adaptive estimation of regression models via moment restrictions abstract this paper considers adaptive estimation of regression models by means of generalized method of moments estimators two models are considered one with an i i d disturbance that is independent of the regressors and one with a conditionally symmetric but possibly heteroskedastic disturbance for both cases the paper develops linearized estimators that are asymptotically efficient if the number and variety of moment conditions are allowed to grow at an appropriate rate with the sample size in the general symmetric case no other adaptive estimator has yet been proposed also results of a small monte carlo study indicate that in the independence case the small sample performance of the generalized method of moments estimator can be quite good vis a vis other estimators previously proposed

series estimation under cross sectional dependence an asymptotic theory is developed for series estimation of nonparametric and semiparametric regression models for cross sectional data under conditions on disturbances that allow for forms of cross sectional dependence and hetero geneity including conditional and unconditional heteroskedascity along with conditions on regressors that allow dependence and do not require existence of a density the conditions aim to accommodate various settings plausible in economic applications and can apply also to panel spatial and time series data a mean square rate of convergence of nonparametric regression estimates is established followed by asymptotic normality of a quite general statistic data driven studentizations that rely on single or double indices to order the data are justified in a partially linear model setting monte carlo investigation of finite sample properties and two empirical applications are carried out

asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

a new approach to assess product lifetime performance for small data sets abstract because of cost and time limit factors the number of samples is usually small in the early stages of manufacturing systems and the scarcity of actual data will cause problems in decision making in order to solve this problem this paper constructs a counter intuitive hypothesis testing method by choosing the maximal p value based on a two parameter weibull distribution to enhance the estimate of a nonlinear and asymmetrical shape of product lifetime distribution further we systematically generate virtual data to extend the small data set to improve learning robustness of product lifetime performance this study provides simulated data sets and two practical examples to demonstrate that the proposed method is a more appropriate technique to increase estimation accuracy of product lifetime for normal or non normal data with small sample sizes

properties of hazard based residuals and implications in model diagnostics abstract model diagnostic procedures in failure time models using hazard based residuals rely on the assumption that the residual vector closely resembles a random sample from a unit exponential distribution when the model holds this article formally investigates the validity of this critical assumption by deriving and examining the properties of parametrically semiparametrically and nonparametrically estimated residuals for complete and right censored data the joint distribution of the residual vector is characterized and the behavior of some tests for exponentiality when applied to the residuals is examined analytically and through monte carlo methods findings reveal that the critical assumption of approximate unit exponentiality of the residual vector may not be viable and consequently the model diagnostic procedures considered which revolve on checking the approximate unit exponentiality of the residual vector specifically hazard plotting and the use of spacings and total time on test stati

particularities of newton s method in space frame force determination utilising eigenpair functions abstract redundant space frame dynamics are modelled through the structural eigenproblem which is formulated to account for the geometric stiffness due to self equilibrating membrane forces the resulting mathematical eigenvalues and eigenvectors respectively indicative of natural frequencies and modes of oscillation are then assumed to be continuous functions of a scalar factor upon a normalised set of forces in equilibrium newton s method or sensitivity analysis provides a means for minimising the difference between mathematical and physically observed eigenvalues whereupon the axial forces are inferred from the model issues of convergence and root uniqueness are anticipated eigenvalue coalescence in which eigenvalues transitorily coalesce to permute their arbitrarily numerical ordering is seen to define non smooth eigenvalue functions and hence encumber newton s method mode tracing strategies to overcome this are discussed the existence of various degrees of eigenvalue degeneracy owing to frame cyclic symmetry or otherwise is anticipated in terms of the influence upon newton s method if the degree of frame static redundancy is greater than one and there exist a number of linearly independent force distributions then the required force determination is a multidimensional newton method problems encountered in these manifold dimensions including those arising from frame spatial periodicity and the adversity of newton s method are overcome emphasis is placed upon minimising the dimensionality of newton s method through enforcement of equilibrium constraints illustrative numerical simulations are given and some applications of the method are proposed

