bias correction of two state latent markov process parameter estimates under misclassification a discretely observed two state process may misclassify the state of an unobservable continuous time two state markov process we examine the behaviour of maximum likelihood transition probability estimates as functions of known misclassification probabilities since maximum likelihood estimators are not available in closed form we provide two alternatives for bias adjusted estimation in the case of large samples the asymptotic bias is quantified and estimators are constructed iteratively using transition counts and specified misclassification probabilities for finite samples we provide an approximation based on partial derivatives estimators that are bias adjusted to a first approximation are easily constructed and may serve well when misclassification probabilities are known to be small simulation studies reveal the effect of misclassification on estimation repeated diagnostic testing data illustrate the approaches

efficient treatment allocation in 2 2 multicenter trials when costs and variances are heterogeneous at the design stage of a study it is crucial to compute the sample size needed for treatment effect estimation with maximum precision and power the optimal design depends on the costs which may be known at the design stage and on the outcome variances which are unknown a balanced design optimal for homogeneous costs and variances is typically used an alternative to the balanced design is a design optimal for the known and possibly heterogeneous costs and homogeneous variances called costs considering design both designs suffer from loss of efficiency compared with optimal designs for heterogeneous costs and variances for 2 2 multicenter trials we compute the relative efficiency of the balanced and the costs considering designs relative to the optimal designs we consider 2 heterogeneous costs and variance scenarios in 1 scenario 2 treatment conditions have small and 2 have large costs and variances in the other scenario 1 treatment condition has small 2 have intermediate and 1 has large costs and variances within these scenarios we examine the relative efficiency of the balanced design and of the costs considering design as a function of the extents of heterogeneity of the costs and of the variances and of their congruence congruent when the cheapest treatment has the smallest variance incongruent when the cheapest treatment has the largest variance we find that the costs considering design is generally more efficient than the balanced design and we illustrate this theory on a 2 2 multicenter trial on lifestyle improvement of patients in general practices

a simple procedure to compute the sample size needed to compare two independent groups when the population variances are unequal the usual methods of sample size determination which assume the homogeneity of within group variances are not sufficiently robust against the violation of this assumption a method using satterthwaite s correction for unequal variances is given it is shown that in the case of unequal variances the minimum total sample size is attained when the allocation ratio is equal to the proportion of the standard deviations

on finite sample properties of alternative estimators of coefficients in a structural equation with many instruments abstract we compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables as the classical methods we consider the limited information maximum likelihood liml estimator and the two stage least squares tsls estimator and as the semi parametric estimation methods we consider the maximum empirical likelihood mel estimator and the generalized method of moments gmm or the estimating equation estimator tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most linear models of interest and we include some heteroscedastic cases and nonlinear cases we have found that the liml estimator has good performance in terms of the bounded loss functions and probabilities when the number of instruments is large that is the micro econometric models with many instruments in the terminology of recent econometric literature

a general goodness of fit test for markov and hidden markov models markov models are a convenient and useful method of estimating transition rates between levels of a categorical response variable such as a disease stage which changes over time in medical applications the response variable is typically observed at irregular intervals a pearson type goodness of fit test for such models was proposed by aguirre hernandez and farewell statist med 2002 21 1899 1911 but this test is not applicable in the common situation where the process includes an absorbing state such as death for which the time of entry is known precisely nor when the data include censored state observations this paper presents a modification to the pearson type test to allow for these cases an extension of the method to allow for the class of hidden markov models where the response variable is subject to misclassification error is given the method is applied to data on cardiac allograft vasculopathy in post heart transplant patients

stopping time resampling for sequential monte carlo methods summary motivated by the statistical inference problem in population genetics we present a new sequential importance sampling with resampling strategy the idea of resampling is key to the recent surge of popularity of sequential monte carlo methods in the statistics and engineering communities but existing resampling techniques do not work well for coalescent based inference problems in population genetics we develop a new method called stopping time resampling which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on to illustrate the idea we first apply the new method to approximate the solution of a dirichlet problem and the likelihood function of a non markovian process then we focus on its application in population genetics all our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods

t test in a structural equation properties of t ratios associated with the liml tsls and ols estimators in a structural form estimation are studied the existence of moments of these t ratios including the liml form is proved first second monte carlo simulations are performed to find out real sizes of the t test and the likelihood ratio test third asymptotic expansions of the distributions of t ratios are derived under the null hypothesis to find out deviations of real sizes from nominal sizes theoretically the asymptotic power functions are also derived

a noniterative sample size procedure for tests based on t distributions a noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending guenther s approach for the one sample and two sample t tests the generalized procedure is employed to determine the sample size for treatment comparisons using the analysis of covariance ancova and the mixed effects model for repeated measures in randomized clinical trials the sample size is calculated by adding a few simple correction terms to the sample size from the normal approximation to account for the nonnormality of the t statistic and lower order variance terms which are functions of the covariates in the model but it does not require specifying the covariate distribution the noniterative procedure is suitable for superiority tests noninferiority tests and a special case of the tests for equivalence or bioequivalence and generally yields the exact or nearly exact sample size estimate after rounding to an integer the method for calculating the exact power of the two sample t test with unequal variance in superiority trials is extended to equivalence trials we also derive accurate power formulae for ancova and mixed effects model for repeated measures and the formula for ancova is exact for normally distributed covariates numerical examples demonstrate the accuracy of the proposed methods particularly in small samples

batch size effects on the efficiency of control variates in simulation abstract this paper considers the combined use of control variates and batching for estimating the steady state mean of an infinite horizon process via simulation properties of the point and interval estimators from such a procedure are derived as functions of the number of batches and the number of control variates when the total sample size is fixed

control variate method for stationary processes abstract the sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample however if some control variate is available it is known that the control variate method reduces the variance of the sample mean the control variate method often assumes that the variable of interest and the control variable are i i d here we assume that these variables are stationary processes with spectral density matrices i e dependent then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator it is shown that this estimator improves the sample mean in the sense of mean square error also this analysis is extended to the case when the mean dynamics is of the form of regression then we propose a control variate estimator for the regression coefficients which improves the least squares estimator lse numerical studies will be given to see how our estimator improves the lse

the jackknife estimate of variance tukey s jackknife estimate of variance for a statistic s x 1 x 2 cdots x n which is a symmetric function of i i d random variables x i is investigated using an anova like decomposition of s it is shown that the jackknife variance estimate tends always to be biased upwards a theorem to this effect being proved for the natural jackknife estimate of operatorname var s x 1 x 2 cdots x n 1 based on x 1 x 2 cdots x n

batch size effects in the analysis of simulation output batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and or independence and the resulting incorrect probabilities of the confidence interval covering the mean this paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions these effects include 1 correct probability of covering the mean 2 an increase in expected half length 3 an increase in the standard deviation and coefficient of variation of the half length and 4 an increase in the probability of covering points not equal to the mean for any sample size and independent and normal batch means the results are 1 the effects of less than 10 batches are large and the effects of more than 30 batches small and 2 additional batches have lesser effects on

large sample properties of weighted monte carlo estimators a general approach to improving simulation accuracy uses information about auxiliary control variables with known expected values to improve the estimation of unknown quantities we analyze weighted monte carlo estimators that implement this idea by applying weights to independent replications the weights are chosen to constrain the weighted averages of the control variables we distinguish two cases unbiased and biased depending on whether the weighted averages of the controls are constrained to equal their expected values or some other values in both cases the number of constraints is usually smaller than the number of replications so there may be many feasible weights we select maximally uniform weights by minimizing a separable convex function of the weights subject to the control variable constraints estimators of this form arise sometimes implicitly in several settings including at least two in finance calibrating a model to market data as in the work of avellaneda et al 2001 and calculating conditional expectations to price american options we analyze properties of these estimators as the number of replications increases we show that in the unbiased case weighted monte carlo reduces asymptotic variance and that all convex objective functions within a large class produce estimators that are very close to each other in a strong sense in contrast in the biased case the choice of objective function does matter we show explicitly how the choice of objective determines the limit to which the estimator converges

