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142
An analysis of transformations
 Journal of the Royal Statistical Society. Series B (Methodological
, 1964
"... In the analysis of data it is often assumed that observations y,, y,,...,y, are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters 0. In this paper we make the less restrictive assumption that such a normal, homoscedasti ..."
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Cited by 1029 (3 self)
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In the analysis of data it is often assumed that observations y,, y,,...,y, are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters 0. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples. 1.
Development of quantitative structureactivity relationships and its application in rational drug design
"... Abstract—Quantitative structureactivity relationships are mathematical models constructed based on the hypothesis that structure of chemical compounds is related to their biological activity. A linear regression model is often used to estimate and/or to predict the nature of the relationship betwe ..."
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Cited by 54 (1 self)
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Abstract—Quantitative structureactivity relationships are mathematical models constructed based on the hypothesis that structure of chemical compounds is related to their biological activity. A linear regression model is often used to estimate and/or to predict the nature of the relationship between a measured activity and some measure or calculated descriptors. Linear regression helps to answer main three questions: does the biological activity depend on structure information; if so, the nature of the relationship is linear; and if yes, how good is the model in prediction of the biological activity of new compound(s). This manuscript presents the steps on linear regression analysis moving from theoretical knowledge to an example conducted on sets of endocrine disrupting chemicals. Keywordsrobust regression; validation; diagnostic; pre
On the robust estimation of power spectra, coherences, and transfer functions
 J. Geophys. Res
, 1987
"... Robust estimation of power spectra, coherences, and transfer functions is investigated in the context of geophysical data processing. The methods described are frequencydomain extensions of current techniques from the statistical iterature and are applicable in cases where sectionaveraging methods ..."
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Cited by 43 (4 self)
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Robust estimation of power spectra, coherences, and transfer functions is investigated in the context of geophysical data processing. The methods described are frequencydomain extensions of current techniques from the statistical iterature and are applicable in cases where sectionaveraging methods would be used with data that are contaminated by local nonstationarity or isolated outliers. The paper begins with a review of robust estimation theory, emphasizing statistical principles and the maximum likelihood or Mestimators. These are combined with sectionaveraging spectral techniques to obtain robust estimates of power spectra, coherences, and transfer functions in an automatic, dataadaptive fashion. Because robust methods implicitly identify abnormal data, methods for monitoring the statistical behavior of the estimation process using quantilequantile plots are also discussed. The results are illustrated using a variety of examples from electromagnetic geophysics.
Simulationbased finitesample tests for heteroskedasticity and ARCH effects
, 2001
"... paper was also partly written at the Centre de recherche en Économie et Statistique (INSEE, Paris) and the Technische ..."
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Cited by 34 (22 self)
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paper was also partly written at the Centre de recherche en Économie et Statistique (INSEE, Paris) and the Technische
BehrensFisher: the probable difference between two means when s1 2= s2 2
 Journal of Modern Applied Statistical Methods
"... The history of the BehrensFisher problem and some approximate solutions are reviewed. In outlining relevant statistical hypotheses on the probable difference between two means, the importance of the BehrensFisher problem from a theoretical perspective is acknowledged, but it is concluded that this ..."
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Cited by 12 (0 self)
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The history of the BehrensFisher problem and some approximate solutions are reviewed. In outlining relevant statistical hypotheses on the probable difference between two means, the importance of the BehrensFisher problem from a theoretical perspective is acknowledged, but it is concluded that this problem is irrelevant for applied research in psychology, education, and related disciplines. The focus is better placed on “shift in location ” and, more importantly, “shift in location and change in scale ” treatment alternatives.
HIGHER ORDER SEMIPARAMETRIC FREQUENTIST INFERENCE WITH THE PROFILE SAMPLER
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2006
"... We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine (2005) is extended to second order validity in the setting ..."
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Cited by 12 (9 self)
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We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine (2005) is extended to second order validity in the setting where the infinite dimensional nuisance parameter achieves the parametric rate. Specifically, we obtain higher order estimates of the maximum profile likelihood estimator and of the efficient Fisher information. Moreover, we prove that an exact frequentist confidence interval for the parametric component at level alpha can be estimated by the alpha level credible set from the profile sampler with an error of order OP (n −1). As far as we are aware, these results are the first higher order frequentist results obtained for semiparametric estimation. A fully Bayesian interpretation is established under a certain data dependent prior. The theory is verified for three specific examples.
Central Limit Theorems for Classical Likelihood Ratio Tests for HighDimensional Normal Distributions
"... For random samples of size n obtained from pvariate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the highdimensional setting. These test statistics have been extensively studied in multivariate analysis and their limiting d ..."
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Cited by 11 (4 self)
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For random samples of size n obtained from pvariate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the highdimensional setting. These test statistics have been extensively studied in multivariate analysis and their limiting distributions under the null hypothesis were proved to be chisquare distributions as n goes to infinity and p remains fixed. In this paper, we consider the highdimensional case where both p and n go to infinity with p/n → y ∈ (0, 1]. We prove that the likelihood ratio test statistics under this assumption will converge in distribution to normal distributions with explicit means and variances. We perform the simulation study to show that the likelihood ratio tests using our central limit theorems outperform those using the traditional chisquare approximations for analyzing highdimensional data.
GENERAL FREQUENTIST PROPERTIES OF THE POSTERIOR PROFILE DISTRIBUTION
, 2008
"... In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higherorder validity of the profile sampler obtained in Cheng and Kosorok [Ann. Statist. 36 (2008) ..."
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Cited by 11 (5 self)
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In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higherorder validity of the profile sampler obtained in Cheng and Kosorok [Ann. Statist. 36 (2008)] is extended to semiparametric models in which the infinite dimensional nuisance parameter may not have a rootn convergence rate. This is a nontrivial extension because it requires a delicate analysis of the entropy of the semiparametric models involved. We find that the accuracy of inferences based on the profile sampler improves as the convergence rate of the nuisance parameter increases. Simulation studies are used to verify this theoretical result. We also establish that an exact frequentist confidence interval obtained by inverting the profile loglikelihood ratio can be estimated with higherorder accuracy by the credible set of the same type obtained from the posterior profile distribution. Our theory is verified for several specific examples.