efficient estimation of a semiparametric partially linear varying coefficient model in this paper we propose a general series method to estimate a semiparametric partially linear varying coefficient model we establish the consistency and sqrt n normality property of the estimator of the finite dimensional parameters of the model we further show that when the error is conditionally homoskedastic this estimator is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator of the finite dimensional parameter reaches the semiparametric efficiency bound of this model a small scale simulation is reported to examine the finite sample performance of the proposed estimator and an empirical application is presented to illustrate the usefulness of the proposed method in practice we also discuss how to obtain an efficient estimation result when the error is conditional heteroskedastic

efficiency of age adjusted tests in animal carcinogenicity experiments based on asymptotic relative efficiency calculations ryan 1985 biometrics 41 525 531 concludes that in the analysis of animal carcinogenicity experiments age adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors we recalculate the asymptotic efficiencies of the simple proportions test relative to the log rank test for the lethal tumor case for a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice more generally we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by ryan and using simulations examine the relevance of asymptotic efficiencies to typical sample sizes contrary to the numerical results of ryan we find for experiments with good survival and typical tumor rates that the relative efficiencies are greater than 95 usually about 99 in the nonlethal tumor case similar results follow from ryan for tumor rates and survival rates typically encountered in practice as it is often difficult to determine whether or not a tumor is lethal we conclude for equal interim mortality rates that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments

a generalization of the product limit estimator with an application to censored regression the product limit estimator ple and weighted empirical processes are two important ingredients of almost any censored regression analysis a link between them is provided by the generalized ples introduced in this paper these generalized ples are the product limit integrals of the empirical cumulative hazard function estimators in which weighted empirical processes are used to replace the standard empirical processes the weak convergence and some large sample approximations of the generalized ples are established as an application these generalized ples are used to define some minimum distance estimators which are shown to be asymptotically normal these estimators are qualitatively robust in some submodels an optimal choice of the weight matrix is the covariate matrix and some of these estimators are quite efficient at a few common survival distributions to implement these estimators some computational aspects are discussed and an algorithm is given from a real data example and some preliminary simulation results these estimators seem to be very competitive to and more robust than some more traditional estimators such as the buckley james estimator

extended weighted log rank estimating functions in censored regression abstract in the censored regression model some regression estimators are introduced using weighted integrals of the log rank estimating functions their limiting covariance matrices do not involve the error density and can be reliably estimated inference can then be easily obtained some of these estimators have high asymptotic efficiency at some important submodels some lack of fit tests are derived that require little extra computing time these tests are asymptotically normal under the model and consistent against certain monotone or convex model misspecifications numerical studies show that for some weight functions the estimators and tests perform well implementation of the proposed procedures is discussed and illustrated in a real data example

a comparison of several methods of estimating the survival function when there is extreme right censoring summary when there is extreme censoring on the right the kaplan meier product limit estimator is known to be a biased estimator of the survival function several modifications of the kaplan meier estimator are examined and compared with respect to bias and mean squared error

choice of time scale and its effect on significance of predictors in longitudinal studies time to event regression is a frequent tool in biomedical research in clinical trials this time is usually measured from the beginning of the study the same approach is often adopted in the analysis of longitudinal observational studies however in recent years there has appeared literature making a case for the use of the date of birth as a starting point and thus utilize age as the time to event in this paper we explore different types of age scale models and compare them with time on study models in terms of the estimated regression coefficients they produce we consider six proportional hazards regression models that differ in the choice of time scale and in the method of adjusting for the years before the study by considering the estimating equations of these models as well as numerical simulations we conclude that correct adjustment for the age at entry is crucial in reducing bias of the estimated coefficients the unadjusted age scale model is inferior to any of the five other models considered regardless of their choice of time scale additionally if adjustment for age at entry is made our analyses show very little to suggest that there exists any practically meaningful difference in the estimated regression coefficients depending on the choice of time scale these findings are supported by four practical examples from the framingham heart study

