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The asymptotic bias and variance of a general class of local polynomial estimators of M-regression functions are studied over the whole compact support of the multivariate covariate under a minimal assumption on the support. The support assumption ensures that the vicinity of the boundary of the support will be visited by the multivariate covariate. The results show that like in the univariate case, multivariate local polynomial estimators have good bias and variance properties near the boundary. For the local polynomial regression estimator, we establish its asymptotic normality near the boundary and the usual optimal uniform convergence rate over the whole support. For local polynomial quantile regression, we establish a uniform linearization result which allows us to obtain similar results to the local polynomial regression. We demonstrate both theoretically and numerically that with our uniform results, the common practice of trimming local polynomial regression or quantile estimators to avoid “the boundary effect” is not needed.

Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We survey the available methods in the literature, discuss the challenges that present themselves when empirically implementing these methods, and extend an existing method to handle general nonlinear constraints. A heuristic discussion on the empirical implementation for methods that use sequential quadratic programming is provided for the reader, and simulated and empirical evidence on the distinction between constrained and unconstrained nonparametric regression surfaces is covered.

This paper examines Aman Ullah’s contributions to robust inference, finite sample econometrics, nonparametrics and semiparametrics, and panel and spatial models. His early works on robust inference and finite sample theory were mostly motivated by his thesis advisor, Professor Anirudh Lal Nagar. They eventually led to his most original rethinking of many statistics and econometrics models that developed into the monograph Finite Sample Econometrics published in 2004. His desire to relax distributional and functional-form assumptions lead him in the direction of nonparametric estimation and he summarized his views in his most influential textbook Nonparametric Econometrics (with Adrian Pagan) published in 1999 that has influenced a whole generation of econometricians. His innovative contributions in the areas of seemingly unrelated regressions, parametric, semiparametric and nonparametric panel data models, and spatial models have also inspired a larger literature on nonparametric and semiparametric estimation and inference and spurred on research in robust estimation and inference in these and related areas.

We propose a quasi–maximum likelihood estimator for the location parameters of a linear regression model with bounded and symmetrically distributed errors. The error outcomes are restated as the convex combination of the bounds, and we use the method of maximum entropy to derive the quasi–log likelihood function. Under the stated model assumptions, we show that the proposed estimator is unbiased, consistent, and asymptotically normal. We then conduct a series of Monte Carlo exercises designed to illustrate the sampling properties of the quasi–maximum likelihood estimator relative to the least squares estimator. Although the least squares estimator has smaller quadratic risk under normal and skewed error processes, the proposed QML estimator dominates least squares for the bounded and symmetric error distribution considered in this paper.

Local polynomial regression is extremely popular in applied settings. Recent developments in shape-constrained nonparametric regression allow practitioners to impose constraints on local polynomial estimators thereby ensuring that the resulting estimates are consistent with underlying theory. However, it turns out that local polynomial derivative estimates may fail to coincide with the analytic derivative of the local polynomial regression estimate which can be problematic, particularly in the context of shape-constrained estimation. In such cases, practitioners might prefer to instead use analytic derivatives along the lines of those proposed in the local constant setting by Rilstone and Ullah (1989). Demonstrations and applications are considered.

In this paper, we follow the same logic as in Hausman (1978) to create a testing procedure that checks for the presence of outliers by comparing a regression estimator that is robust to outliers (S-estimator), with another that is more efficient but affected by them. Some simulations are presented to illustrate the good behavior of the test for both its size and its power.

It is known that model averaging estimators are useful when there is uncertainty governing which covariates should enter the model. We argue that in applied research there is also uncertainty as to which method one should deploy, prompting model averaging over user-defined choices. Specifically, we propose, and detail, a nonparametric regression estimator averaged over choice of kernel, bandwidth selection mechanism and local-polynomial order. Simulations and an empirical application are provided to highlight the potential benefits of the method.

A common approach to dealing with missing data is to estimate the model on the common subset of data, by necessity throwing away potentially useful data. We derive a new probit type estimator for models with missing covariate data where the dependent variable is binary. For the benchmark case of conditional multinormality we show that our estimator is efficient and provide exact formulae for its asymptotic variance. Simulation results show that our estimator outperforms popular alternatives and is robust to departures from the parametric assumptions adopted in the benchmark case. We illustrate our estimator by examining the portfolio allocation decision of Italian households.

Public management researchers commonly model dichotomous dependent variables with parametric methods despite their relatively strong assumptions about the data generating process. Without testing for those assumptions and consideration of semiparametric alternatives, such as maximum score, estimates might be biased, or predictions might not be as accurate as possible.

To guide researchers, this paper provides an evaluative framework for comparing parametric estimators with semiparametric and nonparametric estimators for dichotomous dependent variables. To illustrate the framework, the article estimates the factors associated with the passage of school district bond referenda in all Texas school districts from 1998 to 2015.

Estimates show that the correct prediction of a bond passing increases from 77.2 to 78%, with maximum score estimation relative to a commonly used parametric alternative. While this is a small increase, it is meaningful in comparison to the random prediction base model.

Future research modeling any dichotomous dependent variable can use the framework to identify the most appropriate estimator and relevant statistical programs.