The power of the optimal asymptotic tests of composite statistical hypotheses.
Reads0
Chats0
TLDR
The present paper gives the upper and the lower bounds for beta(xi,n).Abstract:
The easily computable asymptotic power of the locally asymptotically optimal test of a composite hypothesis, known as the optimal C(α) test, is obtained through a “double” passage to the limit: the number n of observations is indefinitely increased while the conventional measure ξ of the error in the hypothesis tested tends to zero so that ξnn½ → τ ≠ 0. Contrary to this, practical problems require information on power, say β(ξ,n), for a fixed ξ and for a fixed n. The present paper gives the upper and the lower bounds for β(ξ,n). These bounds can be used to estimate the rate of convergence of β(ξ,n) to unity as n → ∞. The results obtained can be extended to test criteria other than those labeled C(α). The study revealed a difference between situations in which the C(α) test criterion is used to test a simple or a composite hypothesis. This difference affects the rate of convergence of the actual probability of type I error to the preassigned level α. In the case of a simple hypothesis, the rate is of the order of n-½. In the case of a composite hypothesis, the best that it was possible to show is that the rate of convergence cannot be slower than that of the order of n-½ ln n.read more
Citations
More filters
ReportDOI
Locally robust semiparametric estimation
Victor Chernozhukov,Juan Carlos Escanciano,Hidehiko Ichimura,Whitney K. Newey,James M. Robins +4 more
TL;DR: In this article, a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to first steps, is given and debiased machine learning estimators of functionals of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables.
Posted Content
Bootstrap Testing in Nonlinear Models
TL;DR: In this article, the authors show that it is possible to reduce computational costs by performing only a fixed, small number of Newton steps or artificial regressions for each bootstrap sample.
Journal ArticleDOI
GEL Criteria for Moment Condition Models
TL;DR: In this article, a smoothed version of the moment indicators using kernel function weights that incorporate a bandwidth parameter has been proposed, and a unified set of test statistics for overidentifying moment restrictions and combinations of parametric and moment restriction hypotheses is presented.
ReportDOI
Testing for homogeneity in mixture models
TL;DR: In this paper, a new approach to likelihood ratio testing for general mixture models is proposed, based on estimation of general nonparametric mixing distribution with the Kiefer and Wolfowitz (1956) maximum likelihood estimator.
Journal ArticleDOI
Testing correct model specification using extreme learning machines
Jin Seo Cho,Halbert White +1 more
TL;DR: The Wald ELM (WELM) test statistic proposed here is easy to compute and has a large-sample standard chi-squared distribution under the null hypothesis of correct specification of artificial neural network models of the conditional mean.
References
More filters
Journal ArticleDOI
»Smooth test» for goodness of fit
TL;DR: In this article, Pearson's test for goodness of fit is dedicated to the memory of Karl Pearson (27 March 1857-27 April 1936) who originated the problem of a test for fit and was first to advance its solution.
Journal ArticleDOI
Asymptotically optimal tests of composite hypotheses for randomized experiments with noncontrolled predictor variables
Jerzy Neyman,Elizabeth L. Scott +1 more
TL;DR: In this article, two randomization schemes are considered: randomized pairs and unrestricted randomization, and the authors deduce the locally asymptotically optimal test of the hypothesis that the treatment has no effect.
Note on techniques of evaluation of single rain stimulation experiments
Jerzy Neyman,Elizabeth L. Scott +1 more
TL;DR: In this paper, the authors present a list of the formulas used in their treatment of rain stimulation experiments and also some extensions that may be useful in deducing optimal C(a) tests, which, in some cases, are too sweeping.