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13
Accurate Parametric Inference for Small Samples
, 2008
"... We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical asymptotic approximations, the focus of this paper is not on theory ..."
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Cited by 5 (2 self)
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We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical asymptotic approximations, the focus of this paper is not on theory but on implementation and applications. Numerical illustrations are given for logistic regression, nonlinear models, and linear nonnormal models, and we describe a sampling approach for the third of these classes. In the case of logistic regression, we argue that approximations are often more appropriate than ‘exact’ procedures, even when these exist.
HigherOrder Asymptotics Unleashed Software Design for Nonlinear Heteroscedastic Regression
, 2001
"... One of the main criticisms against the use of higherorder asymptotics is that the algebraic expressions involved are far too complex to be derived by hand in a reasonable amount of time. A further drawback is that the results are so closely tuned to the specic problem at hand that they almost alway ..."
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Cited by 5 (1 self)
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One of the main criticisms against the use of higherorder asymptotics is that the algebraic expressions involved are far too complex to be derived by hand in a reasonable amount of time. A further drawback is that the results are so closely tuned to the specic problem at hand that they almost always exclude the possibility of transferring available computer code to a dierent though similar problem. The aim of this paper is to show that higherorder asymptotics can be implemented in a general and exible way so as to provide easytouse and selfcontained software useful in routine data analysis. The programming strategy we develop easily applies to many parametric models. We illustrate it by describing the design of the core routines of the nlreg section of the SPLUS library HOA (HOA, 2000) which implements higherorder solutions for nonlinear heteroscedastic regression models. Keywords: Asymptotic Theory, HigherOrder Solution, Symbolic Computation, SPLUS. 1 Introduction The mai...
2013a). Accurate directional inference for vector parameters
"... We consider a vectorvalued parameter of interest in the presence of a finitedimensional nuisance parameter, based on higher order asymptotic theory for likelihood inference. We propose a directional test for the vector parameter of interest, that is computed using onedimensional integration. For d ..."
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Cited by 2 (1 self)
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We consider a vectorvalued parameter of interest in the presence of a finitedimensional nuisance parameter, based on higher order asymptotic theory for likelihood inference. We propose a directional test for the vector parameter of interest, that is computed using onedimensional integration. For discrete responses this extends the development of Davison et al. (2006), and several examples below concern testing hypotheses in contingency tables. For continuous responses the work extends the directional test of Cheah et al. (1994). Exponential family examples and simulations illustrate the high accuracy of the method, which we compare with an adjusted likelihood ratio test of Skovgaard (2001). In a highdimensional covariance selection example the approach works essentially perfectly, whereas its competitors fail catastrophically.
Asymptotically Normal Vectors by
, 2007
"... Abstract We obtain the Edgeworth expansion for P(n 1/2 ( ˆ θ − θ) < x) and its derivatives, and the tilted Edgeworth (or saddlepoint or small sample) expansion for P ( ˆ θ < x) and its derivatives where ˆθ is any vector estimate having the standard cumulant expansions in powers of n −1. ..."
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Abstract We obtain the Edgeworth expansion for P(n 1/2 ( ˆ θ − θ) < x) and its derivatives, and the tilted Edgeworth (or saddlepoint or small sample) expansion for P ( ˆ θ < x) and its derivatives where ˆθ is any vector estimate having the standard cumulant expansions in powers of n −1.
Institution that will administer the grant
, 1508
"... For NSERC office use only Form 101 Application for a Grant Send to NSERC with your attachments, if applicable ..."
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For NSERC office use only Form 101 Application for a Grant Send to NSERC with your attachments, if applicable
Accurate directional inference for vector parameters in linear exponential families
, 2013
"... We consider inference on a vectorvalued parameter of interest in a linear exponential family, in the presence of a finitedimensional nuisance parameter. Based on higher order asymptotic theory for likelihood, we propose a directional test whose pvalue is computed using onedimensional integration ..."
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We consider inference on a vectorvalued parameter of interest in a linear exponential family, in the presence of a finitedimensional nuisance parameter. Based on higher order asymptotic theory for likelihood, we propose a directional test whose pvalue is computed using onedimensional integration. For discrete responses this extends the development of Davison et al. (2006), and some of our examples concern testing in contingency tables. For continuous responses the work extends the directional test of Cheah et al. (1994). Examples and simulations illustrate the high accuracy of the method, which we compare with the usual likelihood ratio test and with an adjusted version due to Skovgaard (2001). In highdimensional settings, such as covariance selection, the approach works essentially perfectly, whereas its competitors can fail catastrophically.
THE 2000 WALD MEMORIAL LECTURES ASYMPTOTICS AND THE THEORY OF INFERENCE
"... Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this infor ..."
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Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twentysome years provides an illustration of the interplay between techniques of approximation and statistical theory. 1. Introduction. The
HigherOrder Asymptotics Unleashed
, 2000
"... One of the main criticism against the use of higherorder asymptotics is that the algebraic expression involved are far too complex to be derived by hand in a reasonable amount of time. The results are furthermore so closely tuned to the specific problem at stake that they exclude the possibility of ..."
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One of the main criticism against the use of higherorder asymptotics is that the algebraic expression involved are far too complex to be derived by hand in a reasonable amount of time. The results are furthermore so closely tuned to the specific problem at stake that they exclude the possibility of reusing available computer code in a different though similar problem. The aim of this paper is to show that higherorder asymptotics can be implemented in a general and flexible way such as to provide easytouse and selfcontained software to be used in routine data analysis. We will demonstrate this by illustrating the main programming strategy that underlies the SPLUS library HOA. This library implements higherorder solutions for three main parametric model classes: logistic and loglinear models, linear nonnormal models and nonlinear heteroscedastic regression models.
Tests Concerning Equicorrelation Matrices with Grouped Normal Data
"... Key Words: intraclass correlation; likelihood ratio test; maximum likelihood estimation; score test; smallsample inference. This paper considers three practical hypotheses involving the equicorrelation matrix for grouped normal data. We obtain statistics and computing formulae for common test proce ..."
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Key Words: intraclass correlation; likelihood ratio test; maximum likelihood estimation; score test; smallsample inference. This paper considers three practical hypotheses involving the equicorrelation matrix for grouped normal data. We obtain statistics and computing formulae for common test procedures such as the score test and the likelihood ratio test. In addition, statistics and computing formulae are obtained for various small sample procedures as proposed in Skovgaard (2001). The properties of the tests for each of the three hypotheses are compared using Monte Carlo simulations. 1 1