moment based estimation of smooth transition regression models with endogenous variables nonlinear regression models have been widely used in practice for a variety of time series and cross section datasets for purposes of analyzing univariate and multivariate time series data in particular smooth transition regression str models have been shown to be very useful for representing and capturing asymmetric behavior most str models have been applied to univariate processes and have made a variety of assumptions including stationary or cointegrated processes uncorrelated homoskedastic or conditionally heteroskedastic errors and weakly exogenous regressors under the assumption of exogeneity the standard method of estimation is nonlinear least squares the primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment based methods for estimating str models the paper analyzes the properties of the str model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity developing an estimation procedure and a misspecification test for the str model presenting the results of monte carlo simulations to show the usefulness of the model and estimation method and providing an empirical application for inflation rate targeting in brazil we show that str models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature

planning group sizes in clinical trials with a continuous outcome and repeated measures simple formulae have been derived for the accurate computation of sample sizes when the two sample t test is used required sample sizes may be reduced by taking repeated measures especially if correlations are about equal in a trial with two parallel groups repeated measures may be summarized by a pre treatment mean and a post treatment mean in a cross over trial measures may be repeated within each treatment period in case the difference between two independent groups increases in time individual slopes may be used if the correlation between two measures hardly depends on distance in time between these measures however it may be more efficient to use only the first and last measure in the statistical test if correlations strongly depend on time distance

indirect estimation via l w for a large class of queueing systems little s law l w helps provide a variety of statistical estimators for the long run time average queue length l and the long run customer average waiting time w we apply central limit theorem versions of little s law to investigate the asymptotic efficiency of these estimators we show that an indirect estimator for l using the natural estimator for w plus the known arrival rate is more efficient than a direct estimator for l provided that the interarrival and waiting times are negatively correlated thus extending a variance reduction principle for the gi g s model due to a m law and j s carson we also introduce a general framework for indirect estimation which can be applied to other problems besides l w we show that the issue of indirect versus direct estimation is related to estimation using nonlinear control variables we also show under mild regularity conditions that any nonlinear control variable scheme is equivalent to a linear control va

selecting control variates to estimate multiresponse simulation metamodels abstract in this paper we discuss the optimal selection of control variates for simulation experiments in which the objective is estimation of a multiresponse metamodel that is a linear regression model for an output vector of simulation response variables expressed in terms of an input vector of design variables for the target system we consider the control variate selection problem in the context of some specific covariance structures for the responses and the candidate controls that commonly occur in certain types of econometric and psychometric simulation studies we conslude that in these situations the optimal set of controls is frequently larger than would be obtained by certain conventional control variate selection procedures moreover as a function of the number of selected controls the efficiency of the controlled metamodel point estimator is often relatively insensitive in the neighborhood of the optimal number of controls

optimal design of multi subject blocked fmri experiments the design of a multi subject fmri experiment needs specification of the number of subjects and scanning time per subject for example for a blocked design with conditions a or b fixed block length and block order abn where n denotes a null block the optimal number of cycles of abn and the optimal number of subjects have to be determined this paper presents a method to determine the optimal number of subjects and optimal number of cycles for a blocked design based on the a optimality criterion and a linear cost function by which the number of cycles and the number of subjects are restricted estimation of individual stimulus effects and estimation of contrasts between stimulus effects are both considered the mixed effects model is applied and analytical results for the a optimal number of subjects and a optimal number of cycles are obtained under the assumption of uncorrelated errors for correlated errors with a first order autoregressive ar1 error structure numerical results are presented our results show how the optimal number of cycles and subjects depend on the within to between subject variance ratio our method is a new approach to determine the optimal scanning time and optimal number of subjects for a multi subject fmri experiment in contrast to previous results based on power analyses the optimal number of cycles and subjects can be described analytically and costs are considered

sample size determination for logistic regression revisited there is no consensus on the approach to compute the power and sample size with logistic regression some authors use the likelihood ratio test some use the test on proportions some suggest various approximations to handle the multivariate case we advocate the use of the wald test since the z score is routinely used for statistical significance testing of regression coefficients the null variance formula became popular from early studies which contradicts modern software which utilizes the method of maximum likelihood estimation mle when the variance of the mle is estimated at the mle not at the null we derive general wald based power and sample size formulas for logistic regression and then apply them to binary exposure and confounder to obtain a closed form expression these formulas are applied to minimize the total sample size in a case control study to achieve a given power by optimizing the ratio of controls to cases approximately the optimal number of controls to cases is equal to the square root of the alternative odds ratio our sample size and power calculations can be carried out online at www dartmouth edu approximately eugened

