This paper reviews important concepts and methods that are useful for hypothesis testing. First, we discuss the Neyman-Pearson framework. Various approaches to optimality are presented, including finite-sample and large-sample optimality. Then, some of the most important methods are summarized,...

Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized familywise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and stepdown procedures that control the k-FWER...

This paper considers the problem of testing s null hypotheses simultaneously while controlling the false discovery rate (FDR). Benjamini and Hochberg (1995) provide a method for controlling the FDR based on p-values for each of the null hypotheses under the assumption that the p-values are...

This paper shows how asymptotically valid inference in regression models based on the weighted least squares (WLS) estimator can be obtained even when the model for reweighting the data is misspecified. Like the ordinary least squares estimator, the WLS estimator can be accompanied by...

We present a theoretical basis for testing related endpoints. Typically, it is known how to construct tests of the individual hypotheses, and the problem is how to combine them into a multiple test procedure that controls the familywise error rate. Using the closure method, we emphasize the role...

Consider the problem of testing k hypotheses simultaneously. In this paper, we discuss finite and large sample theory of stepdown methods that provide control of the familywise error rate (FWE). To improve upon the Bonferroni method or Holm's stepdown method, Westfall and Young (1993) make use...

It is common in econometric applications that several hypothesis tests are carried out at the same time. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. In this paper, we suggest a stepwise multiple testing procedure which asymptotically...

We consider the problem of making inference for the autocorrelations of a time series in the possible presence of a unit root. Even when the underlying series is assumed to be strictly stationary, the robustness against a unit root is a desirable property to ensure good finite-sample coverage in...

This paper considers the problem of testing a finite number of moment inequalities. We propose a two-step approach. In the first step, a confidence region for the moments is constructed. In the second step, this set is used to provide information about which moments are “negative.” A...

Confidence intervals in econometric time series regressions suffer from notorious coverage problems. This is especially true when the dependence in the data is noticeable and sample sizes are small to moderate, as is often the case in empirical studies. This paper suggests using the studentized...