seminonparametric bayesian estimation of the asymptotically ideal production model abstract recently it has been shown that seminonparametric methods can be used to produced high quality approximations to a firm s technology unlike the local approximations provided by the conventional class of flexible functional forms seminonparametric methods generate global spans within large classes of functions however that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling an exception is the asymptotically ideal model aim generated from the muntz szatz series expansion since every basis function in that expansion is within the neoclassical function space a straightforward method exists for imposing neoclassical regularity when all factors are substitutes since the relevant constraints are inequality restrictions we implement the approach using bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods we further discuss the relevant extensions that would permit complementary factors nonconstant returns to scale and technological change

smooth inference for survival functions with arbitrarily censored data we propose a procedure for estimating the survival function of a time to event random variable under arbitrary patterns of censoring the method is predicated on the mild assumption that the distribution of the random variable and hence the survival function has a density that lies in a class of smooth densities whose elements can be represented by an infinite hermite series truncation of the series yields a parametric expression that can well approximate any plausible survival density and hence survival function provided the degree of truncation is suitably chosen the representation admits a convenient expression for the likelihood for the parameters in the approximation under arbitrary censoring truncation that is straightforward to compute and maximize a test statistic for comparing two survival functions which is based on an integrated weighted difference of estimates of each under this representation is proposed via simulation studies and application to a number of data sets we demonstrate that the approach yields reliable inferences and can result in gains in efficiency over traditional nonparametric methods

estimation of nonparametric models with simultaneity we introduce methods for estimating nonparametric nonadditive models with simultaneity the methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables such as ratios of derivatives or averages of products of derivatives of this density the estimators are therefore easily computed functionals of a nonparametric estimator of the density of the observable variables we consider in detail a model where to each structural equation there corresponds an exclusive regressor and a model with one equation of interest and one instrument that is included in a second equation for both models we provide new characterizations of observational equivalence on a set in terms of the density of the observable variables and derivatives of the structural functions based on those characterizations we develop two estimation methods in the first method the estimators of the structural derivatives are calculated by a simple matrix inversion and matrix multiplication analogous to a standard least squares estimator but with the elements of the matrices being averages of products of derivatives of nonparametric density estimators in the second method the estimators of the structural derivatives are calculated in two steps in a first step values of the instrument are found at which the density of the observable variables satisfies some properties in the second step the estimators are calculated directly from the values of derivatives of the density of the observable variables evaluated at the found values of the instrument we show that both pointwise estimators are consistent and asymptotically normal

sieve m inference on irregular parameters abstract this paper presents sieve inferences on possibly irregular i e slower than root n estimable functionals of semi nonparametric models with i i d data we provide a simple consistent variance estimator of the plug in sieve m estimator of a possibly irregular functional and the asymptotic standard normality of the sieve t statistic we show that for hypothesis testing of irregular functionals the sieve likelihood ratio statistic is asymptotically chi square distributed these results are useful in inference on structural parameters that may have singular semiparametric efficiency bounds a simulation study and an empirical application of heckman and singer 1984 duration model are presented

regressions with berkson errors in covariates a nonparametric approach this paper establishes that so called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with berkson type measurement error in the regressors an estimator is proposed and proven to be consistent its practical performance and feasibility are investigated via monte carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health these examples illustrate that berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy

colored multiplicative and additive non gaussian noise driven dynamical system mean first passage time abstract we have studied the barrier crossing dynamics in presence of non gaussian noises it has been observed that multiplicative colored non gaussian noise can induce resonant activation ra the conspicuous dependence of mean first passage time mfpt on correlation time 2 of additive colored noise having fixed variance have been analyzed beyond a critical value of 2 the mfpt increases for a given rate of increase of noise strength with 2 if the additive colored noise is non gaussian the mfpt first decreases with increase of the non gaussian parameter measures deviation from gaussian character of multiplicative colored noise followed by an increase exhibiting a minimum the appearance of the minimum critically depends on the additive noise

