A loss function approach to model specification testing and its relative efficiency

The relationship between economic growth and environment. Testing the EKC hypothesis for Latin American countries

We employ an ARDL bounds testing approach to cointegration and Unrestricted Error Correction Models (UECMs) to estimate the relationship between income and CO2 emissions per capita in 21 Latin American Countries (LACs) over 1960-2017. Using time series we estimate six different specifications of the model to take into account the independent effect on CO2 emissions per capita of different factors considered as drivers of different dynamics of CO2 emissions along the development path. This approach allows to address two concerns. First, the estimation of the model controlling for different vari…

Data-driven rate-optimal specification testing in regression models

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/\sqrtn. Asymptotic critical values come from the standard normal distribution and the bootstrap can be used in small samples. A general formalization allows one to consider a large class of linear smoothing methods, which can be tailore…

Consistent specification testing under spatial dependence

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing dimension, semiparametric or any combination thereof, thus covering a vast variety of settings. These include spatial error models of varying types and levels of complexity. Under a new smooth spatial dependence condition, our test statistic is asymptotically standard normal. To prove the latter property, we establish a central limit theorem for quadratic forms i…

基于数据依赖划分的条件分布设定检验

Conditional Distribution Specification Testing Based on Data-Dependent Partitions

本文提出一种基于数据依赖划分的Pearson型检验，用于检验连续响应条件分布模型的参数设定，其在高维场景下的尺度控制与功效优于现有自助法检验。

关于基于暴露映射的干扰模型规范检验不可能性的研究

On the Impossibility of Specification Testing of Interference Models Based on Exposure Mappings

本文研究了基于暴露映射的干扰模型规范检验问题，证明了现有检验方法的低效力是不可避免的，并指出任何检验方法的最坏情况I型和II型错误率之和必须为一，因此不存在统一一致的检验方法。

Testing Endogeneity with High Dimensional Covariates

Modern, high dimensional data has renewed investigation on instrumental variables (IV) analysis, primarily focusing on estimation of effects of endogenous variables and putting little attention towards specification tests. This paper studies in high dimensions the Durbin-Wu-Hausman (DWH) test, a popular specification test for endogeneity in IV regression. We show, surprisingly, that the DWH test maintains its size in high dimensions, but at an expense of power. We propose a new test that remedies this issue and has better power than the DWH test. Simulation studies reveal that our test achieve…

Flexible Specification Testing in Quantile Regression Models

We propose three novel consistent specification tests for quantile regression models which generalize former tests in three ways. First, we allow the covariate effects to be quantile-dependent and nonlinear. Second, we allow parameterizing the conditional quantile functions by appropriate basis functions, rather than parametrically. We are hence able to test for functional forms beyond linearity, while retaining the linear effects as special cases. In both cases, the induced class of conditional distribution functions is tested with a Cramér-von Mises type test statistic for which we derive th…

Parameter estimation and model testing for Markov processes via conditional characteristic functions

Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for Lévy-driven processes. We propose an empirical likelihood approach, for both parameter estimation and model specification testing, based on the conditional characteristic function for processes with either continuous or discontinuous sample paths. Theoretical properties of the empirical likelihood estimator for parameters and a smoothed empirical likelihood ra…

A specification test for nonlinear nonstationary models

We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with endogenous regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self-intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This…

Testing for threshold effects in the TARMA framework

We present supremum Lagrange Multiplier tests to compare a linear ARMA specification against its threshold ARMA extension. We derive the asymptotic distribution of the test statistics both under the null hypothesis and contiguous local alternatives. Moreover, we prove the consistency of the tests. The Monte Carlo study shows that the tests enjoy good finite-sample properties, are robust against model mis-specification and their performance is not affected if the order of the model is unknown. The tests present a low computational burden and do not suffer from some of the drawbacks that affect …

Bayesian sequential composite hypothesis testing in discrete time

We study the sequential testing problem of two alternative hypotheses regarding an unknown parameter in an exponential family when observations are costly. In a Bayesian setting, the problem can be embedded in a Markovian framework. Using the conditional probability of one of the hypotheses as the underlying spatial variable, we show that the cost function is concave and that the posterior distribution becomes more concentrated as time goes on. Moreover, we study time monotonicity of the value function. For a large class of model specifications, the cost function is non-decreasing in time, and…