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A new class of specification tests for stochastic differential equations (SDE) is proposed to determine whether the probability integral transform of the estimated model generates an independent and identically distributed uniform random variable. The tests are based on Neyman's smooth test, appropriately adjusted to correct for both the size distortion arising from having to estimate the unknown parameters of the SDE and possible dependence in the uniform random variable. The suite of tests is compared against other commonly used specification tests for SDEs. The finite sample properties of the tests are investigated using a range of Monte Carlo experiments. The tests are then applied to testing the specification of SDEs used to model the spot interest rate and financial asset volatility. [ABSTRACT FROM AUTHOR]

Abstract: The Pareto distribution is found in a large number of real world situations and is also a well-known model for extreme events. In the spirit of Neyman [1937. Smooth tests for goodness of fit. Skand. Aktuarietidskr. 20, 149–199] and Thomas and Pierce [1979. Neyman''s smooth goodness-of-fit test when the hypothesis is composite. J. Amer. Statist. Assoc. 74, 441–445], we propose a smooth goodness of fit test for the Pareto distribution family which is motivated by LeCam''s theory of local asymptotic normality (LAN). We establish the behavior of the associated test statistic firstly under the null hypothesis that the sample follows a Pareto distribution and secondly under local alternatives using the LAN framework. Finally, simulations are provided in order to study the finite sample behavior of the test statistic. [Copyright &y& Elsevier]

An easy-to-implement global procedure for testing the four assumptions of the linear model is proposed. The test can be viewed as a Neyman smooth test and relies only on the standardized residual vector. If the global procedure indicates a violation of at least one of the assumptions, then the components of the global test statistic can be used to gain insight into which assumptions have been violated. The procedure can also be used in conjunction with associated deletion statistics to detect unusual observations. Simulation results are presented indicating the sensitivity of the procedure in detecting model violations under a variety of situations, and its performance is compared with three potential competitors, including a procedure based on the Box-Cox power transformation. The procedure is demonstrated by applying it to a new car mileage dataset and a water salinity dataset that has been used earlier to illustrate model diagnostics. [ABSTRACT FROM AUTHOR]

In this article we construct three smooth goodness-of-fit tests for testing for the zero-inflated Poisson (ZIP) distribution against general smooth alternatives in the sense of Neyman. We apply our tests to a data set previously claimed to be ZIP distributed, and show that the ZIP is not a good model to describe the data. At rejection of the null hypothesis of ZIP, the individual components of the test statistic, which are directly related to interpretable parameters in a smooth model, may be used to gain insight into an alternative distribution. [ABSTRACT FROM AUTHOR]