some scale estimators and lack of fit tests for the censored two sample accelerated life model some new scale estimators for the censored two sample accelerated life model are introduced they are zeros of some integrated weighted difference between the two cumulative hazard estimators these estimators are asymptotically normal the weight is chosen to result in estimators whose asymptotic variances do not involve the destiny functions and can be easily estimated this provides a fast and simple means of statistical inference in the censored two sample accelerated life model through investigating the asymptotic relative efficiency at some important censoring submodels and the finite example behaviors in various numerical studies we obtain some estimators with very competitive performance from the new class of scale estimators some lack of fit tests for the accelerated life model are also derived these tests are related to gill schumacher type tests and require little extra computing time once the estimator is obtained the estimators and tests are illustrated in two applications for a vaginal cancer data set for rats the effect of pretreatment regime was found to be well described by the two sample accelerated life model for a data set on progression of ovarian cancer it was found that the effect of grade of disease could not be described either by the two sample proportional hazards model or the two sample accelerated life model

an exact chi squared decomposition theorem for inverse gaussian variates on montre que la deviance d echelle d un echantillon normal inverse de dimension n peut etre exprimee comme la somme de n 1 variables khi deux independantes

nonparametric methods for imperfect repair models in the age dependent minimal repair model of block borges and savits bbs a system failing at age t undergoes one of two types of repair with probability p t a perfect repair is performed and the system is returned to the good as new state while with probability 1 p t a minimal repair is performed and the system is repaired but is only as good as a working system of age t whitaker and samaniego propose an estimator for the system life distribution f when data are collected under this model in the present article an appropriate probability model for the bbs process is developed and a counting process approach is used to extend the large sample theorems of whitaker and samaniego to the whole line applications of these results to confidence bands and an extension of the wilcoxon two sample test are examined

maximum likelihood estimation for two parameter decreasing hazard rate distributions using censored data abstract problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions typically either mixed exponential or work hardened sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure even with highly censored data that the mle s exist from such dhr distributions whenever the sample satisfies a certain condition otherwise a constant hazard rate is estimated as a limiting case some computational methods are given and applications made

a comparison of the bias in four versions of the product limit estimator summary the bias of the product limit estimator depends entirely on the method used to complete the estimator beyond the last observation when it is censored the bias has been investigated for the upper gill 1980 and lower efron 1967 bounds on these methods rather than using a completion method investigators in practice commonly truncate the estimator using data driven rules the bias under two common truncation rules are considered i truncating at the last observation if it is censored and ii truncating at the n l th order statistic a number of inequalities between these biases are derived and properties of the bias functions are proved this investigation shows

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

a partially parametric estimator of survival in the presence of randomly censored data many biological or medical experiments have as their goal to estimate the survival function of a specified population of subjects when the time to the specified event may be censored due to loss to follow up the occurrence of another event that precludes the occurrence of the event of interest or the study being terminated before the event of interest occurs this paper suggests an improvement of the kaplan meier product limit estimator when the censoring mechanism is random the proposed estimator treats the uncensored observations nonparametrically and uses a parametric model only for the censored observations one version of this proposed estimator always has a smaller bias and mean squared error than the product limit estimator an example estimating the survival function of patients enrolled in the ohio state university bone marrow transplant program is presented

what price kaplan meier summary the asymptotic efficiency of the kaplan meier product limit estimator relative to the maximum likelihood estimator of a parametric survival function is examined under a random censoring model

on the small sample performance of efron s and of gill s version of the product limit estimator under nonproportional hazards various proposals have been made to extend the product limit estimator to survival times beyond the largest observation in case that observation is censored two extreme extensions are examined with respect to bias and mean squared error mse their quality depends considerably on the censoring constellation the mse of one extension appears to be robust against a wide variety of nonproportionalities of the hazard rates of the distributions of lifelength and time to censoring

testing hypotheses about the shape parameter of a gamma distribution the purpose of this expository article is to provide greater access to critical values for testing hypotheses about the shape parameter of a gamma distribution among the possible tests we consider tests of exponentiality against gamma increasing failure rate and or decreasing failure rate alternatives extensive tables of critical values are given for individual sample sizes from 2 to 30 and values of the shape parameter in half integer increments from i to 10 median unbiased estimators are also given for the shape parameter to avoid small sample complications with maximum likelihood methods power curves are given for testing exponentiality against gamma alternatives these curves illustrate certain advantages of this parametric test over nonparametric alternatives

