Asymptotic Expansions of the Null Distributions of Discrepancy Functions for General Covariance Structures Under Nonnormality

Asymptotic expansions of the distributions of likelihood ratio and Lagrange multiplier test statistics for nonlinear restrictions on regression coefficients are derived under the null hypothesis. Nonlinear restrictions include, as a special case, the identifiability restrictions in the simultaneous equations models. Our analyses of simultaneous equations deal not only with single equations but also subsystems and complete systems. The asymptotic expansions we derive are informative about deviations of the real size of test from the nominal asymptotic size.

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Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence

The Annals of Mathematical Statistics ◽

10.1214/aoms/1177697599 ◽

1969 ◽

Vol 40 (3) ◽

pp. 942-952 ◽

Cited By ~ 70

Author(s):

Nariaki Sugiura ◽

Yasunori Fujikoshi

Keyword(s):

Likelihood Ratio ◽

Asymptotic Expansions ◽

Linear Hypothesis ◽

Null Distributions

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Multiple-snapshots BSS with general covariance structures: A partial maximum likelihood approach involving weighted joint diagonalization

Signal Processing ◽

10.1016/j.sigpro.2011.09.036 ◽

2012 ◽

Vol 92 (8) ◽

pp. 1832-1843 ◽

Cited By ~ 2

Author(s):

Arie Yeredor

Keyword(s):

Maximum Likelihood ◽

Covariance Structures ◽

General Covariance ◽

Joint Diagonalization ◽

Maximum Likelihood Approach ◽

Likelihood Approach

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Some Asymptotic Analysis of Resistant Rules For Outlier Labeling

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800001042 ◽

1989 ◽

Vol 3 (1) ◽

pp. 157-164

Author(s):

John E. Angus

Keyword(s):

Asymptotic Analysis ◽

Order Statistics ◽

Outlier Detection ◽

Asymptotic Expansions ◽

Null Distribution ◽

Symmetric Distributions ◽

Null Distributions ◽

Double Exponential ◽

True Distribution

Previous studies have examined the behavior of outlier detection rules for symmetric distributions that label as “outside” any observations that fall outside the interval [FL – k(Fu – FL), Fu + k(Fu – FL)], where FL and FU are functions of the order statistics estimating the 0.25 and 0.75 quantiles of the distribution underlying the i.i.d. sample. A measure of the performance of this type of rule is the “some-outside rate” per sample computed with respect to a given (usually Gaussian) null distribution. The “some-outside rate” (SOR) per sample is the probability that the sample will contain one or more observations labeled as “outside,” given that the null distribution is the true distribution. In this paper, asymptotic expansions of k = kn as a function of n that guarantee an asymptotically constant, prespecified SOR are given for a variety of symmetric null distributions including the Gaussian, double exponential, logistic, and Cauchy distributions. The main theorem also applies to the case of a nonsymmetric null distribution by slightly modifying the labeling rule.

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