20,374 research outputs found
Testing for Non-Normality in the Presence of One-Sided Slope Parameters
In a recent paper, Hughes (1999) showed that the power of tests of linear regression parameters could be improved by utilizing one-sided information regarding the nuisance parameters in the testing problem. In this paper, we extend this principle to the problem of diagnosing departures from the assumption of normality in linear regression residuals. We show that the asymptotic theory of the popular normality test developed by Jarque and Bera (1987) is also applicable when inequality constraints are imposed on the slope parameters. Monte Carlo evidence is then presented which suggests that the size of tests based on inequality constrained residuals is roughly equivalent to the size of tests based on unconstrained residuals using both asymptotic and bootstrap critical values. We then demonstrate that significant improvements in the power of the Jarque-Bera test can be made via the application of one-sided information concerning the slope parameters in the model.Jarque-Bera test; inequality constraints; power; bootstrap; Monte Carlo simulations
Statistical Models with Uncertain Error Parameters
In a statistical analysis in Particle Physics, nuisance parameters can be
introduced to take into account various types of systematic uncertainties. The
best estimate of such a parameter is often modeled as a Gaussian distributed
variable with a given standard deviation (the corresponding "systematic
error"). Although the assigned systematic errors are usually treated as
constants, in general they are themselves uncertain. A type of model is
presented where the uncertainty in the assigned systematic errors is taken into
account. Estimates of the systematic variances are modeled as gamma distributed
random variables. The resulting confidence intervals show interesting and
useful properties. For example, when averaging measurements to estimate their
mean, the size of the confidence interval increases for decreasing
goodness-of-fit, and averages have reduced sensitivity to outliers. The basic
properties of the model are presented and several examples relevant for
Particle Physics are explored.Comment: 26 pages, 27 figure
A model independent safeguard for unbinned Likelihood
We present a universal method to include residual un-modeled background shape
uncertainties in likelihood based statistical tests for high energy physics and
astroparticle physics. This approach provides a simple and natural protection
against mismodeling, thus lowering the chances of a false discovery or of an
over constrained confidence interval, and allows a natural transition to
unbinned space. Unbinned likelihood allows optimal usage of information for the
data and the models, and enhances the sensitivity.
We show that the asymptotic behavior of the test statistic can be regained in
cases where the model fails to describe the true background behavior, and
present 1D and 2D case studies for model-driven and data-driven background
models. The resulting penalty on sensitivities follows the actual discrepancy
between the data and the models, and is asymptotically reduced to zero with
increasing knowledge
Local Asymptotic Equivalence of the Bai and Ng (2004) and Moon and Perron (2004) Frameworks for Panel Unit Root Testing
This paper considers unit-root tests in large n and large T heterogeneous
panels with cross-sectional dependence generated by unobserved factors. We
reconsider the two prevalent approaches in the literature, that of Moon and
Perron (2004) and the PANIC setup proposed in Bai and Ng (2004). While these
have been considered as completely different setups, we show that, in case of
Gaussian innovations, the frameworks are asymptotically equivalent in the sense
that both experiments are locally asymptotically normal (LAN) with the same
central sequence. Using Le Cam's theory of statistical experiments we determine
the local asymptotic power envelope and derive an optimal test jointly in both
setups. We show that the popular Moon and Perron (2004) and Bai and Ng (2010)
tests only attain the power envelope in case there is no heterogeneity in the
long-run variance of the idiosyncratic components. The new test is
asymptotically uniformly most powerful irrespective of possible heterogeneity.
Moreover, it turns out that for any test, satisfying a mild regularity
condition, the size and local asymptotic power are the same under both data
generating processes. Thus, applied researchers do not need to decide on one of
the two frameworks to conduct unit root tests. Monte-Carlo simulations
corroborate our asymptotic results and document significant gains in
finite-sample power if the variances of the idiosyncratic shocks differ
substantially among the cross sectional units
Is the demand for euro area M3 stable?
JEL Classification: C22, C32, E41Aggregation, Bootstrap, Money demand, Own Rate of Money, Parameter Constancy
Permutation Inference for Canonical Correlation Analysis
Canonical correlation analysis (CCA) has become a key tool for population
neuroimaging, allowing investigation of associations between many imaging and
non-imaging measurements. As other variables are often a source of variability
not of direct interest, previous work has used CCA on residuals from a model
that removes these effects, then proceeded directly to permutation inference.
We show that such a simple permutation test leads to inflated error rates. The
reason is that residualisation introduces dependencies among the observations
that violate the exchangeability assumption. Even in the absence of nuisance
variables, however, a simple permutation test for CCA also leads to excess
error rates for all canonical correlations other than the first. The reason is
that a simple permutation scheme does not ignore the variability already
explained by previous canonical variables. Here we propose solutions for both
problems: in the case of nuisance variables, we show that transforming the
residuals to a lower dimensional basis where exchangeability holds results in a
valid permutation test; for more general cases, with or without nuisance
variables, we propose estimating the canonical correlations in a stepwise
manner, removing at each iteration the variance already explained, while
dealing with different number of variables in both sides. We also discuss how
to address the multiplicity of tests, proposing an admissible test that is not
conservative, and provide a complete algorithm for permutation inference for
CCA.Comment: 49 pages, 2 figures, 10 tables, 3 algorithms, 119 reference
A symptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameter
This papers studies and compares the asymptotic bias of GMM and generalized empirical likelihood (GEL) estimators in the presence of estimated nuisance parameters. We consider cases in which the nuisance parameter is estimated from independent and identical samples. A simulation experiment is conducted for covariance structure models. Empirical likelihood offers much reduced mean and median bias, root mean squared error and mean absolute error, as compared with two-step GMM and other GEL methods. Both analytical and bootstrap bias-adjusted two-step GMM estima-tors are compared. Analytical bias-adjustment appears to be a serious competitor to bootstrap methods in terms of finite sample bias, root mean squared error and mean absolute error. Finite sample variance seems to be little affected
Identification of and correction for publication bias
Some empirical results are more likely to be published than others. Such
selective publication leads to biased estimates and distorted inference. This
paper proposes two approaches for identifying the conditional probability of
publication as a function of a study's results, the first based on systematic
replication studies and the second based on meta-studies. For known conditional
publication probabilities, we propose median-unbiased estimators and associated
confidence sets that correct for selective publication. We apply our methods to
recent large-scale replication studies in experimental economics and
psychology, and to meta-studies of the effects of minimum wages and de-worming
programs
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