splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

a unified semiparametric framework for quantitative trait loci analyses with application to spike phenotypes this article proposes a general semiparametric model for multiple quantitative trait loci qtl analyses of complex phenotypes in backcross and intercross designs the model provides tests about genetic hypotheses such as additivity dominance and epistasis that do not require specifying the form of the phenotypic distribution this contrasts with previous approaches based on transformations to normality and generalized linear models which require careful consideration of the phenotypic distribution inferences involve extensions of partial and conditional likelihoods developed for single qtl backcross models we demonstrate that conditional likelihood is robust to unobserved selective genotyping whereas partial likelihood and other standard methods are not to facilitate genome screens a novel resampling method is proposed that is similar in spirit to the popular permutation tests its main advantages are that it is broadly applicable to multiple qtls with nonnormal phenotypes and achieves a substa

bayesian isotonic regression and trend analysis in many applications the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor controlling for covariates in such cases interest often focuses on estimating the regression function while also assessing evidence of an association this article proposes a new framework for bayesian isotonic regression and order restricted inference approximating the regression function with a high dimensional piecewise linear model the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses accounting for flat regions and truncated normal densities to borrow information across the intervals and smooth the curve the prior is formulated as a latent autoregressive normal process this structure facilitates efficient posterior computation since the full conditional distributions of the parameters have simple conjugate forms point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single mcmc run generalizations to categorical outcomes and multiple predictors are described and the approach is applied to an epidemiology application

testing violations of the exponential assumption in cancer clinical trials with survival endpoints personalized cancer therapy requires clinical trials with smaller sample sizes compared to trials involving unselected populations that have not been divided into biomarker subgroups the use of exponential survival modeling for survival endpoints has the potential of gaining 35 efficiency or saving 28 required sample size miller 1983 making personalized therapy trials more feasible however the use of exponential survival has not been fully accepted in cancer research practice due to uncertainty about whether or not the exponential assumption holds we propose a test for identifying violations of the exponential assumption using a reduced piecewise exponential approach compared with an alternative goodness of fit test which suffers from inflation of type i error rate under various censoring mechanisms the proposed test maintains the correct type i error rate we conduct power analysis using simulated data based on different types of cancer survival distribution in the seer registry database and demonstrate the implementation of this approach in existing cancer clinical trials

on testing an unspecified function through a linear mixed effects model with multiple variance components summary we examine a generalized f test of a nonparametric function through penalized splines and a linear mixed effects model representation with a mixed effects model representation of penalized splines we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null the procedure can be used to test a nonparametric function or varying coefficient with clustered data compare two spline functions test the significance of an unspecified function in an additive model with multiple components and test a row or a column effect in a two way analysis of variance model through a spectral decomposition of the residual sum of squares we provide a fast algorithm for computing the null distribution of the test which significantly improves the computational efficiency over bootstrap the spectral representation reveals a connection between the likelihood ratio test lrt in a multiple variance components model and a single component model we examine our methods through simulations where we show that the power of the generalized f test may be higher than the lrt depending on the hypothesis of interest and the true model under the alternative we apply these methods to compute the genome wide critical value and p value of a genetic association test in a genome wide association study gwas where the usual bootstrap is computationally intensive up to 108 simulations and asymptotic approximation may be unreliable and conservative

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

generalized additive and index models with shape constraints summary we study generalized additive models with shape restrictions e g monotonicity convexity and concavity imposed on each component of the additive prediction function we show that this framework facilitates a non parametric estimator of each additive component obtained by maximizing the likelihood the procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals more generally our methodology can be applied to generalized additive index models here again the procedure can be justified on theoretical grounds and like the original algorithm has highly competitive finite sample performance practical utility is illustrated through the use of these methods in the analysis of two real data sets our algorithms are publicly available in the r package scar short for shape constrained additive regression

homoclinic orbits and hopf bifurcations in delay differential systems with t b singularity abstract the paper carries the results on takens bogdanov bifurcation obtained in t faria l t magalhaes normal forms for retarded functional differential equations and applications to bogdanov takens singularity j differential equations 122 1995 201 224 for scalar delay differential equations over to the case of delay differential systems with parameters firstly we give feasible algorithms for the determination of takens bogdanov singularity and the generalized eigenspace associated with zero eigenvalue in r n next through center manifold reduction and normal form calculation a concrete reduced form for the parameterized delay differential systems is obtained finally we describe the bifurcation behavior of the parameterized delay differential systems with t b singularity in detail and present an example to illustrate the results