experimental evaluation of variance reduction techniques for queueing simulation using generalized concomitant variables in a companion paper we developed a unified scheme for using poststratified sampling and control variables to improve the efficiency of regenerative queueing simulations we adapted these variance reduction techniques to the estimation methods of replication analysis and regenerative analysis by exploiting the asymptotic joint normality of certain standardized concomitant variables that are defined on each input process sampled during a queueing simulation in this paper we present an experimental evaluation of the reductions in point estimator variance and confidence interval width that can be achieved with each procedure in several closed and mixed machine repair systems for the analytically tractable model nominal and actual confidence interval coverage probabilities are also compared poststratification generally produced variance reductions ranging from 10 to 40 and confidence interval reductions between 1 and 20 the control variates schemes yielded variance reductions ranging from 20 to 90 and confidence interval reductions between 10 and 70 in some instances where small sample sizes were used the poststratification schemes produced confidence interval width increases between 1 and 10 with a small number of regenerative cycles some loss of confidence interval coverage was observed with both post stratified and controlled regenerative analysis when larger sample sizes were used all of the estimation schemes yielded fairly consistent efficiency gains

estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments abstract a well known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments in this paper we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability these unconditional moments depend on the instruments generated from a generically comprehensively revealing function and they are further projected along the exponential fourier series the objective function is based on the resulting fourier coefficients from which an estimator can be easily computed a novel feature of our method is that the full continuum of unconditional moments is incorporated into each fourier coefficient we show that when the number of fourier coefficients in the objective function grows at a proper rate the proposed estimator is consistent and asymptotically normally distributed an efficient estimator is also readily obtained via the conventional two step gmm method our simulations confirm that the proposed estimator compares favorably with that of dominguez and lobato 2004 econometrica in terms of bias standard error and mean squared error

properties of the cue estimator and a modification with moments abstract in this paper we analyze properties of the continuous updating estimator cue proposed by hansen et al 1996 which has been suggested as a solution to the finite sample bias problems of the two step gmm estimator we show that the estimator should be expected to perform poorly in finite samples under weak identification in particular the estimator is not guaranteed to have finite moments of any order we propose the regularized cue rcue as a solution to this problem the rcue solves a modification of the first order conditions for the cue estimator and is shown to be asymptotically equivalent to cue under many weak moment asymptotics our theoretical findings are confirmed by extensive monte carlo studies

fitting semi markov models to interval censored data with unknown initiation times in a semi markov model the hazard of making a transition between stages depends on the time spent in the current stage but is independent of time spent in other stages if the initiation time time of entry into the network is not known for some persons and if transition time data are interval censored i e if transition times are not known exactly but are known only to have occurred in some interval then the length of time these persons spent in any stage is not known we show how a semi markov model can still be fit to interval censored data with missing initiation times for the special case of models in which all persons enter the network at the same initial stage and proceed through the same succession of stages to a unique absorbing stage we present discrete time nonparametric maximum likelihood estimators of the waiting time distributions for this type of data

efficient design of cluster randomized trials with treatment dependent costs and treatment dependent unknown variances cluster randomized trials evaluate the effect of a treatment on persons nested within clusters where treatment is randomly assigned to clusters current equations for the optimal sample size at the cluster and person level assume that the outcome variances and or the study costs are known and homogeneous between treatment arms this paper presents efficient yet robust designs for cluster randomized trials with treatment dependent costs and treatment dependent unknown variances and compares these with 2 practical designs first the maximin design mmd is derived which maximizes the minimum efficiency minimizes the maximum sampling variance of the treatment effect estimator over a range of treatment to control variance ratios the mmd is then compared with the optimal design for homogeneous variances and costs balanced design and with that for homogeneous variances and treatment dependent costs cost considered design the results show that the balanced design is the mmd if the treatment to control cost ratio is the same at both design levels cluster person and within the range for the treatment to control variance ratio it still is highly efficient and better than the cost considered design if the cost ratio is within the range for the squared variance ratio outside that range the cost considered design is better and highly efficient but it is not the mmd an example shows sample size calculation for the mmd and the computer code spss and r is provided as supplementary material the mmd is recommended for trial planning if the study costs are treatment dependent and homogeneity of variances cannot be assumed

