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In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different statistical paradigms. First, in the frequentist paradigm, Fisher information is used to construct hypothesis tests and confidence intervals using maximum likelihood estimators; second, in the Bayesian paradigm, Fisher information is used to define a default prior; lastly, in the minimum description length paradigm, Fisher information is used to measure model complexity.MSC 2010 subject classifications: Primary 62-01, 62B10; secondary 62F03, 62F12, 62F15, 62B10.

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A Tutorial on Fisher information

Marsman

Verhagen

et al. 2017

Journal of Mathematical Psychology

213

117

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Information and Statistical Efficiency When Quantizing Noisy DC Values

Moschitta

Schoukens

Carbone

2015

IEEE Trans. Instrum. Meas.

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This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are considered. It provides expressions for the statistical efficiency of the arithmetic mean by comparing its variance to the proper Cramér-Rao lower bound. It is conjectured that the arithmetic mean is optimal among all estimators with an exactly known bias. Conditions under which its statistical performance are improved by the other estimation procedures when the exact bias is not known are found and analyzed. Using simulations and analysis of experimental data, it is shown that both momentbased and maximum-likelihood-based estimators provide better results, when the noise standard deviation is comparable with the quantization step and the noise model of quantization can not be applied.Index Terms-Cramér-Rao lower bound (CRLB), estimation, nonlinear quantizers, quantization.

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On the Singularities of the Information Matrix and Multipath Change-Point Problems

Asgharian¹

2014

Theory Probab. Appl.

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Nonsingularity of the information matrix plays a key role in model identification and the asymptotic theory of statistics. For many statistical models, however, this condition seems virtually impossible to verify. An example of such models is a class of mixture models associated with multipath change-point problems (MCPs). The question then arises as to how often this assumption fails to hold. Using the subimmersion theorem and upper semicontinuity of the spectrum, we show that the set of singularities of the information matrix is a nowhere dense set, i.e., geometrically negligible, if the model is identifiable and some mild smoothness conditions hold. Under further smoothness conditions we show that the set is also of measure zero, i.e., both geometrically and analytically negligible. In view of our main results, we further study a flexible class of MCP models, thus paving the way for establishing asymptotic normality of the maximum likelihood estimates (MLEs) and statistical inference of the unknown parameters in such models.

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Cited by 4 publications

References 5 publications

A Tutorial on Fisher information

A Tutorial on Fisher information

Information and Statistical Efficiency When Quantizing Noisy DC Values

On the Singularities of the Information Matrix and Multipath Change-Point Problems

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