a fast scaling algorithm for minimizing separable convex functions subject to chain constraints we consider the problem of minimizing j nc j x j subject to the following chain constraints x 1 x 2 x 3 x n where c j x j is a convex function of x j for each j n 1 2 n this problem is a generalization of theisotonic regression problems with complete order an important class of problems in regression analysis that has been examined extensively in the literature we refer to this problem as thegeneralized isotonic regression problem in this paper we focus on developing a fast scaling algorithm to obtain an integer solution of the generalized isotonic regression problem letu denote the difference between an upper bound on an optimal value of x n and a lower bound on an optimal value of x 1 under the assumption that the evaluation of any function c j x j takeso 1 time we show that the generalized isotonic regression problem can be solved ino n logu time this improves by a factor of n the previous best running time ofo n 2 logu to solve the same problem in addition when our algorithm is specialized to theisotonic median regression problem where c j x j c j x j a ji for specified values ofc js anda js the algorithm obtains a real valued optimal solution ino n logn time this time bound matches the best available time bound to solve the isotonic median regression problem but our algorithm uses simpler data structures and may be easier to implement

on the asymptotic behaviour of the pseudolikelihood ratio test statistic this paper concerns the asymptotic distribution of the likehood ratio statistic t for testing h 0 0 based on the pseudolikelihood l where is a simple estimator of we show that the asymptotic distribution of t under h 0 is a weighted sum of indepepdent x 1 2 variables where the weights involve the asymptotic joint covariance matrix of and the score function for some sufficient conditions are provided for the limiting distribution to be x 2 the result is extended to allow 0 to be a boundary value of the parameter space and to be misspecified in l we also examine the issue of power loss when is misspecified in l several examples including variance component models multivariate survival models genetic linkage analysis and the behrens fisher problem are presented to demonstrate the scope of the problems considered and to illustrate the results

marginal models for the analysis of longitudinal measurements with nonignorable non monotone missing data summary we propose methods for the analysis of continuous responses subject to nonignorable non monotone missing data we form a pseudolikelihood by naively assuming independence over time and using a product of marginal likelihoods at each time point and we obtain consistent and asymptotically normal estimators of the mean and missingness parameters our primary interest is in estimating the parameters of the marginal model at each time point and we make no assumption about the correlation structure an approximate variance is found for the parameter estimates using a sandwich estimate we provide an example and present a simulation study that assesses the performance of the model

a bivariate pseudolikelihood for incomplete longitudinal binary data with nonignorable nonmonotone missingness for analyzing longitudinal binary data with nonignorable and non monotone missing responses a full likelihood method is complicated algebraically and often requires intensive computation especially when there are many follow up times as an alternative a pseudo likelihood approach has been proposed in the literature under minimal parametric assumptions this formulation only requires specification of the marginal distributions of the responses and missing data mechanism and uses an independence working assumption however this estimator can be inefficient for estimating both time varying and time stationary effects under moderate to strong within subject associations among repeated responses in this article we propose an alternative estimator based on a bivariate pseudo likelihood and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudo likelihood obtained under the assumption of independence we illustrate the method using longitudinal data on cd4 counts from two clinical trials of hiv infected patients

a class of grouped brunk estimators and penalized spline estimators for monotone regression we study a class of monotone univariate regression estimators we use b splines to approximate an underlying regression function and estimate spline coefficients based on grouped data we investigate asymptotic properties of two monotone estimators a grouped brunk estimator and a penalized monotone estimator these estimators are consistent at the boundary and their mean square errors achieve optimal convergence rates under suitable assumptions of the true regression function asymptotic distributions are developed and are shown to be independent of spline degrees and the number of knots simulation results and car data illustrate performance of the proposed estimators

analysis on takens bogdanov points for delay differential equations abstract the paper analyzes the takens bogdanov points for the nonlinear system of differential equations with one constant delay and two parameters by representing the delay differential equations as abstract ordinary differential equations in their phase spaces the quadratic takens bogdanov point is defined and an enlarged system for it is produced based on the descriptions for the eigenspace associated with the double zero eigenvalue we reduce the enlarged system to a finite dimensional algebraic equation the quadratic takens bogdanov point together with the corresponding values of parameters is proved to be a regular solution of the reduced enlarged system and then can be computed by the standard newton iteration directly

