# The local power of the gradient test

@article{Lemonte2010TheLP, title={The local power of the gradient test}, author={Artur J. Lemonte and Silvia L. P. Ferrari}, journal={Annals of the Institute of Statistical Mathematics}, year={2010}, volume={64}, pages={373-381} }

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n−1/2, n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

## 40 Citations

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## References

SHOWING 1-10 OF 33 REFERENCES

The likelihood ratio criterion and the asymptotic expansion of its distribution

- Mathematics
- 1977

SummaryAsymptotic expansion of the distribution of the likelihood ratio criterion (LRC) for testing a composite hypothesis is derived under null hypothesis and a correction factor ρ which makes the…

The likelihood ratio criterion for a composite hypothesis under a local alternative

- Mathematics
- 1975

SUMMARY The asymptotic expansions of the distributions of the likelihood ratio criterion and Wald's statistic are derived for a composite hypothesis under a sequence of local alternative hypotheses…

The local power of the efficient scores test statistic

- Mathematics
- 1980

SUMMARY The test statistic based on the efficient scores is shown to be locally biased in general. Comparisons of the local powers of this statistic, the likelihood ratio and maximum likelihood…

Likelihood ratio and associated test criteria

- Mathematics
- 1971

SUMMARY A more accurate approximation is derived for the power function of the likelihood ratio criterion for testing a simple null hypothesis against a class of composite alternative hypotheses. Two…

Score Test: Historical Review and Recent Developments

- Mathematics
- 2005

The three asymptotic tests, Neyman and Pearson Likelihood Ratio (LR), Wald’s statistic (W) and Rao’s score (RS)are referred to in statistical literature on testing of hypotheses as the Holy Trinity.…

Local power properties of some asymptotic tests in symmetric linear regression models

- Mathematics
- 2012

Asymptotic expansions of the distributions of some test statistics

- Mathematics
- 1985

A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as…

Local power of three classic criteria in generalised linear models with unknown dispersion

- Mathematics
- 1997

In this paper we obtain asymptotic expansions for the nonnull distribution functions of the likelihood ratio, score and Wald test statistics in exponential family generalised linear models under…

Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation

- Mathematics
- 1948

If the probability differential of a set of stochastic variates contains k unknown parameters, the statistical hypotheses concerning them may be simple or composite. The hypothesis leading to a…

Bias reduction of maximum likelihood estimates

- Mathematics
- 1993

SUMMARY It is shown how, in regular parametric problems, the first-order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function. In…