron 1979

lower bounds on the restitution error in the hopfield model this paper contains a first rigorous results at the direction of the converse to newman s bounds 11 on the storage capacity for the hopfield model of associative memory let m denote the number of stored patterns and n that of neurons assuming that m n to alpha as n to infty we show that for alpha 0 the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value approximately 0 05 as alpha to infty

the consistency of the nearest neighbor estimator of the density function based on wod samples abstract in this paper the consistency of the nearest neighbor estimator of the density function based on widely orthant dependent wod in short samples is investigated the convergence rate of strong consistency the complete consistency the uniformly complete consistency and uniformly strong consistency of the nearest neighbor estimator of the density function based on wod samples are established our results established in the paper generalize or improve the corresponding ones for independent samples and some negatively dependent samples

m matrices as covariance matrices of multinormal distributions abstract the class of multivariate normal densities n 0 whose inverse covariance matrix 1 is an m matrix is equivalent to this normal density being multivariate totally positive of order 2 mtp 2 equivalent characterizations are given in terms of certain partial correlation coefficients being positive it is further shown that related partial and multiple regression coefficients and canonical correlation are positive when is an m matrix the corresponding normal random vector components are negatively associated this concept and some extensions are discussed

manifest characterization and testing for certain latent properties work due to junker and more recently due to junker and ellis characterized desired latent properties of an educational testing procedure in terms of a collection of other manifest properties this is important because one can only propose tests for manifest quantities not latent ones here we complete the conversion of a pair of latent properties to equivalent conditions in terms of four manifest quantities and identify a general method for producing tests for manifest properties 1 introduction item response theory irt is the statistical theory of standardized tests which are commonly used in educational testing applications the goal is to combine the data generated by many examinees answering a collection of test items so as to estimate the value of a parameter or trait say for each of the examinees the parameter is intended to quantify a latent trait such as mathematics ability the traits are latent in the sense that they cannot be measured directly more specifically desired properties of suchtesting procedures are called latent when their statement depends explicitly on the the latent trait being estimated most efforts at modeling involve the introduction of latent parameters one specifies parameters to reflect aspects of the physical problem such as the individual achievement of each examinee the difficulty of each test item specialized knowledge that certain examinees might possess etc this is in contrast to the manifest properties of a testing procedure which can be phrased in a way that does not explicitly depend on the latent trait the limitation of a latent model is that it contains parameters for the latent trait the experimenter wants to estimate each examinee s parameter value and so cannot perform hypothesis tests on a conjectured model in the usual way the solution to this problem is to convert latent models or latent statements about them to physically meaningful manifest properties which are provably mathematically equivalent to the latent properties actually wanted manifest statements are amenable to conventional hypothesis testing and the problem then becomes the identification of optimal hypothesis tests for the manifest quantities in this way one can test hypotheses that are independent of the latent structure at least in principle the goal of characterizing latent properties in terms of manifest properties to be tested begins with stout 1987 stout considers the requirement that

a strong approximation theorem for positively dependent gaussian sequences and its applications abstract under the polynomial decay rates and finite second moment a strong approximation theorem for partial sums of linear positive quadrant dependent gaussian sequences is derived as applications the law of the iterated logarithm the chung type law of the iterated logarithm and the almost sure central limit theorem are obtained with minimal conditions

on the failure of the bootstrap for matching estimators matching estimators are widely used in empirical economics for the evaluation of programs or treatments researchers using matching methods often apply the bootstrap to calculate the standard errors however no formal justification has been provided for the use of the bootstrap in this setting in this article we show that the standard bootstrap is in general not valid for matching estimators even in the simple case with a single continuous covariate where the estimator is root n consistent and asymptotically normally distributed with zero asymptotic bias valid inferential methods in this setting are the analytic asymptotic variance estimator of abadie and imbens 2006a as well as certain modifications of the standard bootstrap like the subsampling methods in politis and romano 1994

on the strong convergence rate for positively associated random variables abstract for sequences of the positively associated random variables which are strictly weaker than the classical associated random ones introduced by esary et al 1967 7 strong convergence rate n 1 2 log n 1 2 is obtained which reaches the available one for independent random variables in terms of berstein type inequality further we give the corresponding precise asymptotics with respect to the rate mentioned above which extend and improve the relevant results in fu 2009 8

