this paper. We introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics. New Wilks phenomenon is unveiled. We demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow

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The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an approximation to the distribution of an estimator or test statistic that is at least as accurate as the

. 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...

This paper reviews the literature on tests for the correct specification of the functional form of parametric conditional expectation and conditional distribution models. In particular I will discuss various versions of the Integrated Conditional Moment (ICM) test and the ideas behind them. 1

Previous papers estimate base-independent equivalence scales and test base-independence using strict parametric assumptions on Engel curves and equivalence scale functions. These parametric tests reject the hypothesis of base independence. I construct a semiparametric estimator of a household equivalence scale under the assumption of base independence without putting any further restrictions on the shape of household Engel curves. This estimator uses cross-equation restrictions on a system of estimated nonparametric engel curves to identify equivalence scale parameters. I test the hypothesis of base independence against a fully nonparametric alternative and find that preferences are consistent with the existence of a base-independent equivalence scale for some

this paper we examine its potential in linearity testing. For example it is convenient to look at derivatives of nonparametric estimates in this framework, and one can construct new tests of linearity exploiting that the first order derivative is a constant, and the second order derivative is zero for a linear model. It is also easier to look at the transition between parametric and nonparametric modeling. This transition is intimately connected to the choice of bandwidth. Choosing the bandwidth is a very important aspect of nonparametric linearity testing, but it was virtually neglected in Hjellvik and Tjøstheim (1995,1996). In the present paper it is studied in some detail and both data driven and theoretically determined bandwidths are investigated. In contrast to Hjellvik and Tjøstheim (1995,1996) we present a fair amount of asymptotic theory. One reason for this is that the asymptotic theory yields useful input to the problem of choosing the bandwidth. Also the asymptotic theory is of interest in itself, and in Appendix 1 we extend some results on degenerate U-statistics, which has hitherto only been proved for iid

Kernel smoothing in nonparametric autoregressive schemes offers a powerful tool in modelling time series. In this paper it is shown that the bootstrap can be used for estimating the distribution of kernel smoothers. This can be done by mimicking the stochastic nature of the whole process in the bootstrap resampling or by generating a simple regression model. Consistency of these bootstrap procedures will be shown. 1 Introduction Nonlinear modelling of time series has appeared as a promising approach in applied time series analysis. A lot of parametric models can be found in the books of Priestley (1988) and Tong (1990). In this paper we consider nonparametric models of nonlinear autoregression. Motivated by econometric applications, we allow for heteroschedastic errors: X t = m(X t\Gamma1 ; : : : ; X t\Gammap ) + oe(X t\Gamma1 ; : : : ; X t\Gammaq ) " t ; t = 0; 1; 2; : : : : (1.1) Here (" t ) are i.i.d. random variables with mean 0 and variance 1. Furthermore, m and oe are unknown ...

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.

Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric ts is negligible by using the adaptive Neyman test and other methods. The testing procedures formalize the traditional model diagnostic tools based on residual plots. We examine the rates of contiguous alternatives that can be detected consistently by the adaptive Neyman test. Applications of the procedures to the partially linear models are thoroughly discussed. Our simulation studies show that the new testing procedures are indeed powerful and omnibus. The power of the proposed tests is comparable to the F-test statistic even in the situations where F -test is known to be suitable and can be far more powerful than the F-test statistic in other situations. An application to testing linear models versus additive models are discussed.