an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

local polynomial variance function estimation the conditional variance function in a heteroscedastic nonparametric regression model is estimated by linear smoothing of squared residuals attention is focused on local polynomial smoothers both the mean and variance functions are assumed to be smooth but neither is assumed to be in a parametric family the biasing effect of preliminary estimation of the mean is studied and a degrees of freedom correction of bias is proposed the corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known a proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions the proposal is illustrated with data from the lidar method of measuring atmospheric pollutants and from turbulence model computations

a semi parametric censored regression estimator abstract this paper introduces a semi parametric method for estimating regression co underlying parent population of errors in censored the method is an example of the method of sieves and it provides simultaneous estimates of the regression coefficients and the density of the underlying parent population in the very simplest terms the underlying unknown density is approximated by a spline with mesh size approaching zero with the sample size the values of the density at the knots are then added to the list of the usual unknown parameters in a censored regression model e g the regression coefficients and scale parameter a quasi likelihood function using the approximate spline density is then maximized over all the parameters mentioned above the method is shown to result in strongly consistent parameter estimates

efficient estimates in semiparametric additive regression models with unknown error distribution several authors have shown how to efficiently estimate beta in the semiparametric additive model y x beta g t text error g t smooth but unknown when the error distribution is normal however the general theory suggests that efficient estimation should be possible for general error distributions with finite fisher information even when the error distribution is unknown in this note we construct a sequence of estimators which achieves this goal under technical assumptions

efficient semiparametric estimation via moment restrictions conditional moment restrictions can be combined through gmm estimation to construct more efficient semiparametric estimators this paper is about attainable efficiency for such estimators we define and use a moment tangent set the directions of departure from the truth allowed by the moments to characterize when the semiparametric efficiency bound can be attained the efficiency condition is that the moment tangent set equals the model tangent set we apply these results to transformed censored and truncated regression models e g finding that the conditional moment restrictions from powell s 1986 censored regression quantile estimators can be combined to approximate efficiency when the disturbance is independent of regressors

optimal forecast combinations under general loss functions and forecast error distributions existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss under this loss function empirical studies have generally found that equally weighted combined forecasts lead to better performance than estimates of optimal forecast combination weights which in turn outperform the best individual predictions we show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed we characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights we also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise

temporal aggregation of garch processes the authors derive low frequency say weekly models implied by high frequency say daily arma models with symmetric garch errors they show that low frequency models exhibit conditional heteroskedasticity of the garch form as well the parameters in the conditional variance equation of the low frequency model depend upon mean variance and kurtosis parameters of the corresponding high frequency model moreover strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data the common assumption in applications that rescaled innovations are independent is disputable since it depends upon the available data frequency copyright 1993 by the econometric society

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

inference on endogenously censored regression models using conditional moment inequalities under a quantile restriction randomly censored regression models can be written in terms of conditional moment inequalities we study the identified features of these moment inequalities with respect to the regression parameters where we allow for covariate dependent censoring endogenous censoring and endogenous regressors these inequalities restrict the parameters to a set we show regular point identification can be achieved under a set of interpretable sufficient conditions we then provide a simple way to convert conditional moment inequalities into unconditional ones while preserving the informational content our method obviates the need for nonparametric estimation which would require the selection of smoothing parameters and trimming procedures without the point identification conditions our objective function can be used to do inference on the partially identified parameter maintaining the point identification conditions we propose a quantile minimum distance estimator which converges at the parametric rate to the parameter vector of interest and has an asymptotically normal distribution a small scale simulation study and an application using drug relapse data demonstrate satisfactory finite sample performance

semiparametric inference in a partial linear model in a partial linear model the dependence of a response variate y on covariates w x is given by y w x e where e is independent of w x with densities g and f respectively in this paper an asymptotically efficient estimator of is constructed solely under mild smoothness assumptions on the unknown f and g thereby removing the assumption of finite residual variance on which all least squares type estimators available in the literature are based

biharmonic hypersurfaces of the 4 dimensional semi euclidean space es4 abstract a submanifold m r n of a semi euclidean space e s m is said to have harmonic mean curvature vector field if h 0 where h denotes the mean curvature vector submanifolds with harmonic mean curvature vector are also known as biharmonic submanifolds in this paper we prove that every nondegenerate hypersurface of e s 4 the shape operator of which is diagonalizable with harmonic mean curvature vector field is minimal