validity of dependent bootstrapping in finite populations abstract the traditional bootstrap resamples with replacement from the original sample observations to form arrays of row wise independent and identically distributed bootstrap random variables there are situations for example when sampling from finite populations where resampling without replacement provides a more realistic bootstrap procedure and produces dependent bootstrap random variables the desired properties of consistency and asymptotic validity are shown to hold for certain nonparametric dependent bootstrap estimators in addition it is shown that the smaller variation in dependent bootstrap estimators can be used to increase precision in some of the estimators

critical ratios of beluga whales delphinapterus leucas and masked signal duration this article examines the masking of a complex beluga vocalization by natural and anthropogenic noise the call consisted of six 150ms pulses exhibiting spectral peaks between 800hz and 8khz comparing the spectra and spectrograms of the call and noises at detection threshold showed that the animal did not hear the entire call at threshold it only heard parts of the call in frequency and time from the masked hearing thresholds in broadband continuous noises critical ratios were computed fletcher critical bands were narrower than either 15 or 111 of an octave at the low frequencies of the call 2khz depending on which frequency the animal cued on from the masked hearing thresholds in intermittent noises the audible signal duration at detection threshold was computed the intermittent noises differed in gap length gap number and masking but the total audible signal duration at threshold was the same 660ms this observation supports a multiple looks model the two amplitude modulated noises exhi

jacobians of reflection groups steinberg showed that when a finite reflection group acts on a real or complex vector space of finite dimension the jacobian determinant of a set of basic invariants factors into linear forms which define the reflecting hyperplanes this result generalizes verbatim to fields whose characteristic is prime to the order of the group our main theorem gives a generalization of steinberg s result for groups with a polynomial ring of invariants over arbitrary fields using a ramification formula of benson and crawley boevey

the law of the iterated logarithm for positively dependent random variables the levy s type maximal inequality is a key to establish the law of the iterated logarithm for associated random variables unfortunately this type inequality cannot be obtained for a generalization of association i e linear positive quadrant dependence because of their special dependence structure the purpose of this paper is to provide a different approach to obtain a law of the iterated logarithm for a sequence of linear positive quadrant dependent random variables

exact rates in log law for positively associated random variables abstract let x n n 1 be a strictly stationary sequence of positively associated random variables with mean zero and finite variance set s n k 1 n x k m n max k n s k n 1 suppose 2 e x 1 2 2 k 2 e x 1 x k in this paper we study the exact convergence rates of a kind of weighted infinite series of p m n e n log n p s n e n log n and i s n e n log n as e 0 respectively

on the connectivity of sensor networks under random pairwise key predistribution we investigate the connectivity of wireless sensor networks under the random pairwise key predistribution scheme of chan under the assumption of full visibility this reduces to studying the connectivity in the so called random k out graph h n k here n is the number of nodes and k n is an integer parameter affecting the number of keys stored at each node we show that if k 2 respectively k 1 the probability that h n k is a connected graph approaches 1 respectively 0 as n goes to infinity for the one law this is done by establishing an explicitly computable lower bound on the probability of connectivity using this bound we see that with high probability network connectivity can already be guaranteed with k 2 by a relatively small number of sensors this corrects earlier predictions made on the basis of a heuristic transfer of connectivity results available for erdos renyi graphs

anti concentration and honest adaptive confidence bands modern construction of uniform condence e and nickl 2010 this condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process equivalently for the supremum of a gaussian process with the same covariance function as that of the studentized empirical process the principal contribution of this paper is to remove the need for this classical condition we show that a considerably weaker sucient condi tion is derived from an anti concentration property of the supremum of the approximating gaussian process and we derive an inequality lead ing to such a property for separable gaussian processes we refer to the new condition as a generalized sbr condition our new result shows that the supremum does not concentrate too fast around any value we then apply this result to derive a gaussian multiplier bootstrap procedure for constructing honest condence bands for nonparametric density estimators this result can be applied in other nonparametric problems as well an essential advantage of our approach is that it ap plies generically even in those cases where the limit distribution of the supremum of the studentized empirical process does not exist or is un known this is of particular importance in problems where resolution levels or other tuning parameters have been chosen in a data driven fash ion which is needed for adaptive constructions of the condence bands furthermore our approach is asymptotically honest at a polynomial rate namely the error in coverage level converges to zero at a fast polynomial speed with respect to the sample size in sharp contrast the approach based on extreme value theory is asymptotically honest only at a logarithmic rate the error converges to zero at a slow loga rithmic speed finally of independent interest is our introduction of a new practical version of lepski s method which computes the optimal non conservative resolution levels via a gaussian multiplier bootstrap method

