A Note on Specification Testing in Some Structural Regression Models

In the context of testing the specification of a nonlinear parametric regression function, we adopt a nonparametric minimax approach to determine the maximum rate at which a set of smooth alternatives can approach the null hypothesis while ensuring that a test can uniformly detect any alternative in this set with some predetermined power. We show that a smooth nonparametric test has optimal asymptotic minimax properties for regular alternatives. As a by-product, we obtain the rate of the smoothing parameter that ensures rate-optimality of the test. We show that, in contrast, a class of nonsmooth tests, which includes the integrated conditional moment test of Bierens (1982, Journal of Econometrics 20, 105–134), has suboptimal asymptotic minimax properties.

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SPECIFICATION TESTING WHEN THE NULL IS NONPARAMETRIC OR SEMIPARAMETRIC

Econometric Theory ◽

10.1017/s0266466614000504 ◽

2014 ◽

Vol 31 (6) ◽

pp. 1281-1309 ◽

Cited By ~ 2

Author(s):

Juan M. Rodríguez-Póo ◽

Stefan Sperlich ◽

Philippe Vieu

Keyword(s):

Null Hypothesis ◽

Regression Models ◽

Semiparametric Regression ◽

Large Family ◽

Econometric Models ◽

Gravity Models ◽

Finite Sample ◽

Specification Testing ◽

Omnibus Test ◽

Limited Dependent Variable

This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions. We focus on two main issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood or pseudo-ML methods like, for example, limited dependent variable or gravity models. Second, often one might not want to fully specify the null hypothesis. Instead, one would rather impose some structure like separability or monotonicity. In order to address these points we introduce an adaptive omnibus test. Special emphasis is given to practical issues like adaptive bandwidth choice, general but simple requirements on the estimates, and finite sample performance, including the resampling approximations.

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Prediction Model of Academic Performance and Satisfaction With School According to Some Subjects of Compulsory Secondary Education

Psychological Reports ◽

10.1177/0033294118805004 ◽

2018 ◽

Vol 123 (2) ◽

pp. 435-451 ◽

Cited By ~ 3

Author(s):

Raúl Baños ◽

Antonio Baena-Extremera ◽

María del Mar Ortiz-Camacho

Keyword(s):

Academic Performance ◽

Secondary Education ◽

Physical Education ◽

Prediction Model ◽

Regression Models ◽

Structural Model ◽

School Satisfaction ◽

Structural Regression ◽

The Subject ◽

Academic Grades

The purpose of the study was to know which subjects in the curriculum best predict school satisfaction and boredom as well as the student’s academic grade. The sample was of 680 adolescents of physical education (339 males, 341 females) with age between 12 and 18 years (M = 14.83; SD = 1.45). We used a questionnaire composed of the satisfaction scales with the subjects, intrinsic satisfaction in the school and related to academic grades. Descriptive analyses, correlations, and structural regression models were performed. The high levels of satisfaction and academic performance in physical education stand out. In the structural model, English is the subject that most predicts academic grades, while language predicts satisfaction at school and physical education boredom at it.

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Specification testing in semi-parametric transformation models

Test ◽

10.1007/s11749-021-00756-0 ◽

2021 ◽

Author(s):

Nick Kloodt ◽

Natalie Neumeyer ◽

Ingrid Van Keilegom

Keyword(s):

Regression Models ◽

Goodness Of Fit ◽

Asymptotic Theory ◽

Regression Function ◽

Parametric Model ◽

Specification Testing ◽

Nonparametric Transformation ◽

Bootstrap Algorithm ◽

Parametric Transformation ◽

Parametric Class

AbstractIn transformation regression models, the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression function is modeled nonparametrically. We suggest a test for goodness-of-fit of a parametric transformation class based on a distance between a nonparametric transformation estimator and the parametric class. We present asymptotic theory under the null hypothesis of validity of the semi-parametric model and under local alternatives. A bootstrap algorithm is suggested in order to apply the test. We also consider relevant hypotheses to distinguish between large and small distances of the parametric transformation class to the ‘true’ transformation.

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