testing nonnested euler conditions with quadrature based methods of approximation abstract singleton 1985 proposed a test of the validity of an euler equation specification which incorporates information on a nonnested set of euler equations from an alternative economic model the information about the alternative model is introduced into the testing framework by constructing a sequence of local alternatives to the euler equations of the maintained model which are in the direction of the euler equations of the alternative model singleton s test is easy to apply but is designed to have power against an alternative that in many cases does not have a straightforward economic interpretation in this paper we reexamine the construction of local alternatives to euler equations we compare singleton s approach with a method based on perturbing the data generation process dgp of the maintained model in the direction of the dgp of the alternative model the second approach leads to tests which are always of interest but require the complete specification of the dgp in this paper we derive a test for discriminating between two nonnested sets of euler conditions which have been estimated us ing generalized method of moments gmm the test is based on the encompassing principle of cox 1961 and mizon and richard 1986 and uses tauchen s 1986 quadrature based nethods for approximating the expectation of nonlinear functions of stationary random variables singleton s empirical examples are also reconsidered

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

graded contractions of lie algebras and central extensions we use the concept of grading of lie algebras to investigate the appearance of central charges during the contraction process as for the usual graded contractions one finds simultaneously the central extensions of classes of algebras rather than specific lie algebras to illustrate the method we consider in detail two physical applications the kinematical algebras of spacetime and the u n bosons limits of some lie algebras

heteroscedastic nonlinear regression several parameter estimation methods for dealing with heteroscedasticity in nonlinear regression are described these include variations on ordinary weighted iteratively reweighted extended and generalized least squares some of these variations are new and one of them in particular modified extended iteratively reweighted least squares meirls allows parameters of an assumed heteroscedastic variance model to be estimated with an adjustment for bias due to estimation of the regression parameters the context of the discussion is primarily that of pharmacokinetic type data although an example is given involving chemical reaction data using simulated data from 21 heteroscedastic pharmacokinetic type models some of the methods are compared in terms of mean absolute error and 95 confidence interval coverage from these comparisons meirls and the variations on generalized least squares emerge as the methods of choice

stochastic resonance in time delayed bistable systems driven by weak periodic signal abstract we study theoretically a bistable system with time delayed feedback driven by a weak periodic force the effective potential function and the steady state probability density are derived the delay time and the strength of its feedback can change the shapes of the potential wells in the adiabatic approximation the signal to noise ratio snr of the system with a weak periodic force is obtained the time delayed feedback modulates the magnitude of snr by changing the shape of the potential and the effective strength of the signal the maximum of snr decreases with increasing the feedback intensity when is negative or positive the time delay can suppress or promote the stochastic resonance phenomenon

linear mixed models with flexible distributions of random effects for longitudinal data normality of random effects is a routine assumption for the linear mixed model but it may be unrealistic obscuring important features of among individual variation we relax this assumption by approximating the random effects density by the seminonparameteric snp representation of gallant and nychka 1987 econometrics 55 363 390 which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior controlled by a user chosen tuning parameter an advantage is that the marginal likelihood may be expressed in closed form so inference may be carried out using standard optimization techniques we demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality and we illustrate the approach via simulation and using longitudinal data from the framingham study

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

nonparametric analysis of a duration model with stochastic unobserved heterogeneity abstract this paper develops nonparametric identification and estimation results for a single spell hazard model where the unobserved heterogeneity is specified as a levy subordinator the identification approach solves a nonlinear volterra integral equation of the first kind with an unknown kernel function both the kernel of the integral operator which models the distribution of the unobserved heterogeneity and the functions that enter it are identified given regularity conditions and minimal variation in the observed covariates the paper proposes a shape constrained nonparametric two step sieve minimum distance estimator rates of convergence are derived and monte carlo experiments show the finite sample performance of the estimator

semi nonparametric cointegration testing this paper considers a semi nonparametric cointegration test the test uses the lm testing principle the score function needed for the lm test is estimated from the data using an expansion of the density around a student t distribution in this way we capture both the possible fat tailedness and the skewness of the innovation process using a monte carlo experiment we show that the semi nonparametric cointegration test has good size and power properties over a broad class of distributions for the innovation process we also investigate the effect of order selection of the underlying var on inference the complete methodology is illustrated using an interest rate example

the relative efficiency of method of moments estimators abstract the asymptotic relative efficiency of efficient method of moments when implemented with a seminonparametric auxiliary model is compared to that of conventional method of moments when implemented with polynomial moment functions because the expectations required by these estimators can be computed by simulation these two methods are commonly used to estimate the parameters of nonlinear latent variables models the comparison is for the models in the marron wand test suite a scale mixture of normals and the second largest order statistic of the lognormal distribution the latter models are representative of financial market data and auction data respectively which are the two most common applications of simulation estimators efficient method of moments dominates conventional method of moments over these models