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

maximally selected chi square statistics two samples can be compared by selecting a cut point and then forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample when the cut point is selected so as to maximize the standard chi square statistic the chi square percentile points are inappropriate actual significance levels are computed for large samples and correct percentile poillts are tabulated

the reduced monotonic regression method abstract medical researchers often desire to categorize patients into monotonic response groups based on the relationship between continuous variables isotonic regression fits consist of level sets of increasing value for which the estimated response is constant however the number of level sets obtained is often large preventing simple description this article introduces two new nonparametric methods called reduced isotonic regression and reduced monotonic regression the latter being a two sided extension of the former for use when the direction of the trend is unknown using a backward elimination algorithm the new procedures reduce the number of level sets by combining those whose values do not differ greatly for the statistical relations examined here the reduced monotonic method averaged at most 30 of the number of level sets obtained for isotonic regression the method is illustrated with an example that examines the relationship between risk factors for survival among children with leukem

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

isotonic modeling with non differentiable loss functions with application to lasso regularization in this paper we present an algorithmic approach for fitting isotonic models under convex yet non differentiable loss functions it is a generalization of the greedy non regret approach proposed by luss and rosset 2014 for differentiable loss functions taking into account the sub gradiental extensions required we prove that our suggested algorithm solves the isotonic modeling problem while maintaining favorable computational and statistical properties as our suggested algorithm may be used for any non differentiable loss function we focus our interest on isotonic modeling for either regression or two class classification with appropriate log likelihood loss and lasso penalty on the fitted values this combination allows us to maintain the non parametric nature of isotonic modeling while controlling model complexity through regularization we demonstrate the efficiency and usefulness of this approach on both synthetic and real world data an implementation of our suggested solution is publicly available from the first author s website https sites google com site amichaipainsky software

tables for testing ordered alternatives in an analysis of variance without replications summary given a series of k normal populations with a common but unknown variance and supposing that an observation is drawn from each one of them then a likelihood ratio test of homogeneity of the means against the simple order alternative is possible when the significance level oc is less than 1 k for these possible combinations of a and k tables for testing the hypothesis are provided where oc 0 10 0 05 0 025 0 01 0 005 0 0025

on the application of linear relative risk regression models motivations for considering linear relative risk models are described these include covariate data reduction and the testing of additivity of covariate effects on the relative risk a simulation study was conducted in order to study properties of asymptotic distributional approximations and iterative convergence properties parameter transformations and likelihood ratio approximations are considered for confidence interval calculation

bogdanov takens singularity in the hindmarsh rose neuron with time delay abstract in this paper we study the bogdanov takens singularity in the hindmarsh rose neuron model with time delay we use the center manifold reduction and the normal form method by means of which the dynamics near this nonhyperbolic equilibrium can be reduced to the study of the dynamics of the corresponding normal form restricted to the associated two dimensional center manifold we show that changes in the time delay length can lead to the saddle node bifurcation to the hopf bifurcation and to the homoclinic bifurcation

on pseudolikelihood inference for semiparametric models with boundary problems consider a semiparametric model indexed by a euclidean parameter of interest and an infinite dimensional nuisance parameter in many applications pseudolikelihood provides a convenient way to infer the parameter of interest where the nuisance parameter is replaced by a consistent estimator the purpose of this paper is to establish the asymptotic behaviour of the pseudolikelihood ratio statistic under semiparametric models in particular we consider testing the hypothesis that the parameter of interest lies on the boundary of its parameter space under regularity conditions we establish the equivalence between the asymptotic distributions of the pseudolikelihood ratio statistic and a likelihood ratio statistic for a normal mean problem with a misspecified covariance matrix this result holds when the nuisance parameter is estimated at a rate slower than the usual rate in parametric models we study three examples in which the asymptotic distributions are shown to be mixtures of chi squared variables we conduct simulation studies to examine the finite sample performance of the pseudolikelihood ratio test

hopf transcritical bifurcation in retarded functional differential equations abstract firstly we analyze a codimension two unfolding for the hopf transcritical bifurcation and give complete bifurcation diagrams and phase portraits in particular we express explicitly the heteroclinic bifurcation curve and obtain conditions under which the secondary bifurcation periodic solutions and the heteroclinic orbit are stable secondly we show how to reduce general retarded functional differential equation with perturbation parameters near the critical point of the hopf transcritical bifurcation to a 3 dimensional ordinary differential equation which is restricted on the center manifold up to the third order with unfolding parameters and further reduce it to a 2 dimensional amplitude system where these unfolding parameters can be expressed by those original perturbation parameters finally we apply the general results to the van der pol s equation with delayed feedback and obtain the existence of stable or unstable equilibria periodic solutions and quasi periodic solutions

