analytic smoothing for equipercentile equating under the common item nonequivalent populations design a cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described statistical techniques based on bootstrap estimation are presented that are designed to aid in choosing an equating method degree of smoothing these include a asymptotic significance tests that compare no equating and linear equating to equipercentile equating b a scheme for estimating total equating error and for dividing total estimated error into systematic and random components the smoothing technique and statistical procedures are explored and illustrated using data from forms of a professional certification test

a smooth nonparametric estimator of a quantile function abstract a smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile function is proposed the proposed estimator is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sample quantile the mean squared convergence rate of the proposed estimator is also estimated monte carlo studies are conducted to compare the proposed estimator with the sample quantile and the estimator proposed by kaigh and lachenbruch the feasibility of using bootstrap techniques to estimate the optimal window width for the proposed estimator is also considered

jackknifing l statistics with smooth weight functions abstract the behavior of linear combinations of order statistics l statistics under jackknifing is discussed the asymptotic behavior of a jackknifed l statistic is described and the pseudovalue based variance estimate is shown to be consistent under moderate smoothness and a trimming condition on the weight function the results extend easily to functions of l statistics and thus answer a question posed in miller 1974 monte carlo results support small sample applicability of the large sample results for the construction of approximate confidence intervals

comparison of quantile estimators in normal sampling ten nonparametric quantile estimators are compared with respect to small sample performance characteristics including bias and mean squared error the estimators considered are all linear functions of order statistics with properties that depend on sample size graphical presentations are given for the case of a normal parent distribution and comparisons are made with the minimum variance unbiased estimator for normal sampling

nonparametric conditional quantile estimation a locally weighted quantile kernel approach abstract nonparametric conditional cumulative distribution function cdf estimation has emerged as a powerful tool having widespread potential application which has led to a literature on estimators of conditional quantile functions that are obtained via inversion of the nonparametrically estimated conditional cdf other nonparametric estimators of conditional quantiles that are based on an alternative characterization of the quantile i e as the function that minimizes the expectation of the check function have also appeared in the literature in this paper we propose a novel nonparametric approach relative to its inverse cdf based and the check function based peers our proposed estimator has a simple expression we also show that under certain conditions our estimator is more efficient in tail regions when the data has unbounded support our theoretical results underscore this property theoretical underpinnings are developed a method for data driven smoothing parameter selection is provided and monte carlo simulations and empirical examples are considered two empirical examples illustrate how the proposed approach can deliver more reasonable quantile and quantile derivative estimates than its inverse cdf based and the check function based counterparts particularly in tail regions

ultra efficient fuzzy min max circuits based on carbon nanotube fets to implement a fuzzy system the first and the most essential step is to design basic fuzzy modules such as analog min and max circuits this paper presents efficient minimum and maximum circuits using carbon nanotube fets cntfets for nanotechnology based fuzzy circuits and systems the proposed approach considerably reduces the design complexity in the fuzzy space in the proposed design the chirality of carbon nanotubes is utilized for threshold voltage determination extensive simulations conducted using hspice and the stanford cntfet model at 16 nm feature size demonstrate that the proposed fuzzy logic blocks considerably improve the performance parameters and function much more robustly even in the presence of process variations as compared to their cntfet based counterparts

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

kernel quantile estimators abstract for an estimator of quantiles the efficiency of the sample quantile can be improved by considering linear combinations of order statistics that is l estimators a variety of such methods have appeared in the literature an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a guassian kernel and the bandwidths are identified it is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal in addition the theory of this article suggests a method for choosing the smoothing parameter how much reliance should be placed on the theoretical results is investigated through a simulation study over a variety of distributions little consistent difference is found between various estimators an important conclusion made during the theoretical analysis is that all of these estimators usually provide only modest improvement over the sample quantile the results indicate that even if one knew the best estimator

review papers recent developments in nonparametric density estimation abstract advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where re

generalized fresnel integrals and fractal properties of related spirals abstract we obtain a new asymptotic expansion of generalized fresnel integrals x t 0 t cos q s d s for large t where q s s p when s and p 1 the terms of the expansion are defined via a simple iterative algorithm using this we show that the box dimension of the related q clothoid also called the generalized euler or cornu spiral is equal to d 2 p 2 p 1 furthermore this curve is minkowski measurable and we compute its d dimensional minkowski content we also find oscillatory dimension of fresnel integrals by studying the corresponding chirps

control variates for quantile estimation new point and interval estimators for quantiles that employ a control variate are introduced the properties of these estimators do not depend on the usual assumption of joint normality between the random variable of interest and the control illustrative examples for queueing and stochastic activity network models are given in those examples the new estimators are superior to the standard estimator in terms of the mean squared error of the point estimator and the length of the confidence interval

testing whether independent treatment groups have equal medians the paper suggests new methods for comparing the medians corresponding to independent treatment groups the procedures are based on the harrell davis estimator in conjunction with a slight modification and extension of the bootstrap calibration technique suggested by loh alternatives to the harrell davis estimator are briefly discussed for the special case of two treatment groups the proposed procedure always had more power than the fligner rust solution as well as the procedure examined by wilcox and charlin included is an illustration using real data that comparing medians rather than means can yield a substantially different conclusion as to whether two distributions differ in terms of some measure of central location