identification in a generalization of bivariate probit models with dummy endogenous regressors abstract this paper provides identification results for a class of models specified by a triangular system of two equations with binary endogenous variables the joint distribution of the latent error terms is specified through a parametric copula structure that satisfies a particular dependence ordering while the marginal distributions are allowed to be arbitrary but known this class of models is broad and includes bivariate probit models as a special case the paper demonstrates that having an exclusion restriction is necessary and sufficient for global identification in a model without common exogenous covariates where the excluded variable is allowed to be binary having an exclusion restriction is sufficient in models with common exogenous covariates that are present in both equations the paper then extends the identification analyses to a model where the marginal distributions of the error terms are unknown

bayesian inference in a sample selection model this paper develops methods of bayesian inference in a sample selection model the main feature of this model is that the outcome variable is only partially observed we first present a gibbs sampling algorithm for a model in which the selection and outcome errors are normally distributed the algorithm is then extended to analyze models that are characterized by nonnormality specifically we use a dirichlet process prior and model the distribution of the unobservables as a mixture of normal distributions with a random number of components the posterior distribution in this model can simultaneously detect the presence of selection effects and departures from normality our methods are illustrated using some simulated data and an abstract from the rand health insurance experiment

a maximum likelihood estimation method for random coefficient regression models summary a method for estimating the distribution of the parameters of a random coefficient regression model is proposed this distribution accounting for interindividual variability is assumed to lie in a wide class of probability distributions rather than in a given parametric class estimation is based on observations from a sample of individuals and likelihood is the estimation criterion experimental designs may be different among individuals allowing the method to apply to routinely collected data the problem has strong connections with the theory of optimum design of experiments conditions are given under which the problem has a unique solution which then corresponds to a discrete distribution a simple pharmacokinetic model involving two parameters is used as an example these parameters have a bimodal distribution as statistical specification moreover only one observation is available per individual thus the method applies even when the model is not identifiable

asymmetric probability densities in symmetrically modulated bistable devices a brownian particle hopping in a symmetric double well potential can be statistically confined into a single well by the simultaneous action of a two periodic input signals one tilting the minima and the other one modulating the barrier height and b an additive and a purely multiplicative random signal generated by a unique source and thus preserving a certain degree of statistical correlation the underlying gating mechanism is quite robust when compared for instance with biharmonic rocking in view of technological implementation asymmetric confinement through gating can be conveniently maximized by tuning the input signal parameters correlation time phase time lag amplitudes thus revealing a resonant localization mechanism of general applicability

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

semiparametric maximum likelihood for measurement error model regression this paper presents an em algorithm for semiparametric likelihood analysis of linear generalized linear and nonlinear regression models with measurement errors in explanatory variables a structural model is used in which probability distributions are specified for a the response and b the measurement error a distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood for various types of extra information about the measurement error distribution the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of a and b if the true x were available simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption the approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution

sieve maximum likelihood estimation of the spatial autoregressive tobit model abstract this paper extends the ml estimation of a spatial autoregressive tobit model under normal disturbances in xu and lee 2015b journal of econometrics to distribution free estimation we examine the sieve mle of the model where the disturbances are i i d with an unknown distribution we show that the spatial autoregressive process with tobit censoring and related variables are spatial near epoch dependent ned a related contribution is that we develop some exponential inequalities for spatial ned random fields with these inequalities we establish the consistency of the estimator asymptotic distributions of structural parameters of the model are derived from a functional central limit theorem and projection simulations show that the sieve mle can improve the finite sample performance upon misspecified normal mles as an empirical application we examine the school district income surtax rates in iowa our results show that the spatial spillover effects are significant but they may be overestimated if disturbances are restricted to be normally distributed

a longitudinal measurement error model with a semicontinuous covariate covariate measurement error in regression is typically assumed to act in an additive or multiplicative manner on the true covariate value however such an assumption does not hold for the measurement error of sleep disordered breathing sdb in the wisconsin sleep cohort study wscs the true covariate is the severity of sdb and the observed surrogate is the number of breathing pauses per unit time of sleep which has a nonnegative semicontinuous distribution with a point mass at zero we propose a latent variable measurement error model for the error structure in this situation and implement it in a linear mixed model the estimation procedure is similar to regression calibration but involves a distributional assumption for the latent variable modeling and model fitting strategies are explored and illustrated through an example from the wscs