estimation for the half logistic distribution based on multiply type ii hybrid censoring abstract in this paper some estimators of the scale parameter of the half logistic distribution are derived under the multiply type ii hybrid censoring scheme we propose three methods first we obtain the maximum likelihood estimator of the scale parameter of the half logistic distribution second we propose some approximate maximum likelihood estimators of the scale parameter by employing three different types of taylor series expansions lastly we obtain the bayes estimators by employing some prior distributions and loss functions the interval estimations such as the asymptotic confidence interval and the credible interval and the highest posterior density interval are obtained to assess the performance of the proposed estimators we obtain the mean squared error average length of 95 interval and coverage probability through monte carlo simulation and applies to the real dataset

nonparametric specification testing via the trinity of tests tests are developed for inference on a parameter vector whose dimension grows slowly with sample size the statistics are based on the lagrange multiplier wald and pseudo likelihood ratio principles admit standard normal asymptotic distributions under the null and are straightforward to compute they are shown to be consistent and possessing non trivial power against local alternatives the settings considered include multiple linear regression panel data models with fixed effects and spatial autoregressions when a nonparametric regression function is estimated by series we use our statistics to propose specification tests and in semiparametric adaptive estimation we provide a test for correct error distribution specification these tests are nonparametric but handled in practice with parametric techniques a monte carlo study suggests that our tests perform well in finite samples two empirical examples use them to test for correct shape of an electricity distribution cost function and linearity and equality of engel curves

summarising censored survival data using the mean residual life function the mean residual life function provides a clear and simple summary of the effect of a treatment or a risk factor in units of time avoiding hazard ratios or probability scales which require careful interpretation estimation of the mean residual life is complicated by the upper tail of the survival distribution not being observed as for example patients may still be alive at the end of the follow up period various approaches have been developed to estimate the mean residual life in the presence of such right censoring in this work a novel semi parametric method that combines existing non parametric methods and an extreme value tail model is presented where the limited sample information in the tail prior to study termination is used to estimate the upper tail behaviour this approach will be demonstrated with simulated and real life examples copyright 2015 john wiley sons ltd

small sample results for the kaplan meier estimator abstract whereas much is known about the asymptotic properties of the kaplan meier 1958 estimator kme of a survival function exact results for small samples have been difficult to obtain in this article we obtain an exact expression for the th moment 0 of the kme under a model of proportional hazards this enables us under proportional hazards to a study the bias of the kme and b compare the exact variance of the kme to its asymptotic variance

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

profile quasi maximum likelihood estimation of partially linear spatial autoregressive models abstract we propose profile quasi maximum likelihood estimation of spatial autoregressive models that are partially linear the rate of convergence of the spatial parameter estimator depends on some general features of the spatial weight matrix of the model the estimators of other finite dimensional parameters in the model have the regular n rate of convergence and the estimator of the nonparametric component is consistent but with different restrictions on the choice of bandwidth parameter associated with different natures of the spatial weights monte carlo simulations verify our theory and indicate that our estimators perform reasonably well in finite samples

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

apparently first closed form solutions for inhomogeneous vibrating beams under axial loading closed form solutions are presented for fundamental natural frequencies of inhomogeneous vibrating beams under axially distributed loading the mode shape is postulated as coinciding with the static deflection of the associated homogeneous beam without distributed axial loading then the inverse problem of determining the stiffness and mass density distributions producing the above mode shape is solved to describe these variations the family of polynomial functions is used several sets of boundary conditions are considered it is shown that the natural frequency vanishes when the intensity of the axially distributed loading equals the critical buckling value a linear relationship is established between the square of the natural frequency and the load ratio for all reported sets of boundary conditions in contrast to uniform beams where the exact linear relationship holds for columns with simply supported and or sliding ends

reversal of increasing failure rates when pooling failure data because mixtures of exponential distributions with constant failure rate have the decreasing failure rate dfr property as shown by proschan in the sixties it is not unexpected that mixtures of distributions that have a mildly increasing failure rate ifr also have this property what is perhaps surprising is that mixtures of ifr distributions with rapidly increasing failure rate may also behave in this manner two striking examples of such mixtures are presented here and illustrated graphically this phenomenon could be the cause of concern in practice when it is suspected that a sample is based on pooled data