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

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

best linear inverse probability weighted estimation for two phase designs and missing covariate regression the inverse probability weighted estimator is often applied to two phase designs and regression with missing covariates inverse probability weighted estimators typically are less efficient than likelihood based estimators but in general are more robust against model misspecification in this paper we propose a best linear inverse probability weighted estimator for two phase designs and missing covariate regression our proposed estimator is the projection of the sipw onto the orthogonal complement of the score space based on a working regression model of the observed covariate data the efficiency gain is from the use of the association between the outcome variable and the available covariates which is the working regression model one advantage of the proposed estimator is that there is no need to calculate the augmented term of the augmented weighted estimator the estimator can be applied to general missing data problems or two phase design studies in which the second phase data are obtained in a subcohort the method can also be applied to secondary trait case control genetic association studies the asymptotic distribution is derived and the finite sample performance of the proposed estimator is examined via extensive simulation studies the methods are applied to a bladder cancer case control study

information and entropy econometrics editor s view amos golan department of economics american university roper 200 4400 massachusetts ave nw washington dc 20016 usa

power calculations for matched case control studies power calculations are derived for matched case control studies in terms of the probability po of exposure among the control patients the correlation coefficient phi for exposure between matched case and control patients and the odds ratio psi for exposure in case and control patients for given type i and type ii error probabilities alpha and beta the odds ratio that can be detected with a given sample size is derived as well as the sample size needed to detect a specified value of the odds ratio graphs are presented for paired designs that show the relationship between sample size and power for alpha 05 beta 2 and different values of po phi and psi the sample size needed for designs involving m matched control patients can be derived from these graphs by means of a simple equation these results quantify the loss of power associated with increasing correlation between the exposure status of matched case and control patients sample size requirements are also greatly increased for values of po near 0 or 1 the relationship between sample size psi phi and po is discussed and illustrated by examples

instrumental variable estimation in the presence of many moment conditions abstract this paper develops shrinkage methods for addressing the many instruments problem in the context of instrumental variable estimation it has been observed that instrumental variable estimators may behave poorly if the number of instruments is large this problem can be addressed by shrinking the influence of a subset of instrumental variables the procedure can be understood as a two step process of shrinking some of the ols coefficient estimates from the regression of the endogenous variables on the instruments then using the predicted values of the endogenous variables based on the shrunk coefficient estimates as the instruments the shrinkage parameter is chosen to minimize the asymptotic mean square error the optimal shrinkage parameter has a closed form which makes it easy to implement a monte carlo study shows that the shrinkage method works well and performs better in many situations than do existing instrument selection procedures

efficiency of multivariate control variates in monte carlo simulation this paper considers some statistical aspects of applying control variates to achieve variance reduction in the estimation of a vector of response variables in monte carlo simulation it gives a result that quantifies the loss in variance reduction caused by the estimation of the optimal control matrix for the one dimensional case we derive analytically the optimal size of the vector of control variates under specific assumptions on the covariance matrix for the multidimensional case our numerical results show that good variance reduction is achieved when the number of control variates is relatively small approximately of the same order as the number of unknown parameters finally we give some recommendations for future research

sample size formula with a continuous outcome for unequal group sizes and unequal variances guenther derived a simple formula for the accurate computation of equal sample sizes when the two sample t test with pooled variance estimate is used in the present paper the guenther formula is generalized to the case of unequal sample sizes in addition the case of unequal variances is considered

method of moments estimation and identifiability of semiparametric nonlinear errors in variables models abstract this paper deals with a nonlinear errors in variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric using the instrumental variable approach we propose method of moments estimators for the unknown parameters and simulation based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals both estimators are consistent and asymptotically normally distributed under fairly general regularity conditions moreover root n consistent semiparametric estimators and a rank condition for model identifiability are derived using the combined methods of the nonparametric technique and fourier deconvolution