a cross validatory choice of smoothing parameter in adaptive location estimation abstract this article proposes a new data driven method for selecting the smoothing parameter involved in constructing kernel based adaptive location estimators the method consists of minimizing a cross validatory criterion with respect to the bandwidth occurring in the kernel type estimators of the efficient score function it is shown that the location estimator with a data driven bandwidth selector is indeed an adaptive estimator a simulation study reveals that the method is also practicable showing that our estimator performs well in comparison with some other well known location estimators it also shows that our method has comparable finite sample performance with the bootstrap method of selecting the smoothing parameter and yet has great computational advantages

optimal rank based tests for homogeneity of scatter we propose a class of locally and asymptotically optimal tests based on multivariate ranks and signs for the homogeneity of scatter matrices in m elliptical populations contrary to the existing parametric procedures these tests remain valid without any moment assumptions and thus are perfectly robust against heavy tailed distributions validity robustness nevertheless they reach semiparametric efficiency bounds at correctly specified elliptical densities and maintain high powers under all efficiency robustness in particular their normal score version outperforms traditional gaussian likelihood ratio tests and their pseudo gaussian robustifications under a very broad range of non gaussian densities including for instance all multivariate student and power exponential distributions

properties of optimal forecasts under asymmetric loss and nonlinearity abstract evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast we establish instead that a suitable transformation of the forecast error known as the generalized forecast error possesses an equivalent set of properties the paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts

a semiparametric maximum likelihood estimator this paper presents a procedure for analyzing a model in which the parameter vector has two parts a finite dimensional component 8 and a nonparametric component a the procedure does not require parametric modeling of but assumes that the true density of the data satisfies an index restriction the idea is to construct a parametric model passing through the true model and to estimate by setting the score for the parametric model to zero the score is estimated nonparametrically and the estimator is shown to be n consistent and asymptotically normal the estimator is then shown to attain the semiparametric efficiency bound characterized in begun et al 1983 for multivariate nonlinear regression simultaneous equations partially specified regression index regression censored regression switching regression and disequilibrium models in which the error densities are unknown

second order approximation in the partially linear regression model we examine the second order properties of various quantities of interest in the partially linear regression model we obtain a stochastic expansion with remainder op n 2 4 where u 1 2 for the standardized semiparametric least squares estimator a standard error estimator and a studentized statistic we use the second order expansions to correct the standard error estimates for second order effects and to define a method of bandwidth choice a monte carlo experiment provides favorable evidence on our method of bandwidth choice

estimating with partial statistics the parameters of ergodic finite markov sources parameter estimation based on data emitted from a finite ergodic markov source is discussed this can be considered an extension of the memoryless case first an asymptotically optimal estimator is suggested for the case where the parametric model is completely known for an unknown parametric model e g unknown noise distribution with training sequences available a necessary condition is given for the existence of a universally optimum estimate a universal estimate is then suggested that is asymptotically nearly optimal the results hold under fairly mild regularity conditions

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per

classification of spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension spatial surfaces with parallel mean curvature vector play some important roles in general relativity theory of harmonic maps as well as in differential geometry recently spatial surfaces in four dimensional minkowski space time with parallel mean curvature vector were classified by chen and van der veken complete classification of parallel surfaces in 4 dimensional lorentzian space forms tohoku math j 61 1 2009 in this article we completely classify spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension the main result states that there exist 16 families of such surfaces as by product we achieve the complete classification of spatial surfaces with parallel mean curvature vector in minkowski space times of arbitrary dimension

efficient semiparametric estimation of censored and truncated regressions via a smoothed self consistency equation an asymptotically efficient likelihood based semiparametric estimator is derived for the censored regression tobit model based on a new technique for estimating the density function of the residuals in semiparametric models that involve an underlying partially observed regression smoothing the selfconsistency equation for the nonparametric maximum likelihood estimator of the distribution of the residuals yields an integral equation which in some cases can be solved explicitly the resulting estimated density is smooth enough to be used in a practical implementation of the profile likelihood estimator but is still sufficiently close to the nonparametric maximum likelihood estimator to allow estimation of the semiparametric efficient score the parameter estimates obtained by solving the estimated score equations are then asymptotically efficient details of the method and proofs are given specifically for the censored regression tobit model with a summary of analogous results for the case of random censoring and for truncated regression simulation results are also presented

volatility forecast comparison using imperfect volatility proxies the use of a conditionally unbiased but imperfect volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts we motivate our study with analytical results on the distortions caused by some widely used loss functions when used with standard volatility proxies such as squared returns the intra daily range or realised volatility we then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy and derive some useful special cases of this class of robust loss functions the methods are illustrated with an application to the volatility of returns on ibm over the period 1993 to 2003