efficient estimation of the semiparametric spatial autoregressive model efficient semiparametric and parametric estimates are developed for a spatial autoregressive model containing non stochastic explanatory variables and innovations suspected to be non normal the main stress is on the case of distribution of unknown nonparametric form where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest these estimates are as efficient as the ones based on a correct form in particular they are more efficient than pseudo gaussian maximum likelihood estimates at non gaussian distributions two different adaptive estimates are considered relying on somewhat different regularity conditions a monte carlo study of finite sample performance is included

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

constistent specification testing via nonparametric series regression this paper proposes two consistent one sided specification tests for parametric regression models one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values the other based on the difference in sums of squared residuals between the parametric and nonparametric models we estimate the nonparametric model by series regression the new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate n 1 2 under misspecification while avoiding weighting sample splitting and non nested testing procedures used elsewhere in the literature asymptotically our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero where the dependent variable is the residual from the parametric model and the series terms are functions of the explanatory variables chosen so as to support nonparametric estimation of a conditional expectation we specifically consider fourier series and regression splines and present a monte carlo study of the finite sample performance of the new tests in comparison to consistent tests of bierens 1990 eubank and spiegelman 1990 jayasuriya 1990 wooldridge 1992 and yatchew 1992 the results show the new tests have good power performing quite well in some situations we suggest a joint bonferroni procedure that combines a new test with those of bierens and wooldridge to capture the best features of the three approaches

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

asymptotic behavior of m estimators of p regression parameters when p 2 n is large ii normal approximation in a general linear model y x beta r with y and r n dimensional x a n times p matrix and beta p dimensional let hat beta be an m estimator of beta satisfying 0 sum x i psi y i x i beta let p rightarrow infty such that p log n 3 2 n rightarrow 0 then max i x i hat beta beta rightarrow p 0 and it is possible to find a uniform normal approximation for the distribution of hat beta under which arbitrary linear combinations a n hat beta beta are asymptotically normal when appropriately normalized and hat beta beta x x hat beta beta is approximately chi 2 p

a simple hybrid variance estimator for the kaplan meier survival function in this paper we propose a hybrid variance estimator for the kaplan meier survival function this new estimator approximates the true variance by a binomial variance formula where the proportion parameter is a piecewise non increasing function of the kaplan meier survival function and its upper bound as described below also the effective sample size equals the number of subjects not censored prior to that time in addition we consider an adjusted hybrid variance estimator that modifies the regular estimator for small sample sizes we present a simulation study to compare the performance of the regular and adjusted hybrid variance estimators to the greenwood and peto variance estimators for small sample sizes we show that on average these hybrid variance estimators give closer variance estimates to the true values than the traditional variance estimators and hence confidence intervals constructed with these hybrid variance estimators have more nominal coverage rates indeed the greenwood and peto variance estimators can substantially underestimate the true variance in the left and right tails of the survival distribution even with moderately censored data finally we illustrate the use of these hybrid and traditional variance estimators on a data set from a leukaemia clinical trial

the total time on test concept and its use in reliability theory more than 30 years ago epstein and sobel introduced the total time on test ttt concept during the last 10 years different generalizations of this concept have been defined and studied e g the ttt transform and the ttt plot a basic paper was presented by barlow and campo in 1975 many of these generalizations have proven to be very useful in different areas of reliability both from a theoretical and a practical point of view the purpose of this expository paper is to present some of these generalizations and illustrate their value