a simple method of sample size calculation for linear and logistic regression a sample size calculation for logistic regression involves complicated formulae this paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model one can then adjust the required sample size for a multiple logistic regression model by a variance inflation factor this method requires no assumption of low response probability in the logistic model as in a previous publication one can similarly calculate the sample size for linear regression models this paper also compares the accuracy of some existing sample size software for logistic regression with computer power simulations an example illustrates the methods

common random numbers in multivariate simulations abstract it is shown how common random numbers can be used in computer simulations where the aim is to compare two systems on several parameters conditions are derived under which the use of common random numbers leads to a reduction in the size of the confidence region for the difference between the parameter vectors theoretical and experimental results suggest that this reduction is greatest when the covariance structure is the same for both systems

semi markov models with phase type sojourn distributions continuous time multistate models are widely used for categorical response data particularly in the modeling of chronic diseases however inference is difficult when the process is only observed at discrete time points with no information about the times or types of events between observation times unless a markov assumption is made this assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state such a formulation results in a semi markov model we show that the computational problems associated with fitting semi markov models to panel observed data can be alleviated by considering a class of semi markov models with phase type sojourn distributions this allows methods for hidden markov models to be applied in addition extensions to models where observed states are subject to classification error are given the methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post lung transplantation patients

a consistent nonparametric test for nonlinear causality specification in time series regression abstract since the pioneering work by granger 1969 many authors have proposed tests of causality between economic time series most of them are concerned only with linear causality in mean or if a series linearly affects the conditional mean of the other series it is no doubt of primary interest but dependence between series may be nonlinear and or not only through the conditional mean indeed conditional heteroskedastic models are widely studied recently the purpose of this paper is to propose a nonparametric test for possibly nonlinear causality taking into account that dependence in higher order moments are becoming an important issue especially in financial time series we also consider a test for causality up to the k th conditional moment statistically we can also view this test as a nonparametric omitted variable test in time series regression a desirable property of the test is that it has nontrivial power against t 1 2 local alternatives where t is the sample size also we can form a test statistic accordingly if we have some knowledge on the alternative hypothesis furthermore we show that the test statistic includes most of the omitted variable test statistics as special cases asymptotically the null asymptotic distribution is not normal but we can easily calculate the critical regions by simulation monte carlo experiments show that the proposed test has good size and power properties

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

sample size tables for logistic regression sample size tables are presented for epidemiologic studies which extend the use of whittemore s formula the tables are easy to use for both simple and multiple logistic regressions monte carlo simulations are performed which show three important results firstly the sample size tables are suitable for studies with either high or low event proportions secondly although the tables can be inaccurate for risk factors having double exponential distributions they are reasonably adequate for normal distributions and exponential distributions finally the power of a study varies both with the number of events and the number of individuals at risk

a modified likelihood ratio test for homogeneity in finite mixture models summary testing for homogeneity in finite mixture models has been investigated by many researchers the asymptotic null distribution of the likelihood ratio test lrt is very complex and difficult to use in practice we propose a modified lrt for homogeneity in finite mixture models with a general parametric kernel distribution family the modified lrt has a x2 type of null limiting distribution and is asymptotically most powerful under local alternatives simulations show that it performs better than competing tests they also reveal that the limiting distribution with some adjustment can satisfactorily approximate the quantiles of the test statistic even for moderate sample sizes

integrated variance reduction strategies for simulation we develop strategies for integrated use of certain well known variance reduction techniques to estimate a mean response in a finite horizon simulation experiment the building blocks for these integrated variance reduction strategies are the techniques of conditional expectation correlation induction including antithetic variates and latin hypercube sampling and control variates all pairings of these techniques are examined for each integrated strategy we establish sufficient conditions under which that strategy will yield a smaller response variance than its constituent variance reduction techniques will yield individually we also provide asymptotic variance comparisons between many of the methods discussed with emphasis on integrated strategies that incorporate latin hypercube sampling an experimental performance evaluation reveals that in the simulation of stochastic activity networks substantial variance reductions can be achieved with these integrated strategies both the theoretical and experimental results indicate that superior performance is obtained via joint application of the techniques of conditional expectation and latin hypercube sampling

