. 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 Banach-valued 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...

Dedicated to Professor L. L. Campbell, in celebration of his longstanding career in mathematics and statistics and in tribute to his many scholarly contributions to information theory. An overview is given of the several methods in use for the nonparametric estimation of the differential entropy of a continuous random variable. The properties of various methods are compared. Several applications are given such as tests for goodness-of-fit, parameter estimation, quantization theory and spectral estimation. I

Entropy is a classical statistical concept with appealing properties. Establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time series context. We use this theory to derive the limiting distribution of Granger and Lins (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy-based test for serial dependence, providing an alternative to Robinsons (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is asymptotically locally more powerful than Robinsons (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach.

Abstract not found

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

. This paper presents a framework for individual and joint tests of significance employing nonparametric estimation procedures. The proposed test is based on nonparametric estimates of partial derivatives, is robust to functional mis-specification for general classes of models, and employs nested pivotal bootstrapping procedures. Two simulations and one application are considered to examine size, power relative to mis-specified parametric models, and to test for the linear unpredictability of exchange rate movements for G7 currencies. Keywords. Kernel density estimation, inference, pivotal, nested bootstrap. 1. INTRODUCTION The inability to test hypotheses in a nonparametric framework has remained a source of frustration for many applied researchers and econometricians. The motivation for using nonparametric methods for both estimation and hypothesis testing comes from the fact that employing a mis-specified parametric model for the conditional mean and/or the data generating proces...

. This paper develops nonparametric tests of independence between two stationary stochastic processes. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, I take advantage of a generalized entropic measure so as to build a class of nonparametric tests of independence. Asymptotic normality and local power are derived using the functional delta method for kernels, whereas nite sample properties are investigated through Monte Carlo simulations. JEL classication numbers. C12, C14. Keywords. independence, nonparametric testing, Tsallis entropy. 3 1 Introduction Independence is one of the most valuable concepts in econometrics as virtually all tests boil down to checking some sort of independence assumption. Accordingly, there is an extensive literature on how to test independence, e.g. Hoeding (1948), Baek and Brock (1992), Johnson and McClelland (1998), and Pinkse (1999). Tjstheim (1996)...

Conditional density functions are a useful way to display uncertainty. This paper investigates nonparametric kernel methods for their estimation. The standard estimator is the ratio of the joint density estimate to the marginal density estimate. Our proposal is to instead use a two-step estimator, where the first step consists of estimation of the conditional mean, and the second step consists of estimating

this article, we extend the idea of cross-validation (CV) for choosing the smoothing parameter of the "double-kernel" local linear regression for estimating a conditional density. Our selection rule optimizes the estimated conditional density function by minimizing the integrated square error (ISE). We also discuss three other bandwidth selection rules. The first is an ad-hoc method used by Fan, Yao and Tong (FYT, 1996). The second rule, as suggested by Hall, Wol# and Yao (HWY, 1999), employs the idea of bootstrap for the bandwidth selection in the estimation of conditional distribution functions. We modify the HWY approach to suit the bandwidth selection for the conditional density function. The last is the rule of thumb approach proposed by Hyndman and Yao (2002). The performance of the newly proposed CV approach is compared with these three methods by simulation studies, and our method performs outstandingly. The method is also illustrated by application to two sets of time series

The m-testing approach provides a general and convenient framework in which to view and construct specification tests for econometric models. Previous m-testing frameworks only consider test statistics that involve finite dimensional parameter estimators and infinite dimensional parameter estimators affecting the limit distribution of the m-test statistics. In this paper we propose a new m-testing framework using both finite and infinite dimensional parameter estimators, where the latter may or may not affect the limit distribution of the m-test. This greatly extends the potential and flexibility of m-testing. The new m-testing framework can be used to test hypotheses on parametric, semiparametric and nonparametric models. Some examples are given to illustrate how to use it to develop new specification tests.