Specification Testing When the Null is Nonparametric or Semiparametric (original) (raw)

An Adaptive Specification Test For Semiparametric Models

SSRN Electronic Journal, 2007

This paper introduces a new test of a semiparametric model of a conditional density function against a fully nonparametric alternative. This test is motivated by the fact that many important econometric models need to be estimated through maximum likelihood type procedures, e.g. semiparametric limited dependent variable models. This specification is also important for prediction purposes. Our test statistic combines the methodology of goodness of fit tests and nonparametric methods and the specific difficulty we focus here comes from the fact that we consider a semiparametric null hypothesis and the test statistic depends on a bandwidth parameter that needs to be estimated from the data. In order to handle the previous difficulties we introduce a data adaptive testing procedure that enables us to select the bandwidth parameter in such a way that it maximizes the power of the test. It is also shown that this procedure handles properly the bias problem generated by the introduction of a semiparametric model under the null. The distribution of the standarized test statistic is approximated under the null by both bootstrap and subsampling methods and its power is studied against local alternatives to the null hypothesis. We discuss practical issues for the application statistics and illustrate in an intensive monte carlo study both the feasibility and the performance of the procedure in finite samples of moderate size. 1

Estimation and model specification testing in nonparametric and semiparametric econometric models

Mpra Paper, 2003

This paper considers two classes of semiparametric nonlinear regression models, in which nonlinear components are introduced to reflect the nonlinear fluctuation in the mean. A general estimation and testing procedure for nonparametric time series regression under the α-mixing condition is introduced. Several test statistics for testing nonparametric significance, linearity and additivity in nonparametric and semiparametric time series econometric models are then constructed. The proposed test statistics are shown to have asymptotic normal distributions under their respective null hypotheses. Moreover, the proposed testing procedures are illustrated by several simulated examples. In addition, one of the proposed testing procedures is applied to a continuoustime model and implemented through a set of the US Federal interest rate data. Our research suggests that it is unreasonable to assume the linearity in the drift for the given data as required by some existing studies.

Semiparametric Specification Testing of Non-nested Econometric Models

The Review of Economic Studies, 1994

We consider the non-nested testing prqblem of non-parametric regressions. We show that, when the regression functions are unknown under both the null and the alternative hypotheses, an extension of the J-test procedure of Davidson and Mackinnon (1981) will lead to a test statistic with well defined asymptotic properties. The derivation of the test statistic involves double kernel estimation. Monte Carlo simulations suggest that the test has good size and power characteristics.

Consistent specification tests for semiparametric/nonparametric models based on series estimation methods

Journal of Econometrics, 2003

This paper considers the problem of consistent model specification tests using series estimation methods. The null models we consider in this paper all contain some nonparametric components. A leading case we consider is to test for an additive partially linear model. The null distribution of the test statistic is derived using a central limit theorem for Hilbert valued random arrays. The test statistic is shown to be able to detect local alternatives that approach the null models at the order of O p (n −1/2). We suggest to use the wild bootstrap method to approximate the critical values of the test. A small Monte Carlo simulation is reported to examine the finite sample performance of the proposed test. We also show that the proposed test can be easily modified to obtain series-based consistent tests for other semiparametric/nonparametric models.

A Note on the Bandwidth Choice When the Null Hypothesis is Semiparametric

Revista de Economía del Rosario, 2005

This work presents a tool for the additivity test. The additive model is widely used for parametric and semiparametric modeling of economic data. The additivity hypothesis is of interest because it is easy to interpret and produces reasonably fast convergence rates for non-parametric estimators. Another advantage of additive models is that they allow attacking the problem of the curse of dimensionality that arises in non- parametric estimation. Hypothesis testing is based in the well-known bootstrap residual process. In nonparametric testing literature, the dominant idea is that bandwidth utilized to produce bootstrap sample should be bigger that bandwidth for estimating model under null hypothesis. However, there is no hint so far about how to choose such bandwidth in practice. We will discuss a first step to find some rule of thumb to choose bandwidth in that context. Our suggestions are accompanied by simulation studies.

Bias Corrections in Testing and Estimating Semiparametric, Single Index Models

Econometric Theory, 2010

Semiparametric methods are widely employed in applied work where the ability to conduct inferences is important. To establish asymptotic normality for making inferences, bias control mechanisms are often used in implementing semiparametric estimators. The first contribution of this paper is to propose a mechanism that enables us to establish asymptotic normality with regular kernels. In so doing, we argue that the resulting estimator performs very well in finite samples.Semiparametric models are commonly estimated under a single index assumption. Because the consistency of the estimator critically depends on this assumption being correct, our second objective is to develop a test for it. To ensure that the test statistic has good size and power properties in finite samples, we employ a bias control mechanism similar to that underlying the estimator. Furthermore, we structure the test so that its form adapts to the model under the alternative hypothesis. Monte Carlo results confirm t...

Non-Parametric Specification Testing of Non-Nested Econometric Models

Finite Sample and Asymptotic Analysis, 2007

We consider the non-nested testing prqblem of non-parametric regressions. We show that, when the regression functions are unknown under both the null and the alternative hypotheses, an extension of the J-test procedure of Davidson and Mackinnon (1981) will lead to a test statistic with well defined asymptotic properties. The derivation of the test statistic involves double kernel estimation. Monte Carlo simulations suggest that the test has good size and power characteristics.

Testing the Specification of Econometric Models in Regression and Non-Regression Directions

1986

The asymptotic power of a statistical test depends on the model being tested, the (implicit) alternative against which the test is constructed, and the process which actually generated the data. The exact way in which it does so is examined for several classes of models and tests. First, we analyze the power of tests of nonlinear regression models in regression directions, that is, tests which are equivalent to tests for omitted variables. Next, we consider the power of heteroskedasticity-robust variants of these tests. Finally, we examine the power of very general tests in the context of a very general class of models.

Econometric Theory MS #2412 General Specification Testing with Locally Misspecified Models

2017

A well known result is that many of the tests used in econometrics such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to GMM based tests. We also extend the method proposed in Bera and Yoon (Econometric Theory 9, 1993) for constructing RS tests that are robust to local misspecification to GMM based tests. Finally, a further generalization for general estimating and testing functions is developed. This framework encompasses both the Bera-Yoon likelihood based results as well as its use in the GMM environment. JEL classification: C12; C52