sample size for logistic regression with small response probability abstract the fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented hessian matrix of the moment generating function for the covariates the approximation is valid when the probability of response is small with its use one can obtain a simple closed form estimate of the asymptotic covariance matrix of the maximum likelihood parameter estimates and thus approximate sample sizes needed to test hypotheses about the parameters the method is developed for selected distributions of a single covariate and for a class of exponential type distributions of several covariates it is illustrated with an example concerning risk factors for coronary heart disease

a penalized likelihood approach for a progressive three state model with censored and truncated data application to aids summary we consider the estimation of the intensity and survival functions for a continuous time progressive three state semi markov model with intermittently observed data the estimator of the intensity function is defined nonparametrically as the maximum of a penalized likelihood we thus obtain smooth estimates of the intensity and survival functions this approach can accommodate complex observation schemes such as truncation and interval censoring the method is illustrated with a study of hemophiliacs infected by hiv the intensity functions and the cumulative distribution functions for the time to infection and for the time to aids are estimated covariates can easily be incorporated into the model

a modified approach to estimating sample size for simple logistic regression with one continuous covariate different methods for the calculation of sample size for simple logistic regression lr with one normally distributed continuous covariate give different results sometimes the difference can be large furthermore some methods require the user to specify the prevalence of cases when the covariate equals its population mean rather than the more natural population prevalence we focus on two commonly used methods and show through simulations that the power for a given sample size may differ substantially from the nominal value for one method especially when the covariate effect is large while the other method performs poorly if the user provides the population prevalence instead of the required parameter we propose a modification of the method of hsieh et al that requires specification of the population prevalence and that employs schouten s sample size formula for a t test with unequal variances and group sizes this approach appears to increase the accuracy of the sample size estimates for lr with one continuous covariate

moment restriction based econometric methods an overview the 2011 special issue of the journal of econometrics discusses papers based on moment restriction based econometric methods in the first paper peter robinson of london school of economics considers asymptotic theory for nonparametric regression with spatial data specifically nonparametric regression with spatial or spatio temporal data the author discusses application of the established conditions to spatial autoregressive models and models defined on a regular lattice liqun wang and cheng hsiao consider method of moments estimation and identifiability of semiparametric nonlinear errors in variables models their paper deals with a nonlinear errors in variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric shih hsun hsu and chung ming kuan examine estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments

control variate remedies other than common random numbers control variates is the most promising variance reduction technique in terms of its potential for widespread use control variates is applicable in single or multiple response simulation it does not require altering the simulation run in any way and any stochastic simulation contains potential control variates a rich theory of control variates has been developed in recent years most of this theory assumes a specific probabilistic structure for the simulation output process usually joint normality of the response and the control variates when these assumptions are not satisfied desirable properties of the estimator such as unbiasedness may be lost a number of remedies for violations of the assumptions have been proposed including jackknifing and splitting however there has been no systematic analytical and empirical evaluation of these remedies this paper presents such an evaluation including evaluation of the small sample statistical properties of the proposed remedies

using common random numbers and control variates in multiple comparison procedures this paper considers the determination of the relative merits of two or more system designs via stochastic simulation experiments by constructing simultaneous interval estimates of certain differences in expected performance tukey s all pairwise comparisons procedure hsu s multiple comparisons with the best procedure and dunnett s multiple comparisons with a control procedure are standard methods for making such comparisons we propose refinements for all three procedures through the use of two variance reduction techniques common random numbers and control variates we show that the proposed procedures are better than the standard multiple comparison procedures in the sense that they have a larger probability of containing the true difference and at the same time not containing zero when a difference exists

tests of specification for parametric and semiparametric models abstract this paper provides a general framework for constructing specification tests for parametric and semiparametric models the paper develops new specification tests using the general framework in particular specification tests for semiparametric partially linear regression and sample selection models are introduced the results apply in time series and cross sectional contexts the method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes

linear programming based estimators in simple linear regression in this paper we introduce a linear programming estimator lpe for the slope parameter in a constrained linear regression model with a single regressor the lpe is interesting because it can be superconsistent in the presence of an endogenous regressor and hence preferable to the ordinary least squares estimator lse two different cases are considered as we investigate the statistical properties of the lpe in the first case the regressor is assumed to be fixed in repeated samples in the second the regressor is stochastic and potentially endogenous for both cases the strong consistency and exact finite sample distribution of the lpe is established conditions under which the lpe is consistent in the presence of serially correlated heteroskedastic errors are also given finally we describe how the lpe can be extended to the case with multiple regressors and conjecture that the extended estimator is consistent under conditions analogous to the ones given herein finite sample properties of the lpe and extended lpe in comparison to the lse and instrumental variable estimator ive are investigated in a simulation study one advantage of the lpe is that it does not require an instrument

multivariate batch means and control variates we consider applying the nonoverlapping batch means output analysis method in conjunction with the control variate variance reduction technique to estimate a steady state multivariate mean vector the effects of the number of batches and the number of control variates on the multivariate point and region estimators and the univariate point and interval estimators are considered the results are experiment analysis guidelines in terms of an appropriate range of the number of batches to choose as a function of the number of responses and control variates the results have implications for terminating simulations as well

estimation of multiresponse simulation metamodels using control variates this paper provides a unified development of the method of control variates for simulation experiments in which the objective is estimation of a multiresponse metamodel that is a linear model for an output vector of simulation performance measures expressed in terms of an input vector of decision variables for the target system in contrast to previous treatments of this topic we allow both the input and output of the metamodel to be multidimensional so that control variates can be applied to multipopulation multiresponse simulation experiments assuming that the responses and controls are jointly normal with a homogeneous covariance structure across the points of the experimental design we develop control variates procedures for point and confidence region estimation and for hypothesis testing on the coefficients of a postulated metamodel we derive a generalized minimum variance ratio to quantify the maximum efficiency that is achievable with a given set of controls and we formulate a generalized l

control functionals for monte carlo integration summary a non parametric extension of control variates is presented these leverage gradient information on the sampling density to achieve substantial variance reduction it is not required that the sampling density be normalized the novel contribution of this work is based on two important insights a trade off between random sampling and deterministic approximation and a new gradient based function space derived from stein s identity unlike classical control variates our estimators improve rates of convergence often requiring orders of magnitude fewer simulations to achieve a fixed level of precision theoretical and empirical results are presented the latter focusing on integration problems arising in hierarchical models and models based on non linear ordinary differential equations

asymptotic theory for nonparametric regression with spatial data nonparametric regression with spatial or spatio temporal data is considered the conditional mean of a dependent variable given explanatory ones is a nonparametric function while the conditional covariance reflects spatial correlation conditional heteroscedasticity is also allowed as well as non identically distributed observations instead of mixing conditions a possibly non stationary linear process is assumed for disturbances allowing for long range as well as short range dependence while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities a basic triangular array setting is employed with the aim of covering various patterns of spatial observation sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates when the cross sectional dependence is sufficiently mild the asymptotic variance in the central limit theorem is the same as when observations are independent otherwise the rate of convergence is slower we discuss the application of our conditions to spatial autoregressive models and models defined on a regular lattice

bayesian path specific frailty models for multi state survival data with applications multi state models can be viewed as generalizations of both the standard and competing risks models for survival data models for multi state data have been the theme of many recent published works motivated by bone marrow transplant data we propose a bayesian model using the gap times between two successive events in a path of events experienced by a subject path specific frailties are introduced to capture the dependence structure of the gap times in the paths with two or more states under improper prior distributions for the parameters we establish propriety of the posterior distribution an efficient gibbs sampling algorithm is developed for drawing samples from the posterior distribution an extensive simulation study is carried out to examine the empirical performance of the proposed approach a bone marrow transplant data set is analyzed in detail to further demonstrate the proposed methodology

a practical approach for comparing means of two groups without equal variance assumption h wang and s chow statistics in medicine 2002 21 3137 3151