natural frequencies of beams under tensile axial loads abstract the effect of a constant axial tensile force on natural frequencies and mode shapes of a uniform single span beam with different combinations of end conditions is presented numerical observations indicate that the variation of normalized natural frequency parameter with normalized tension parameter is almost the same for clamped pinned and pinned free and similarly for clamped clamped and clamped sliding beams the variation of the sliding free beam is only slightly different from that of the latter pair and the free free beam for pinned pinned pinned sliding and sliding sliding beams this variation may exactly be expressed as 1 u this formula may be used for beams with other types of end constraints when the beam vibrates in a third mode or higher it also gives the upper bound approximation to the fundamental natural frequency of a pinned free beam for beams with other types of boundary conditions this approximation may be expressed as 1 u where the coefficient depends only on the type of the end constraints it is found that when the dimensionless tension parameter u is greater than about 12 then u can be expressed as an analytical function of u where is the dimensionless natural frequency parameter for such a beam in the first few modes the natural frequency is independent of the flexural rigidity and the beam behaves like a string the string solution gives a lower bound approximation to the natural frequency

sieve wald and qlr inferences on semi nonparametric conditional moment models this paper considers inference on functionals of semi nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals which include all of the nonlinear nonparametric instrumental variables iv as special cases these models are often ill posed and hence it is difficult to verify whether a possibly nonlinear functional is root n estimable or not we provide computationally simple unified inference procedures that are asymptotically valid regardless of whether a functional is root n estimable or not we establish the following new useful results 1 the asymptotic normality of a plug in penalized sieve minimum distance psmd estimator of a possibly nonlinear functional 2 the consistency of simple sieve variance estimators for the plug in psmd estimator and hence the asymptotic chi square distribution of the sieve wald statistic 3 the asymptotic chi square distribution of an optimally weighted sieve quasi likelihood ratio qlr test under the null hypothesis 4 the asymptotic tight distribution of a non optimally weighted sieve qlr statistic under the null 5 the consistency of generalized residual bootstrap sieve wald and qlr tests 6 local power properties of sieve wald and qlr tests and of their bootstrap versions 7 asymptotic properties of sieve wald and sqlr for functionals of increasing dimension simulation studies and an empirical illustration of a nonparametric quantile iv regression are presented

accurate confidence limits for quantiles under random censoring in survival analysis estimates of median survival times in homogeneous samples are often based on the kaplan meier estimator of the survivor function confidence intervals for quantiles such as median survival are typically constructed via large sample theory or the bootstrap the former has suspect accuracy for small sample sizes under moderate censoring and the latter is computationally intensive in this paper improvements on so called test based intervals and reflected intervals cf slud byar and green 1984 biometrics 40 587 600 are sought using the edgeworth expansion for the distribution of the studentized nelson aalen estimator derived in strawderman and wells 1997 journal of the american statistical association 92 we propose a method for producing more accurate confidence intervals for quantiles with randomly censored data the intervals are very simple to compute and numerical results using simulated data show that our new test based interval outperforms commonly used methods for computing confidence intervals for small sample sizes and or heavy censoring especially with regard to maintaining specified coverage

pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension pseudo maximum likelihood estimates are developed for higher order spatial autoregressive models with increasingly many parameters including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component and regression models with spatial autoregressive disturbances consistency and asymptotic normality of the estimates are established monte carlo experiments examine finite sample behaviour

survival estimation using splines a nonparametric maximum likelihood procedure is given for estimating the survivor function from right censored data it approximates the hazard rate by a simple function such as a spline with different approximations yielding different estimators a special case is that proposed by nelson 1969 journal of quality technology 1 27 52 and altshuler 1970 mathematical biosciences 6 1 11 the estimators are uniformly consistent and have the same asymptotic weak convergence properties as the kaplan meier 1958 journal of the american statistical association 53 457 481 estimator however in small and in heavily censored samples the simplest spline estimators have uniformly smaller mean squared error than do the kaplan meier and nelson altshuler estimators the procedure is extended to estimate the baseline hazard rate and regression coefficients in the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model and is illustrated using experimental carcinogenesis data