nonparametric estimation of stage occupation probabilities in a multistage model with current status data multistage models are used to describe individuals or experimental units moving through a succession of stages corresponding to distinct states e g healthy diseased diseased with complications dead the resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied traditional survival analysis is the simplest example of a multistage model where individuals begin in an initial stage say alive and move irreversibly to a second stage death in this article we consider general multistage models with a directed tree structure progressive models in which individuals traverse through stages in a possibly non markovian manner we construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards empirical calculations of these quantities are not possible due to the lack of complete data we consider current status information which represents a more severe form of censoring than the commonly used right censoring asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators finite sample behavior of our estimators is studied by simulation in which we show that our estimators based on these limited data compare well with those based on complete data we also apply our method to a real life data set arising from a cardiovascular diseases study in taiwan

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

inference in nonparametric instrumental variables with partial identification this paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework we construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction the same test statistic can be employed under identification in which case the hypothesis is whether the true model satisfies the posited property an almost sure consistent bootstrap procedure is provided for obtaining critical values possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set as an illustration we obtain confidence intervals for the level and slope of brazilian fuel engel curves a monte carlo study examines finite sample performance

semiparametric bayesian inference in autoregressive panel data models this paper develops bayesian methods for inference in dynamic panel data models with individual effects and applies them to study longitudinal data on earnings from the panel study of income dynamics psid we study semiparametric versions of commonly used random effects autoregressive models in which the distribution of the disturbances is not restricted to fall in a parametric class to model the unknown distributions without resorting to strong parametric assumptions we draw upon recent advances in the theory and computation of nonparametric bayesian models using dirichlet process priors the overall approach can be viewed as an application of the general semiparametric bayesian approach of west muller and escobar 1994 which in turn makes use of results on bayesian density estimation by escobar 1994 and escobar and west 1995 most conventional panel data methods e g anderson and hsiao 1981 macurdy

two stage non gaussian qml estimation of garch models and testing the efficiency of the gaussian qmle abstract in generalized autoregressive conditional heteroskedastic garch models the standard identifiability assumption that the variance of the iid process is equal to 1 can be replaced by an alternative moment assumption we show that for estimating the original specification based on the standard identifiability assumption efficiency gains can be expected from using a quasi maximum likelihood qml estimator based on a non gaussian density and a reparameterization based on an alternative identifiability assumption a test allowing to determine whether a reparameterization is needed that is whether the more efficient qmle is obtained with a non gaussian density is proposed

estimating stochastic differential equations efficiently by minimum chi squared summary we propose a minimum chi squared estimator for the parameters of an ergodic system of stochastic differential equations with partially observed state we prove that the efficiency of the estimator approaches that of maximum likelihood as the number of moment functions entering the chi squared criterion increases and as the number of past observations entering each moment function increases the minimised criterion is asymptotically chi squared and can be used to test system adequacy when a fitted system is rejected inspecting studentised moments suggests how the fitted system might be modified to improve the fit the method and diagnostic tests are applied to daily observations on the u s dollar to deutschmark exchange rate from 1977 to 1992

using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution previously hansen and jagannathan 1990a derived and computed mean standard deviation frontiers for intertemporal marginal rates of substitution imrs implied by asset market data these frontiers give the lower bounds on the standard deviations as a function of the mean in this paper we develop a strategy for utilizing conditioning information efficiently and hence improve on the standard deviation bounds computed by hansen and jagannathan we implement this strategy empirically by using the seminonparametric snp methodology suggested by gallant and tauchen 1989 to estimate the conditional distribution of a vector of monthly asset payoffs we use the fitted conditional distributions to calculate both conditional and unconditional standard deviation bounds for the imrs the unconditional bounds are as sharp as possible subject to robustness considerations we also use the fitted distributions to compute the moments of various candidate marginal rates of substitution suggested by economic theory and in particular the time nonseparable preferences of dunn and singleton 1986 and eichenbaum and hansen 1990 for these preferences our findings suggest that habit persistence will put the moments of the imrs inside the frontier at reasonable values of the curvature parameter at the same time we uncover evidence that the implied imrs fails to satisfy all of the restrictions inherent in the euler equation the findings help explain why euler equation estimation methods typically find evidence in favor of local durability instead of habit persistence for monthly data

