Worst-case Cramer-Rao bound for parametric estimation of superimposed signals

We consider a problem in parametric estimation: givennsamples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani (2005), we evaluate an estimator in terms of the chance of being within a specified tolerance of the correct answer, in the worst case. We provide optimal estimators for several families of distributions onℝ. We prove that for distributions on a compact space, there is always an optimal estimator that is translation invariant, and we conjecture that this conclusion also holds for any distribution onℝ. By contrast, we give an example showing that, it does not hold for a certain distribution on an infinite tree.

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Cramér-Rao Bound Expressions for Parametric Estimation of Overlapping Peaks: Influence of Prior Knowledge

Journal of Magnetic Resonance ◽

10.1006/jmre.1999.2002 ◽

2000 ◽

Vol 143 (2) ◽

pp. 311-320 ◽

Cited By ~ 66

Author(s):

S Cavassila ◽

S Deval ◽

C Huegen ◽

D van Ormondt ◽

D Graveron-Demilly

Keyword(s):

Prior Knowledge ◽

Parametric Estimation ◽

Overlapping Peaks ◽

Cramer Rao Bound

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Long-Run Risk is the Worst-Case Scenario: Ambiguity Aversion and Non-Parametric Estimation of the Endowment Process

10.24148/wp2014-16 ◽

2016 ◽

pp. 01-66

Author(s):

Rhys Bidder ◽

◽

Ian Dew-Becker ◽

Keyword(s):

Ambiguity Aversion ◽

Parametric Estimation ◽

Case Scenario ◽

Worst Case ◽

Worst Case Scenario ◽

Long Run ◽

Long Run Risk ◽

Non Parametric Estimation ◽

Non Parametric

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Mosaic Mapping: A Means of Tiling Images to Shorten Acquisition Speed for Lower - Magnification SEM Images and Wavelength Dispersive Spectrometers (WDS) X-Ray Maps

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164659 ◽

1996 ◽

Vol 54 ◽

pp. 438-439

Author(s):

J.D. Geller ◽

C.R. Herrington

Keyword(s):

Limiting Factors ◽

X Rays ◽

Angular Range ◽

Acceptance Angle ◽

Sem Images ◽

Worst Case ◽

X Ray ◽

Focusing Distance ◽

Layered Crystals ◽

Working Distance

The minimum magnification for which an image can be acquired is determined by the design and implementation of the electron optical column and the scanning and display electronics. It is also a function of the working distance and, possibly, the accelerating voltage. For secondary and backscattered electron images there are usually no other limiting factors. However, for x-ray maps there are further considerations. The energy-dispersive x-ray spectrometers (EDS) have a much larger solid angle of detection that for WDS. They also do not suffer from Bragg’s Law focusing effects which limit the angular range and focusing distance from the diffracting crystal. In practical terms EDS maps can be acquired at the lowest magnification of the SEM, assuming the collimator does not cutoff the x-ray signal. For WDS the focusing properties of the crystal limits the angular range of acceptance of the incident x-radiation. The range is dependent upon the 2d spacing of the crystal, with the acceptance angle increasing with 2d spacing. The natural line width of the x-ray also plays a role. For the metal layered crystals used to diffract soft x-rays, such as Be - O, the minimum magnification is approximately 100X. In the worst case, for the LEF crystal which diffracts Ti - Zn, ˜1000X is the minimum.

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