a distribution free least squares estimator for censored linear regression models abstract this paper describes a method for estimating simultaneously the parameter vector of the systematic component and the distribution function of the random component of a censored linear regression model the estimator is obtained by minimizing the sum of the squares of the differences between the observed values of the dependent variable and the corresponding expected values of this variable according to the estimated parameter vector and distribution function the resulting least squares parameter estimator incorporates information on the distribution of the random component of the regression model that is available from the estimation sample hence it may often be more efficient than are parameter estimators that do not use such information the results of numerical experiments with the least squares estimator tend to support this hypothesis

integrated variance forecasting model based vs reduced form abstract this paper compares model based and reduced form forecasts of financial volatility when high frequency return data are available we derived exact formulas for the forecast errors and analyzed the contribution of the wrong data modeling and errors in forecast inputs the comparison is made for feasible forecasts i e we assumed that the true data generating process latent states and parameters are unknown as an illustration the same comparison is carried out empirically for spot 5 min returns of dm usd exchange rates it is shown that the comparison between feasible reduced form and model based forecasts is not always in favor of the latter in contrast to their infeasible versions the reduced form approach is generally better for long horizon forecasting and for short horizon forecasting in the presence of microstructure noise

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

the exact multi period mean square forecast error for the first order autoregressive model the finite sample behaviour of the multi period least squares forecast is considered in the simple normal autoregressive model yt yt 1 ut where 1 necessary and sufficient conditions are established for the existence of the forecast bias and the mean square forecast error msfe and an exact expression for the msfe is given exact numerical results are obtained for both the stationary and the fixed start up case our main conclusions are that for small values of the msfe is a decreasing function of the number of forecast periods and that the behaviour of the msfe in the stationary and the fixed start up case is very similar except for values of close to 1

the exact multi period mean square forecast error for the first order autoregressive model with an intercept abstract we study the exact finite sample behaviour of the mean square forecast error msfe of multi period least squares forecasts in the normal autoregressive model y t y t 1 u t we obtain necessary and sufficient conditions for the existence of the msfe and give an exact expression which we use to obtain numerical results for both the stationary and the fixed start up model we conclude inter alia that the behaviour of the msfe in the model with intercept can be very different from that in the model without intercept especially when is close to unity

data based ranking of realised volatility estimators abstract this paper presents new methods for comparing the accuracy of estimators of the quadratic variation of a price process i provide conditions under which the relative accuracy of competing estimators can be consistently estimated as t and show that forecast evaluation tests may be adapted to the problem of ranking these estimators the proposed methods avoid making specific assumptions about microstructure noise and facilitate comparisons of estimators that would be difficult using methods from the extant literature such as those based on different sampling schemes an application to high frequency ibm data between 1996 and 2007 illustrates the new methods

semiparametric estimation of a truncated regression model abstract this paper proposes a new semiparametric estimator for the truncated regression model under the independence restriction many existing approaches such as those in lee 1992 and honore and powell 1994 are moment based methods whereas our approach makes use of the entire truncated distribution as a result our approach is expected to require weaker identification and to have more favorable performance our simulation results suggest that our estimator outperforms that of lee 1992 and honore and powell 1994 in a variety of designs our estimator is shown to be consistent and asymptotically normal

a classification of biconservative hypersurfaces in a pseudo euclidean space abstract in this paper we study biconservative hypersurfaces of index 2 in e 2 5 we give the complete classification of biconservative hypersurfaces with diagonalizable shape operator with exactly three distinct principal curvatures we also give an explicit example of biconservative hypersurfaces with four distinct principal curvatures

residual analysis in the grouped and censored normal linear model graphical and numerical analysis of residual can be informative about model misspecification even when data are censored or grouped this paper provides simple procedures for calculating diagnostic statistics to detect model misspecification when grouped or censored data are analysed using a normal linear model graphs can reveal the nature of the correlations that these statistics pick up but when grouping or censoring is severe they can be difficult to interpret we discuss the processing of graphs so that they are more easily interpreted and provide examples based on artificial data and on grouped data relating to unemployment durations

adaptive estimation in time series regression models this work develops adaptive estimators for a linear regression model with serially correlated errors we show that these results continue to hold when the order of the arma process characterizing the errors is unknown the finite sample results are promising indicating that substantial efficiency gains may be possible for samples as small as 50 observations we use these estimators to investigate the behavior of the forward foreign exchange market