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

efficiency improvements in inference on stationary and nonstationary fractional time series we consider a time series model involving a fractional stochastic component whose integration order can lie in the stationary invertible or nonstationary regions and be unknown and an additive deterministic component consisting of a generalized polynomial the model can thus incorporate competing descriptions of trending behavior the stationary input to the stochastic component has parametric autocorrelation but innovation with distribution of unknown form the model is thus semiparametric and we develop estimates of the parametric component which are asymptotically normal and achieve an m estimation efficiency bound equal to that found in work using an adaptive lam lan approach a major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies this is relevant also when the innovation density is parameterized and we provide a result for that case also our semiparametric estimates employ nonparametric series estimation which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models our work thus also contributes to methods and theory for nonfractional time series models such as autoregressive moving averages a monte carlo study of finite sample performance of the semiparametric estimates is included

the weibull conway maxwell poisson distribution to analyze survival data in this paper we consider the distribution of life length of a series system with random number of components say m considering the distribution of m as com poisson a weibull com poisson distribution wcomp is developed the com poisson is a generalization of the poisson distribution having one extra parameter the structural properties of the resulting distribution are presented and the maximum likelihood estimation of the parameters is investigated extensive simulation studies are carried out to study the performance of the estimates a score test is developed to test the importance of the extra parameter for illustration three real data sets are examined and it is shown that the wcomp model presented here fits better than the exponential poisson and the exponential comp distributions

asymptotics for semiparametric econometric models via stochastic equicontinuity this paper provides a general framework for proving the square root of t consistency and asymptotic normality of a wide variety of semiparametric estimators the class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator the method of proof exploits results concerning the stochastic equicontinuity of stochastic processes the results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models primitive conditions are given for square root of t consistency and asymptotic normality of this estimator copyright 1994 by the econometric society

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

inference on higher order spatial autoregressive models with increasingly many parameters this paper develops consistency and asymptotic normality of parameter estimates for a higher order spatial autoregressive model whose order and number of regressors are allowed to approach infinity slowly with sample size both least squares and instrumental variables estimates are examined and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied besides allowing the number of parameters to increase with the data this has the advantage of accommodating some asymptotic regimes that are suggested by certain spatial settings several of which are discussed a small empirical example is also included and a monte carlo study analyses various implications of the theory in finite samples

semiparametric estimation of count regression models this paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity we use the generalized laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a poisson mixture model we establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated censored and zero inflated count regression models monte carlo evidence shows that the finite sample behavior of the estimator is quite good the paper applies the method to a model of individual shopping behavior

on testing the equality of two exponential distributions this paper derives the null distribution of the likelihood ratio lr criterion for testing the equality of location parameters and scale parameters of two exponential distributions based on type ii censored data it is shown that this null distribution is the same as that of bartlett s modified lr test for equality of two bivariate normal covariance matrices box s chi squared approximation to the criterion is found to be satisfactory both for equal and for unequal sample sizes the power of the criterion is then compared with hogg tanis s iterated procedure and perng s test a numerical example is also included

robust empirical bayes analyses of event rates a collection of i similar items generates point event histories for example machines experience failures or operators make mistakes suppose the intervals between events are modeled as iid exponential i or the counts as poisson i t i for the ith item furthermore so as to represent between item variability each individual rate parameter i is presumed drawn from a fixed super population with density g being a vector parameter a parametric empirical bayes peb setup for g specified alternatively as log student t n or gamma we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates i obtained via bayes s formula three data sets are analyzed and convenient explicit approximate formulas are furnished for i estimates in the student t case the individual estimates are seen to have a robust quality

accurate directional inference for vector parameters in linear exponential families we consider inference on a vector valued parameter of interest in a linear exponential family in the presence of a finite dimensional nuisance parameter based on higher order asymptotic theory for likelihood we propose a directional test whose p value is computed using one dimensional integration the work simplifies and develops earlier research on directional tests for continuous models and on higher order inference for discrete models and the examples include contingency tables and logistic regression examples and simulations illustrate the high accuracy of the method which we compare with the usual likelihood ratio test and with an adjusted version due to skovgaard in high dimensional settings such as covariance selection the approach works essentially perfectly whereas its competitors can fail catastrophically

a correlation goodness of fit test for randomly censored data summary for testing a composite goodness of fit hypothesis with randomly censored data a correlation statistic which is an analogue of the shapiro francia statistic is presented the test for exponentiality in case of light censoring is asymptotically robust against departures from the koziol green model of random censorship the power of the test is compared with the total time on test procedure and the new better than used test using monte carlo simulation as an example the test is applied to some data with prostate cancer