Nonparametric frontier estimation from noisy data

A new nonparametric estimator of production frontiers is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.production frontier, deconvolution, measurement error, efficiency analysis

Nonparametric Frontier Estimation from Noisy Data

A new nonparametric estimator of production a frontier is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.

Bayesian Semiparametric Multivariate Density Deconvolution

We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations being contaminated with additive measurement errors. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density is not known but replicated proxies are available for each unobserved value of the random vector. Additionally, we allow the variability of the measurement errors to depend on the associated unobserved value of the vector of interest through unknown relationships which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in many novel ways to meet the modeling and computational challenges. Theoretical results that show the flexibility of the proposed methods are provided. We illustrate the efficiency of the proposed methods in recovering the true density of interest through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls

Covariate Measurement Error in Endogenous Stratified Samples

In this paper we propose a general framework to deal with the presence of covariate mea-surement error in endogenous stratifield samples. Using Chesher’s (2000) methodology, we develop approximately consistent estimators for the parameters of the structural model, in the sense that their inconsistency is of smaller order than that of the conventional estimators which ignore the existence of covariate measurement error. The approximate bias corrected estimators are obtained by applying the generalized method of moments (GMM) to a modifeld version of the moment indicators suggested by Imbens and Lancaster (1996) for endogenous stratified samples. Only the specification of the conditional distribution of the response vari-able given the latent covariates and the classical additive measurement error model assumption are required, the availability of information on both the marginal probability of the strata in the population and the variance of the measurement error not being essential. A score test to detect the presence of covariate measurement error arises as a by-product of this approach. Monte Carlo evidence is presented which suggests that, in endogenous stratified samples of moderate sizes, the modified GMM estimators perform well

Characterization of AGN and their hosts in the Extended Groth Strip: a multiwavelength analysis

We have employed a reliable technique of classification of Active Galactic Nuclei (AGN) based on the fit of well-sampled spectral energy distributions (SEDs) with a complete set of AGN and starburst galaxy templates. We have compiled ultraviolet, optical, and infrared data for a sample of 116 AGN originally selected for their X-ray and mid-infrared emissions (96 with single detections and 20 with double optical counterparts). This is the most complete compilation of multiwavelength data for such a big sample of AGN in the Extended Groth Strip (EGS). Through these SEDs, we are able to obtain highly reliable photometric redshifts and to distinguish between pure and host-dominated AGN. For the objects with unique detection we find that they can be separated into five main groups, namely: Starburst-dominated AGN (24 % of the sample), Starburst-contaminated AGN (7 %), Type-1 AGN (21 %), Type-2 AGN (24 %), and Normal galaxy hosting AGN (24 %). We find these groups concentrated at different redshifts: Type-2 AGN and Normal galaxy hosting AGN are concentrated at low redshifts, whereas Starburst-dominated AGN and Type-1 AGN show a larger span. Correlations between hard/soft X-ray and ultraviolet, optical and infrared luminosities, respectively, are reported for the first time for such a sample of AGN spanning a wide range of redshifts. For the 20 objects with double detection the percentage of Starburst-dominated AGN increases up to 48%.Comment: 38 pages, 8 figures, 5 tables. Accepted by A