correlation induction techniques for estimating quantiles in simulation experiments a simulation based quantile estimator measures the level of system performance that can be delivered with a prespecified probability to estimate selected quantiles of the response of a finite horizon simulation we develop procedures based on correlation induction techniques for variance reduction with emphasis on antithetic variates and latin hypercube sampling these procedures achieve improved precision by controlling the simulation s random number inputs as an integral part of the experimental design the proposed multiple sample quantile estimator is the average of negatively correlated quantile estimators computed from disjoint samples of the simulation response where negative correlation is induced between corresponding responses in different samples while mutual independence of responses is maintained within each sample the proposed single sample quantile estimator is computed from negatively correlated simulation responses within one all inclusive sample the single sample estimator based on latin hypercube sampling is shown to be asymptotically normal and unbiased with smaller variance than the comparable directsimulation estimator based on independent replications similar asymptotic comparisons of the multiple sample and directsimulation estimators focus on bias and mean square error monte carlo results suggest that the proposed procedures can yield significant reductions in bias variance and mean square error when estimating quantiles of the completion time of a stochastic activity network

recovery of a quantile function from moments the problem of recovering a quantile function of a positive random variable via the values of moments or given the values of its laplace transform is studied two new approximations as well as two new estimates of a quantile function given the sample from underlying distribution are proposed the uniform and l 1 upper bounds of proposed estimates are derived the plots illustrate the behavior of the recovered approximants for the moderate and large sample sizes

a smooth nonparametric conditional quantile frontier estimator abstract traditional estimators for nonparametric frontier models dea fdh are very sensitive to extreme values outliers recently aragon et al 2005 nonparametric frontier estimation a conditional quantile based approach econometric theory 21 358 389 proposed a nonparametric frontier model and estimator based on a suitably defined conditional quantile which is more robust to extreme values outliers their estimator is based on a nonsmooth empirical conditional distribution in this paper we propose a new smooth nonparametric conditional quantile estimator for the frontier model our estimator is a kernel based conditional quantile estimator that builds on early work of azzalini 1981 a note on the estimation of a distribution function and quantiles by a kernel method biometrika 68 326 328 it is computationally simple resistant to outliers and extreme values and smooth in addition the estimator is shown to be consistent and n asymptotically normal under mild regularity conditions we also show that our estimator s variance is smaller than that of the estimator proposed by aragon et al a simulation study confirms the asymptotic theory predictions and contrasts our estimator with that of aragon et al

on robust estimation of effect size under semiparametric models estimation of effect size is of interest in many applied fields such as psychology sociology and education however there are few nonparametric estimators of effect size proposed in the existing literature and little is known about the distributional characteristics of these estimators in this article two estimators based on the sample quantiles are proposed and studied the first one is the estimator suggested by hedges and olkin see page 93 of hedges olkin 1985 for the situation where a treatment effect is evaluated against a control group case a a modified version of the robust estimator by hedges and olkin is also proposed for the situation where two parallel treatments are compared case b large sample distributions of both estimators are derived their asymptotic relative efficiencies with respect to the normal maximum likelihood estimators under several common distributions are evaluated the robust properties of the proposed estimators are discussed with respect to the sample wise breakdown points proposed by akritas 1991 simulation studies are provided in which the performing characteristics of the proposed estimator are compared to that of the nonparametric estimators by kraemer and andrews 1982 interval estimation of the effect sizes is also discussed in an example interval estimates for the data set in kraemer and andrews 1982 are calculated for both cases a and b

a law of the logarithm for kernel quantile density estimators received february 1992 revised february 1993 1this manuscript was prepared using computer facilities supported in part by nsf grants dms 89 05292 dms 87 03942 dms 86 01732 and dms 84 04941 and by the university of chicago block fund ams 1991 subject classifications primary 60f15 secondary 62g05 62g30

graphical exploration of covariate effects on survival data through nonparametric quantile curves kaplan meier curves provide an effective means of presenting the distributional pattern in a sample of survival data however in order to assess the effect of a covariate a standard scatterplot is often difficult to interpret because of the presence of censored observations several authors have proposed a running median as an effective way of indicating the effect of a covariate this article proposes a form of kernel estimation employing double smoothing that can be applied in a simple and efficient manner to construct an estimator of a percentile of the survival distribution as a function of one or two covariates permutations and bootstrap samples can be used to construct reference bands that help identify whether particular features of the estimates indicate real features of the underlying curve or whether this may be due simply to random variation the techniques are illustrated on data from a study of kidney transplant patients

relative deficiency of kernel type estimators of quantiles in this paper the asymptotic relative deficiency of the sample q quantile with respect to kernel type estimators of the q quantile is evaluated the comparison is based on the mean square errors of the estimators the result suggests a purely analytic measure of performance within the class of kernels it is notable that a similar situation occurs when kernel estimators of a distribution function are studied