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Location parameter
About: Location parameter is a research topic. Over the lifetime, 1721 publications have been published within this topic receiving 47467 citations.
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TL;DR: In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.
Abstract: This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)
5,628 citations
TL;DR: In this article, the local power of panel unit root statistics against a sequence of local alternatives is studied and the results of a Monte Carlo experiment suggest that avoiding the bias can improve the power of the test substantially.
Abstract: To test the hypothesis of a difference stationary time series against a trend stationary alternative, Levin & Lin (1993) and Im, Pesaran & Shin (1997) suggest bias adjusted t-statistics. Such corrections are necessary to account for the nonzero mean of the t-statistic in the case of an OLS detrending method. In this chapter the local power of panel unit root statistics against a sequence of local alternatives is studied. It is shown that the local power of the test statistics is affected by two different terms. The first term represents the asymptotic effect on the bias due to the detrending method and the second term is the usual location parameter of the limiting distribution under the sequence of local alternatives. It is argued that both terms can offset each other so that the test has no power against the sequence of local alternatives. These results suggest to construct test statistics based on alternative detrending methods. We consider a class of t-statistics that do not require a bias correction. The results of a Monte Carlo experiment suggest that avoiding the bias can improve the power of the test substantially.
2,038 citations
TL;DR: It is shown that a method that has been used to extend to the overidentified case standard algorithms for Bayesian intervals in reduced form models is incorrect, and it is shown how to obtain correct Bayesian interval intervals.
Abstract: We show how correctly to extend known methods for generating error bands in reduced form VAR's to overidentified models. We argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty, and we show how to generate such measures. We focus on bands that characterize the shape of the likelihood. Such bands are not classical confidence regions. We explain that classical confidence regions mix information about parameter location with information about model fit, and hence can be misleading as summaries of the implications of the data for the location of parameters. Because classical confidence regions also present conceptual and computational problems in multivariate time series models, we suggest that likelihood-based bands, rather than approximate confidence bands based on asymptotic theory, be standard in reporting results for this type of model.
988 citations