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

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

era s a new approach to small sample theory this article proposes a new approach to small sample theory that achieves a meaningful integration of earlier directions of research in this field the approach centers on the constructive technique of approximating distributions developed recently by the author in 10 this technique utilizes extended rational approximants era s which build on the strengths of alternative less flexible approximation methods such as those based on asymptotic expansions and which simultaneously blend information from diverse analytic numerical and experimental sources the first part of the article explores the general theory of approximation of continuous probability distributions by means of era s existence characterization error bound and uniqueness theorems for these approximants are given and a new proof is provided for the convergence result obtained earlier in 10 some further aspects of finding era s by modifications to multiple point pade approximants are presented and the new approach is applied to the noncircular serial correlation coefficient the results of this application demonstrate how era s provide systematic improvements over edgeworth and saddlepoint techniques these results taken with those of the earlier article 10 suggest that the approach offers considerable potential for empirical application in terms of its reliability convenience and generality

an elasticity can be estimated consistently without a priori knowledge of functional form we consider an open question in applied price theory without a priori knowledge of a firm s cost function or a consumer s indirect utility function is it possible to estimate price and substitution elasticities consistently by observing a demand system as the work of white 30 guilkey lovell and sickles 19 and others has shown ordinary flexible functional forms such as the translog cannot achieve this objective we find that if one is prepared to assume that elasticities of substitution cannot oscillate wildly over the region of interest then consistent estimation is possible using the fourier flexible form provided the number of fitted parameters increases as the number of observations increases this result obtains with any of the commonly used statistical methods as for example multivariate least squares maximum likelihood and three stage least squares it obtains if the number of fitted parameters is chosen adaptively by observing the data or chosen deterministically according to some fixed rule we approach the problem along the classical lines of estimability considerations as used in the study of less than full rank linear statistical models and thereby discover that the problem has a fascinating structure which we explore in detail

a parametric approach to flexible nonlinear inference author s hamilton james d abstract this paper proposes a new framework for determining whether a given relationship is nonlinear what the nonlinearity looks like and whether it is adequately described by a particular parametric model the paper studies a regression or forecasting model of the form yt xt et where the functional form of is unknown we propose viewing itself as the outcome of a random process the paper introduces a new stationary random random field m that generalizes finite differenced brownian motion to a vector field and whose realizations could represent a broad class of possible forms for we view the parameters that characterize the relation between a given realization of m and the particular value of for a given sample as population parameters to be estimated by maximum likelihood or bayesian methods we show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions the paper further develops a new test of the null hypothesis of linearity based on the lagrange multiplier principle and small sample confidence intervals based on numerical bayesian methods an empirical application suggests that properly accounting for the nonlinearity of the inflation unemployment tradeoff may explain the previously reported uneven empirical success of the phillips curve

nonparametric errors in variables models with measurement errors on both sides of the equation abstract measurement errors are often correlated as in surveys where respondent s biases or tendencies to err affect multiple reported variables we extend schennach 2007 to identify moments of the conditional distribution of a true y given a true x when both are measured with error the measurement errors in y and x are correlated and the true unknown model of y given x has nonseparable model errors after showing nonparametric identification we provide a sieve generalized method of moments based estimator of the model and apply it to nonparametric engel curve estimation in our application measurement errors on the expenditures of a good y are by construction correlated with measurement errors in total expenditures x this problem which is present in many consumption data sets has been ignored in most demand applications we find that accounting for this problem casts doubt on hildenbrand s 1994 increasing dispersion assumption

large deviation probabilities for certain nonparametric maximum likelihood estimators let x d be a measurable space and p ti q e ee e t e t a family of probability measures given an appropriate estimator sequence for 0 we define a sequence of asymptotic maximum likelihood estimators for t and give bounds for its large deviation probabilities under conditions which are natural for the application to the estimation of mixing distributions this paper generalizes earlier results of pfanzagl to the following cases i estimator sequences restricted to a sieve ii estimator sequences using a given estimator sequence for a nuisance parameter iii convergence under the wrong model iv large deviation probabilities instead of consistency

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