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

a zero inefficiency stochastic frontier estimator traditional stochastic frontier models impose inefficient behavior on all firms in the sample of interest if the data under investigation represent a mixture of both fully efficient and inefficient firms then off the shelf frontier models are statistically inadequate we introduce the zero inefficiency stochastic frontier model which can accommodate the presence of both efficient and inefficient firms in the sample we derive the corresponding log likelihood function conditional mean of inefficiency to estimate observation specific inefficiency and discuss testing for the presence of fully efficient firms we provide both simulated evidence as well as an empirical example which demonstrates the applicability of the proposed method jel classification no c13 c23 c33

normal forms for retarded functional differential equations with parameters and applications to hopf bifurcation abstract the paper addresses for retarded functional differential equations fdes with parameters the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity the analysis is based on the theory previously developed for fdes without parameters by considering an extension of a phase space appropriate to the computation of these normal forms as an application the generic hopf bifurcation for scalar retarded fdes is considered

generalized monotonic regression using random change points we introduce a procedure for generalized monotonic curve fitting that is based on a bayesian analysis of the isotonic regression model conventional isotonic regression fits monotonically increasing step functions to data in our approach we treat the number and location of the steps as random for each step level we adopt the conjugate prior to the sampling distribution of the data as if the curve was unconstrained we then propose to use markov chain monte carlo simulation to draw samples from the unconstrained model space and retain only those samples for which the monotonic constraint holds the proportion of the samples collected for which the constraint holds can be used to provide a value for the weight of evidence in terms of bayes factors for monotonicity given the data using the samples probability statements can be made about other quantities of interest such as the number of change points in the data and posterior distributions on the location of the change points can be provided the method is illustrated throughout by a reanalysis of the leukaemia data studied by schell and singh

ordered multivariate extremes multivariate extreme value models and associated statistical methods are developed for vector observations whose components are subject to an order restriction the approach extends the multivariate threshold methodology of coles and tawn joe and co workers and smith and co workers the results are illustrated by an analysis of extreme rainfalls of different durations and by a study of the problem of linking a long series of daily rainfall extremes with a partially overlapping shorter series of hourly extremes

on the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems this paper considers the asymptotic distribution of the likelihood ratio statistic t for testing a subset of parameter of interest h 0 0 based on the pseudolikelihood l where is a consistent estimator of the nuisance parameter we show that the asymptotic distribution of t under h 0 is a weighted sum of independent chi squared variables some sufficient conditions are provided for the limiting distribution to be a chi squared variable when the true value of the parameter of interest 0 or the true value of the nuisance parameter 0 lies on the boundary of parameter space the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix or from a mixture of multivariate normal distributions a variety of examples are provided for which the limiting distributions of t may be mixtures of chi squared variables we conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments

normal forms for retarded functional differential equations and applications to bogdanov takens singularity abstract the paper addresses for retarded functional differential equations fdes the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity a phase space appropriate to the computation of these normal forms is introduced and adequate nonresonance conditions for the computation of the normal forms are derived as an application the general situation of bogdanov takens singularity and its versal unfolding for scalar retarded fdes with nondegeneracy at second order is considered both in the general case and in the case of differential delay equations of the form t x t x t 1

nonparametric combinatorial regression for shape constrained modeling we introduce a unified approach for calculating nonparametric shape constrained regression enforcement of the shape constraint often accounts for the impact of a physical phenomenon or a specific property it also improves the model s predicability and facilitates subsequent optimizations the regression models are built by transforming the problem into the combinatorial domain where the shape constraints are imposed by bounding the combinatorial search space we start by addressing isotonicity shape constraint using a dynamic programming algorithm and demonstrate how the problem can be mapped to the graph combinatorics domain next we show how a number of other important shape constraints including unimodality convexity limited level set and limited slope can be addressed using the same framework the flexibility of proposed framework enables solving the shape constrained regression problem with an arbitrary user defined error metric this flexibility is exploited to add robustness against outliers to the model the algorithms are described in detail and their computational complexity is established the performance and effectiveness of the shape constrained regression is evaluated on traces of temperature and humidity measurements from a deployed sensor network where a high degree of accuracy and robustness is demonstrated

monotone nonparametric regression in monotone regression procedures one utilizes only the monotonicity of the regression function in nonparametric regression one utilizes only the assumed smoothness the analytic and asymptotic properties of the estimator are superior in the latter case however monotonicity is not guaranteed we study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators

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

exact likelihood ratio tests for penalised splines summary penalised spline based additive models allow a simple mixed model representation where the variance components control departures from linear models the smoothing parameter is the ratio of the random coefficient and error variances and tests for linear regression reduce to tests for zero random coefficient variances we propose exact likelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines their spectral decompositions are used as the basis of fast simulation algorithms we derive the asymptotic local power properties of the tests under weak conditions in particular we characterise the local alternatives that are detected with asymptotic probability one confidence intervals for the smoothing parameter are obtained by inverting the tests for a fixed smoothing parameter versus a general alternative we discuss f and r tests and show that ignoring the variability in the smoothing parameter estimator can have a dramatic effect on their null distributions the powers of several known tests are investigated and a small set of tests with good power properties is identified the restricted likelihood ratio test is among the best in terms of power

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

diagnostics for dependence within time series extremes summary the analysis of extreme values within a stationary time series entails various assumptions concerning its long and short range dependence we present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events these tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and identically distributed variables our diagnostic aids are illustrated through theoretical examples simulation studies and by application to rainfall and exchange rate data on the basis of these diagnostics we can explain characteristics that are found in the observed extreme events of these series and also gain insight into the properties of events that are more extreme than those observed

bayesian semiparametric isotonic regression for count data this article proposes a semiparametric bayesian approach for inference on an unknown isotonic regression function f x characterizing the relationship between a continuous predictor x and a count response variable y adjusting for covariates z a dirichlet process mixture of poisson distributions is used to avoid parametric assumptions on the conditional distribution of y given x and z then to also avoid parametric assumptions on f x a novel prior formulation is proposed that enforces the nondecreasing constraint and assigns positive prior probability to the null hypothesis of no association through the use of carefully tailored hyperprior distributions we allow for borrowing of information across different regions of x in estimating f x and in assessing hypotheses about local increases in the function due to conjugacy properties posterior computation is straightforward using a markov chain monte carlo algorithm the methods are illustrated using data from an epidemiologic study of sleep pr

monotone regression estimates for grouped observations the maximum likelihood estimator of a nondecreasing regression function with normally distributed errors has been considered in the literature its asymptotic distribution at a point is related to a solution of the heat equation and its rate of convergence to the underlying regression function is of order n 1 3 this estimator can be modified by grouping adjacent observations and then isotonizing the corresponding means it is shown that the resulting estimator has an asymptotic normal distribution for certain group sizes and its rate of convergence is of order n 215 the results of a simulation study for small sample sizes are presented and grouping procedures are discussed

the monotone smoothing of scatterplots we consider the problem of summarizing a scatterplot with a smooth monotone curve a solution that combines local averaging and isotonic regression is proposed and we demonstrate its use with two examples in the second example the procedure is applied in a regression setting to some data from box and cox 1964 and it is shown how this new procedure generalizes box and cox s well known family of transformations in the same example the bootstrap is applied to obtain a measure of the variability of the procedure

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

additive isotonic models abstract additive isotonic models generalize linear models by replacing lines with isotonic nondecreasing transformations fitted transformations of several explanatory variables are added together and then transformed by a known function to yield fitted values of the response variable the isotonic transformations are chosen to minimize an explicit criterion such as the negative log likelihood by an algorithm that optimizes one transformation at a time while adjusting for the current fitted values of the others cycling until the criterion converges this approach can be used in various situations notably for generalizing ordinary linear regression and linear logistic regression at each step of the algorithm the needed optimal isotonic transformation is found using a simple generalization of the standard pool adjacent violators algorithm ayer brunk ewing reid and silverman 1955 the fitted transformations are always made up of flat steps so the technique is useful for finding optimal strati

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

tests for monotonicity of a regression mean with guaranteed level in this paper a nonparametric procedure for testing for monotonicity of a regression mean with guaranteed level is proposed the procedure is based on signs of differences of observations from the response variable the test is calibrated against the most difficult null hypothesis when the regression function is constant and produces an exact test in this context in general the test is conservative the power of the test is good and comparable with that of other nonparametric tests it is shown that the testing procedure has asymptotic power 1 against certain local alternatives the method is also robust against heavy tailed error distributions and even maintains good power when the errors are for example cauchy distributed a simulation study is provided to demonstrate finite sample behaviour of the testing procedure

bogdanov takens singularity in tri neuron network with time delay this brief reports a retarded functional differential equation modeling tri neuron network with time delay the bogdanov takens b t bifurcation is investigated by using the center manifold reduction and the normal form method we get the versal unfolding of the norm forms at the b t singularity and show that the model can exhibit pitchfork hopf homoclinic and double limit cycles bifurcations some numerical simulations are given to support the analytic results and explore chaotic dynamics finally an algorithm is given to show that chaotic tri neuron networks can be used for encrypting a color image