addendum to classification of marginally trapped lorentzian flat surfaces in e24 and its application to biharmonic surfaces abstract due to omission an additional family shall be added to the list of marginally trapped lorentzian flat surfaces in e 2 4 given in theorem 4 1 of b y chen classification of marginally trapped lorentzian flat surfaces in e 2 4 and its application to biharmonic surfaces j math anal appl 340 2008 861 875

on maximum likelihood estimation in infinite dimensional parameter spaces an approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions in this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter we provide conditions under which the rate of convergence can be established this rate is essentially governed by the size of the space of score functions as measured by an entropy index we also show that for a large class of smooth functionals the plug in maximum likelihood estimate is asymptotically efficient that is it achieves the minimal fisher information bound the theory is illustrated by several nonparametric or semiparametric examples

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

a nonparametric approach to the truncated regression problem abstract a description is given of a new method of estimating the regression parameters in the linear regression model from data where the dependent variable is subject to truncation the residual distribution is allowed to be unspecified the method is iterative and involves estimation of the residual distribution under the truncated sampling scheme the technique can be interpreted as an iterative bias adjustment of the observations in order to correct the regression relationship in the sampled population to match that of the model a simulation study compares the performance of various estimators including one suggested by bhattacharya chernoff and yang 1983 this truncation regression problem arises in many contexts of scientific and social research in economics tobin 1958 analyzed household expenditure on durable goods using a regression model that took account of the fact that the expenditure is always nonnegative a more general situation was studied by hausman and wise 1976 1977 in conn

profile likelihood and conditionally parametric models in this paper we outline a general approach to estimating the parametric component of a semiparametric model for the case of a scalar parametric component the method is based on the idea of first estimating a one dimensional subproblem of the original problem that is least favorable in the sense of stein the likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem the scalar parameter is then estimated by maximizing this generalized profile likelihood this method of estimation is applied to a particular class of semiparametric models where it is shown that the resulting estimator is asymptotically efficient

non parametric maximum likelihood estimation of censored regression models abstract this paper presents a consistent estimator of a censored linear regression model which does not require knowledge of the distribution of the error term the estimator considered here applies duncan s 1982 suggestion that the likelihood function for the censored regression model be treated as a functional of both the unknown regression vector and the unknown error distribution our estimator is the majorizing regression vector for this non parametric likelihood functional we find conditions which ensure the consistency of the npmle the paper concludes with the results of monte carlo experiments which show the npmle to be more efficient than powell s least absolute deviations lad estimator particularly when the fraction of censored observations is large and the sample size is small

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

semiparametrically efficient inference based on signed ranks in symmetric independent component models we consider semiparametric location scatter models for which the p variate observation is obtained as x lambda z mu where mu is a p vector lambda is a full rank p p matrix and the unobserved random p vector z has marginals that are centered and mutually independent but are otherwise unspecified as in blind source separation and independent component analysis ica the parameter of interest throughout the paper is lambda on the basis of n i i d copies of x we develop under a symmetry assumption on z signed rank one sample testing and estimation procedures for lambda we exploit the uniform local and asymptotic normality ulan of the model to define signed rank procedures that are semiparametrically efficient under correctly specified densities yet as usual in rank based inference the proposed procedures remain valid correct asymptotic size under the null for hypothesis testing and root n consistency for point estimation under a very broad range of densities we derive the asymptotic properties of the proposed procedures and investigate their finite sample behavior through simulations

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

a large sample study of generalized maximum likelihood estimators from incomplete data via self consistency self consistent estimators for estimating distribution functions from incomplete data are presented in many cases these estimators are also generalized maximum likelihood estimators in this paper we discuss the theoretical properties of such estimators existence uniform consistency law of the iterated logarithm and weak convergence applications to the product limit estimator for right censored data and to the estimator proposed by turnbull 1974 1976 for doubly right and left censored data are also given

asymptotic minimax estimation in semiparametric models we give several conditions on the estimator of efficient score function for estimating the parametric component of semiparametric models a semiparametric version of the one step mle using an estimator of efficient score function which fulfills the conditions is shown to converge to the normal distribution with minimum variance locally uniformly over a fairly large neighborhood around the assumed semiparametric model consequently it is shown to be asymptotically minimax with bounded subconvex loss functions a few examples are also considered

