An alternative comparison of classical tests: assessing the effects of curvature

Garderen, Kees Jan van

doi:10.1017/cbo9780511660092.009

Cited by 5 publications

(6 citation statements)

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“…where L is the log likelihood function after concentrating out and . Various authors have noticed that, in curved exponential models, the likelihood ratio test performs well for a wide range of alternatives; see, for example, Van Garderen (2000). In Appendix B we show that the critical value function for the likelihood ratio test has the form…”

Section: Similar Tests Based On Conditioningmentioning

confidence: 83%

A Conditional Likelihood Ratio Test for Structural Models

2003

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This paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. These tests are shown to be similar under weak-instrument asymptotics when the reduced-form covariance matrix is estimated and the errors are non-normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local-to-null asymptotics, but it has better power when identification is weak.

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Section: Similar Tests Based On Conditioningmentioning

confidence: 83%

A Conditional Likelihood Ratio Test for Structural Models

2003

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“…Figure 3 shows the graphs of angular nominal distributions of W , LR, and LM defined in equation (17) and the graph of their angular exact distribution defined in equation (14) for some parameter values. In a sense, we see three nominal and one actual sampling distribution of three statistics together as a function of the same random variable.…”

Section: Angular Equivalents Of Exact and Asymptotic W Lr And Lm Tmentioning

confidence: 99%

“…It can be downloaded from http://www.istanbul.edu.tr/iktisat/econometrics/siniksaran. After entering the data, the parameters in the null hypothesis, and the level of significance, the program computes the angle between the unrestricted and the restricted residuals and compares it with the upper tail values of the four angular distributions in equations (14) and (17). It also gives the results of the traditional approach.…”

Section: Computationsmentioning

confidence: 99%

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On the geometry ofF, Wald, LR, and LM tests in linear regression models

Siniksaran¹

2005

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In this article, we examine F , Wald, LR, and LM test statistics in the linear regression model using vector geometry. These four statistics are expressed as a function of one random variable -the angle between the vectors of unrestricted and restricted residuals. The exact and nominal sampling distributions of this angle are derived to illuminate some facts about the four statistics. Alternatively, we offer that the angle itself can be used as a test statistic. A Mathematica program is also written to carry out the approach.

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“…Abadir, 1993b;Abadir and Lucas, 2004). In spite of work by Van Garderen (1999, 2000, the underlying geometry of non-stationary autoregressive models is still not fully characterized. The shared characteristics between the four-step random walk problem and least-squares estimation in autoregressive models could motivate new approaches towards the latter that embrace machinery currently commonplace in Analytic Number Theory and 26 J. R. McCrorie…”

Section: Discussionmentioning

confidence: 99%

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

McCrorie

2020

Sankhya B

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This paper considers the representation of odd moments of the distribution of a four-step uniform random walk in even dimensions, which are based on both linear combinations of two constants representable as contiguous very well-poised generalized hypergeometric series and as even moments of the square of the complete elliptic integral of the first kind. Neither constants are currently available in closed form. New symmetries are found in the critical values of the L-series of two underlying cusp forms, providing a sense in which one of the constants has a formal counterpart. The significant roles this constant and its counterpart play in multidisciplinary contexts is described. The results unblock the problem of representing them in terms of lower-order generalized hypergeometric series, offering progress towards identifying their closed forms. The same approach facilitates a canonical characterization of the hypergeometry of the parbelos, adding to the characterizations outlined by Campbell, D'Aurozio and Sondow (2020, The American Mathematical Monthly127(1), 23-32). The paper also connects the econometric problem of characterizing the bias in the canonical autoregressive model under the unit root hypothesis to very well-poised generalized hypergeometric series. The confluence of ideas presented reflects a multidisciplinarity that accords with the approach and philosophy of Prasanta Chandra Mahalanobis.

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An alternative comparison of classical tests: assessing the effects of curvature

Cited by 5 publications

References 0 publications

A Conditional Likelihood Ratio Test for Structural Models

A Conditional Likelihood Ratio Test for Structural Models

On the geometry ofF, Wald, LR, and LM tests in linear regression models

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

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