Nonadditive Error Research Articles

The ensemble conditional variance estimator for sufficient dimension reduction

Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models and operates under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. It is a semiparametric forward regression model-based exhaustive sufficient dimension reduction estimation method that is shown to be consistent under mild assumptions. ECVE outperforms central subspace mean average variance estimation (csMAVE), its main competitor, under several simulation settings and in a benchmark data set analysis.

A Bayesian Chi‐Squared Goodness‐of‐Fit Test for Censored Data Models

We propose a Bayesian chi-squared model diagnostic for analysis of data subject to censoring. The test statistic has the form of Pearson's chi-squared test statistic and is easy to calculate from standard output of Markov chain Monte Carlo algorithms. The key innovation of this diagnostic is that it is based only on observed failure times. Because it does not rely on the imputation of failure times for observations that have been censored, we show that under heavy censoring it can have higher power for detecting model departures than a comparable test based on the complete data. In a simulation study, we show that tests based on this diagnostic exhibit comparable power and better nominal Type I error rates than a commonly used alternative test proposed by Akritas (1988, Journal of the American Statistical Association 83, 222-230). An important advantage of the proposed diagnostic is that it can be applied to a broad class of censored data models, including generalized linear models and other models with nonidentically distributed and nonadditive error structures. We illustrate the proposed model diagnostic for testing the adequacy of two parametric survival models for Space Shuttle main engine failures.

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

This paper investigates identification and inference in a nonparametric structural model with instrumental variables and non-additive errors. We allow for non-additive errors because the unobserved heterogeneity in marginal returns that often motivates concerns about endogeneity of choices requires objective functions that are non-additive in observed and unobserved components. We formulate several independence and monotonicity conditions that are sufficient for identification of a number of objects of interest, including the average conditional response, the average structural function, as well as the full structural response function. For inference we propose a two-step series estimator. The first step consists of estimating the conditional distribution of the endogenous regressor given the instrument. In the second step the estimated conditional distribution function is used as a regressor in a nonlinear control function approach. We establish rates of convergence, asymptotic normality, and give a consistent asymptotic variance estimator.

A Robust GM-Estimator for the Automated Detection of External Defects on Barked Hardwood Logs and Stems

The ability to detect defects on hardwood trees and logs holds great promise for the hardwood forest products industry. At every stage of wood processing, there is a potential for improving value and recovery with knowledge of the location, size, shape, and type of log defects. This paper deals with a new method that processes hardwood laser-scanned surface data for defect detection. The detection method is based on robust circle fitting applied to scanned cross-section data sets recorded along the log length. It can be observed that these data sets have missing data and include large outliers induced by loose bark that dangles from the log trunk. Because of that and because of the nonlinearity of the circle model, which presents both additive and nonadditive errors, we initiated a new robust generalized M-estimator, for which the residuals are standardized via scale estimates calculated by means of projection statistics and incorporated in the Huber objective function, yielding a bounded influence method. Our projection statistics are based on the 2-D radial vectors instead of the row vectors of the Jacobian matrix as advocated in the literature dealing with linear regression. These radial distances allow us to develop algorithms aimed at pinpointing large surface rises and depressions from the contour image levels, and thereby, locating severe external defects having at least a height of 0.5 in and a diameter of 5 in.

College Education and Wages in the U.K.: Estimating Conditional Average Structural Functions in Nonadditive Models with Binary Endogenous Variables

We propose and implement an estimator for identifiable features of correlated random coefficient models with binary endogenous variables and nonadditive errors in the outcome equation. It is suitable, e.g., for estimation of the average returns to college education when they are heterogeneous across individuals and correlated with the schooling choice. The estimated features are of central interest to economists and are directly linked to the marginal and average treatment effect in policy evaluation. The advantage of the approach that is taken in this paper is that it allows for non-trivial selection patterns. Identification relies on assumptions weaker than typical functional form and exclusion restrictions used in the context of classical instrumental variables analysis. In the empirical application, we relate wage levels, wage gains from a college degree and selection into college to unobserved ability. Our results yield a deepened understanding of individual heterogeneity which is relevant for the design of educational policy.

Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.

An IV Model of Quantile Treatment Effects

The ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications. However, in observational studies, the variables of interest (e.g., education, prices) are often endogenous, making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes. In order to address this problem, we develop a model of quantile treatment effects (QTE) in the presence of endogeneity and obtain conditions for identification of the QTE without functional form assumptions. The principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states. This feature allows us to overcome the endogeneity problem and recover the true QTE through the use of instrumental variables. The proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors, where QTE can be interpreted as the structural quantile effects (SQE).

Verifying irreducibility and continuity of a nonlinear time series

When considering the stability of a nonlinear time series, verifying aperiodicity, irreducibility and smoothness of the transitions for the corresponding Markov chain is often the first step. Here, we provide reasonably general conditions applicable to nonlinear autoregressive time series, including many with nonadditive errors.

The application of transformations to non-linear models

Abstract A transmuted model is introduced which allows non-additive error terms and is shown to be an extension of the Box-Cox transformation to intrinsically non-linear equations. Post-transformed models are used to analyze the underlying disturbance term structure with an empirical example presented to illustrate the increased flexibility provided by the transmuted model.