the psychophysics of absolute threshold and signal duration a probabilistic approach the absolute threshold for a tone depends on its duration longer tones have lower thresholds this effect has traditionally been explained in terms of temporal integration involving the summation of energy or perceptual information over time an alternative probabilistic explanation of the process is formulated in terms of simple equations that predict not only the time duration dependence but also the shape of the psychometric function at absolute threshold it also predicts a tight relationship between these two functions measurements made using listeners with either normal or impaired hearing show that the probabilistic equations adequately fit observed threshold duration functions and psychometric functions the mathematical formulation implies that absolute threshold can be construed as a two valued function a gain and b sensory threshold and both parameters can be estimated from threshold duration data sensorineural hearing impairment is sometimes associated with a smaller threshold duration effect and sometimes with steeper psychometric functions the equations explain why these two effects are expected to be linked the probabilistic approach has the potential to discriminate between hearing deficits involving gain reduction and those resulting from a raised sensory threshold

a max norm constrained minimization approach to 1 bit matrix completion we consider in this paper the problem of noisy 1 bit matrix completion under a general non uniform sampling distribution using the max norm as a convex relaxation for the rank a max norm constrained maximum likelihood estimate is introduced and studied the rate of convergence for the estimate is obtained information theoretical methods are used to establish a minimax lower bound under the general sampling model the minimax upper and lower bounds together yield the optimal rate of convergence for the frobenius norm loss computational algorithms and numerical performance are also discussed

k connectivity in random k out graphs intersecting erdős renyi graphs we investigate k connectivity in secure wireless sensor networks under the random pairwise key predistribution scheme with unreliable links when wireless communication links are modeled as independent on off channels this amounts to analyzing a random graph model formed by intersecting a random k out graph and an erd s renyi graph we present conditions on how to scale the parameters of this intersection model so that the resulting graph is k connected with probability approaching to one resp zero as the number of nodes gets large the resulting zero one law is shown to improve and sharpen the previous result on the 1 connectivity of the same model we also provide numerical results to support our analysis

mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability abstract from the classical notion of uniform integrability of a sequence of random variables a new concept of integrability called h integrability is introduced for an array of random variables concerning an array of constants we prove that this concept is weaker than other previous related notions of integrability such as cesaro uniform integrability chandra sankhy ser a 51 1989 309 317 uniform integrability concerning the weights ordonez cabrera collect math 45 1994 121 132 and cesaro integrability chandra and goswami j theoret probab 16 2003 655 669 under this condition of integrability and appropriate conditions on the array of weights mean convergence theorems and weak laws of large numbers for weighted sums of an array of random variables are obtained when the random variables are subject to some special kinds of dependence a rowwise pairwise negative dependence b rowwise pairwise non positive correlation c when the sequence of random variables in every row is mixing finally we consider the general weak law of large numbers in the sense of gut statist probab lett 14 1992 49 52 under this new condition of integrability for a banach space setting

negative dependence and the geometry of polynomials we introduce the class of strongly rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter this class covers important models such as determinantal measures e g product measures and uniform random spanning tree measures and distributions for symmetric exclusion processes we show that strongly rayleigh measures enjoy all virtues of negative dependence and we also prove a series of conjectures due to liggett pemantle and wagner respectively moreover we extend lyons recent results on determinantal measures and we construct counterexamples to several conjectures of pemantle and wagner on negative dependence and ultra log concave rank sequences

modeling activity times by the parkinson distribution with a lognormal core theory and validation abstract based on theoretical arguments and empirical evidence we advocate the use of the lognormal distribution as a model for activity times however raw data on activity times are often subject to rounding and to the parkinson effect we address those factors in our statistical tests by using a generalized version of the parkinson distribution with random censoring of earliness ultimately validating our model with field data from several sources we also confirm that project activities exhibit stochastic dependence that can be modeled by linear association

