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Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative
, 1995
"... . The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly ex ..."
Abstract

Cited by 57 (10 self)
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. The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bears closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banachvalued random elements and applying the Banach Central Limit Theorem and Law of Iterated Logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted. 1. Introduction In testing whether or not a parametric statistical model is correctly specified, there are a number of apparently distinct approaches one might take. T...
Consistent Model Specification Tests Against Smooth Transition Alternatives ∗
, 2005
"... In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition " models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberg ..."
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In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition " models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberger (1997), provides maximal power against nonlinear smooth transition ARX specifications, and is consistent against any deviation from the null hypothesis. Of separate interest, we provide substantial detail regarding when and whether Bierenstype tests are asymptotically degenerate. In a simulation experiment in which all parameters are randomly selected, and a linear AR null model is selected by minimizing the AIC, the proposed test has power nearly identical to a most powerful test for true STAR processes, and dominates popular tests. 1. Introduction Smooth Transition Threshold Autoregressive (STAR)
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"... 270 T.H. Lee et al.. Neural netll.ork test.for neglected nonlinearit}. economic series or group of series appears to be generated by a linear model against the alternative that they are nonlinearly related. There are many tests presently available to do this. This paper considers a 'neural net ..."
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270 T.H. Lee et al.. Neural netll.ork test.for neglected nonlinearit}. economic series or group of series appears to be generated by a linear model against the alternative that they are nonlinearly related. There are many tests presently available to do this. This paper considers a 'neural network ' test recently proposed by White (1989b), and compares its performance with several alternative tests using a Monte Carlo study. It is important to be precise about the meaning of the word 'linearity'. Throughout, we focus on a property best described as 'linearity in conditional mean'. Let { Zt} be a stochastic process, and partition Zt as Zt = (Yt, X;)', where (for simplicity) Yt is a scalar and X t is a k x 1 vector. X t may (but need not necessarily) contain a constant and lagged values of Yt.The process {Yt} is linear in mean conditional on X t if P[E(ytIXt} = X;()*] = 1 for some () * E ~k Thll~, ~ process exhibiting autoregressive conditional heteroskedasticity (ARCH) [Engle (1982)] may nevertheless exhibit linearity of this sort because ARCH does not refer to the conditional mean. Our focus is appropriate whenever we are concerned with the adequacy of linear models for forecasting. The alternative of interest is that Yt is not linear in mean conditional on X t, so that P[E(ytIXt} x;eJ < 1 for all
Testing for Multivariate Volatility Functions Using Minimum Volume Sets and Inverse Regression
"... We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilit ..."
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We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii) of a bathtub shape, and (iii) of a given parametric form. The inference based on those tests may be further enhanced through associated diagnostic plots. Although the potential use of those ideas is much wider, we focus on the inference for multivariate volatility functions in this paper, i.e. we test for (i) heteroscedasticity, (ii) the socalled “smiling effect”, and (iii) some parametric volatility models. The asymptotic behavior of the proposed tests is investigated, and practical feasibility is shown via simulation studies. We further illustrate our methods with real financial data.