on methods of sieves and penalization we develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates mle s in parametric semiparametric and nonparametric models we find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices the degree of smoothness of the functional and the local size of the underlying parameter space we show that when the local size of the parameter space is not very large the substitution standard nonsieve substitution sieve and substitution penalized mle s are asymptotically efficient in the fisher sense under certain stochastic equicontinuity conditions of the loglikelihood moreover when the convergence rate of the estimate is slow the degree of smoothness of the functional needs to compensate for the slowness of the rate in order to achieve efficiency when the size of the parameter space is very large the standard and penalized maximum likelihood procedures may be inefficient whereas the method of sieves may be able to overcome this difficulty this phenomenon is particularly manifested when the functional of interest is very smooth especially in the semiparametric case

efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood abstract this paper presents efficient semiparametric estimators for endogenously stratified regression with two strata in the case where the error distribution is unknown and the regressors are independent of the error term the method is based on the use of a kernel smoothed likelihood function which provides an explicit solution for the maximization problem for the unknown density function without losing information in the asymptotic limit we consider both standard stratified sampling and variable probability sampling and allow for the population shares of the strata to be either unknown or known a priori

bayesian estimation and prediction using asymmetric loss functions abstract estimators and predictors that are optimal relative to varian s asymmetric linex loss function are derived for a number of well known models their risk functions and bayes risks are derived and compared with those of usual estimators and predictors it is shown that some usual estimators for example a scalar sample mean or a scalar least squares regression coefficient estimator are inadmissible relative to asymmetric linex loss by providing alternative estimators that dominate them uniformly in terms of risk

a consistent test for nonlinear out of sample predictive accuracy abstract in this paper we draw on both the consistent specification testing and the predictive ability testing literatures and propose an integrated conditional moment type predictive accuracy test that is similar in spirit to that developed by bierens j econometr 20 1982 105 econometrica 58 1990 1443 and bierens and ploberger econometrica 65 1997 1129 the test is consistent against generic nonlinear alternatives and is designed for comparing nested models one important feature of our approach is that the same loss function is used for in sample estimation and out of sample prediction in this way we rule out the possibility that the null model can outperform the nesting generic alternative model it turns out that the limiting distribution of the icm type test statistic that we propose is a functional of a gaussian process with a covariance kernel that reflects both the time series structure of the data as well as the contribution of parameter estimation error as a consequence critical values that are data dependent and cannot be directly tabulated one approach in this case is to obtain critical value upper bounds using the approach of bierens and ploberger econometrica 65 1997 1129 here we establish the validity of a conditional p value method for constructing critical values the method is similar in spirit to that proposed by hansen econometrica 64 1996 413 and inoue econometric theory 17 2001 156 although we additionally account for parameter estimation error in a series of monte carlo experiments the finite sample properties of three variants of the predictive accuracy test are examined our findings suggest that all three variants of the test have good finite sample properties when quadratic loss is specified even for samples as small as 600 observations however non quadratic loss functions such as linex loss require larger sample sizes of 1000 observations or more in order to ensure reasonable finite sample performance

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

efficient estimation in semiparametric garch models abstract it is well known that financial data sets exhibit conditional hereroskedasticity garch type models are often used to model this phenomenon since the distribution of the rescaled innovations is generally far from a normal distribution a semiparametric approach is advisable several publications observed that adaptive estimation of the euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter thus suggesting that adaptive estimation of the autoregression parameters is possible indeed we construct adaptive and hence efficient estimators in a general garch in mean type context including integrated garch models our analysis is based on a general lan theorem for time series models published elsewhere in contrast to recent literature about arch models we do not need moment condition

a missing information principle and m estimators in regression analysis with censored and truncated data a general missing information principle is proposed for constructing mestimators of regression parameters in the presence of left truncation and right censoring on the observed responses by making use of martingale central limit theorems and empirical process theory the asymptotic normality of m estimators is established under certain assumptions asymptotically efficient m estimators are also developed by using data dependent score functions in addition robustness properties of the estimators are discussed and formulas for their influence functions are derived for the robustness analysis

calculating posterior distributions and modal estimates in markov mixture models abstract this paper is concerned with finite mixture models in which the populations from one observation to the next are selected according to an unobserved markov process a new full bayesian approach based on the method of gibbs sampling is developed calculations are simplified by data augmentation achieved by introducing a population index variable into the list of unknown parameters it is shown that the latent variables one for each observation can be simulated from their joint distribution given the data and the remaining parameters this result serves to accelerate the convergence of the gibbs sample modal estimates are also computed by stochastic versions of the em algorithm these provide an alternative to a full bayesian approach and to existing methods of locating the maximum likelihood estimate the ideas are applied in detail to poisson data mixtures of multivariate normal distributions and autoregressive time series

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models