conditional covariance structure of generalized compensatory multidimensional items some nonparametric dimensionality assessment procedures such as dimtest and detect use nonparametric estimates of item pair conditional covariances given an appropriately chosen subtest score as their basic building blocks such conditional covariances given some subtest score can be regarded as an approximation to the conditional covariances given an appropriately chosen unidimensional latent composite where the composite is oriented in the multidimensional test space direction in which the subtest score measures best in this paper the structure and properties of such item pair conditional covariances given a unidimensional latent composite are thoroughly investigated assuming a semiparametric irt modeling framework called a generalized compensatory model it is shown that such conditional covariances are highly informative about the multidimensionality structure of a test the theory developed here is very useful in establishing properties of dimensionality assessment procedures current and yet to be developed that are based upon estimating such conditional covariances in particular the new theory is used to justify the dimtest procedure because of the importance of conditional covariance estimation a new bias reducing approach is presented a byproduct of likely independent importance beyond the study of conditional covariances is a rigorous score information based definition of an item s and a score s direction of best measurement in the multidimensional test space

normal approximation for associated point processes via stein s method with applications to determinantal point processes abstract we use stein s method to provide non asymptotic l 1 bounds also known as wasserstein bounds to the normal for functionals of associated point processes as for supporting tools we use the connection between association and mixing properties that was recently uncovered by 29 we apply our main results to determinantal point processes which are known to be negatively associated a potential application to determinantal point processes in the laguerre gaussian family is also presented

convergence rates in the slln for some classes of dependent random fields abstract let x n n n r be a random field i e a family of random variables indexed by n r r 2 we discuss complete convergence and convergence rates under assumption on dependence structure of random fields in the case of nonidentical distributions results are obtained for negatively associated random fields mixing random fields having maximal coefficient of correlation strictly smaller then 1 and martingale random fields

on the exponential inequalities for negatively dependent random variables a number of exponential inequalities for identically distributed negatively dependent and negatively associated random variables have been established by many authors the proofs use the truncation technique together with the control of the bounded terms and unbounded terms in this paper we improve essentially the control of bounds for the unbounded terms and obtain exponential inequalities for negatively dependent random variables which include negatively associated random variables our results improve on the corresponding ones in the literature

mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables abstract under some conditions of uniform integrability and appropriate conditions mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables are obtained our results extend and improve the results of h s sung s lisawadi a volodin weak laws of large numbers for arrays under a condition of uniform integrability j korean math soc 45 2008 289 300 and m ordonez cabrera a volodin mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability j math anal appl 305 2005 644 658

an almost sure central limit theorem for products of sums of partial sums under association abstract let x n n 1 be a strictly stationary positively or negatively associated sequence of positive random variables with e x 1 0 and var x 1 2 denote s n i 1 n x i t n i 1 n s i and the coefficient of variation under suitable conditions we show that x lim n 1 log n k 1 n 1 k i 2 k j 1 k t j k k 1 k 1 1 k x f x a s where 1 2 1 2 2 j 2 cov x 1 x j f is the distribution function of the random variables e 10 3 n and n is a standard normal random variable

multiprocess parallel antithetic coupling for backward and forward markov chain monte carlo antithetic coupling is a general stratification strategy for reducing monte carlo variance without increasing the simulation size the use of the antithetic principle in the monte carlo literature typically employs two strata via antithetic quantile coupling we demonstrate here that further stratification obtained by using k 2 e g k 3 10 antithetically coupled variates can offer substantial additional gain in monte carlo efficiency in terms of both variance and bias the reason for reduced bias is that antithetically coupled chains can provide a more dispersed search of the state space than multiple independent chains the emerging area of perfect simulation provides a perfect setting for implementing the k process parallel antithetic coupling for mcmc because without antithetic coupling this class of methods delivers genuine independent draws furthermore antithetic backward coupling provides a very convenient theoretical tool for investigating antithetic forward coupling however the generation of k 2 antithetic variates that are negatively associated that is they preserve negative correlation under monotone transformations and extremely antithetic that is they are as negatively correlated as possible is more complicated compared to the case with k 2 in this paper we establish a theoretical framework for investigating such issues among the generating methods that we compare latin hypercube sampling and its iterative extension appear to be generalpurpose choices making another direct link between monte carlo and quasi monte carlo