mathematics

Peter J. Bickel

Peter J. Bickel is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Peter J. Bickel rather than just read about it. In short: Peter John Bickel (born 1940) is an American statistician and Professor of Statistics at the University of California, Berkeley. Bickel has made contributions to bootstrapping, robust statistics, machine learning, and other areas of statistics.

Key takeaways

Peter J. Bickel belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Peter J. Bickel to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Peter J. Bickel from memory before moving on to harder problems.

Reference excerpt

Peter John Bickel (born 1940) is an American statistician and Professor of Statistics at the University of California, Berkeley. Bickel has made contributions to bootstrapping, robust statistics, machine learning, and other areas of statistics.

Education and career Bickel studied physics at the California Institute of Technology. He graduated from University of California, Berkeley, with a Ph.D., in 1963, where he studied under Erich Leo Lehmann. His students include C.F. Jeff Wu, Jianqing Fan, Katerina Kechris, Elizaveta Levina, Jingyi Jessica Li, and Donald Andrews.

Personal He married Nancy Kramer in 1964; they have two children.

Awards 1970 Guggenheim Fellow 1973 Fellow of the American Statistical Association 1981 the recipient of COPSS Presidents' Award 1984 MacArthur Fellow 1986 Fellow of the American Academy of Arts and Sciences 1986 Member of the National Academy of Sciences 1986 Honorary Doctorate degree from Hebrew University, Jerusalem 1995 Foreign member of the Royal Netherlands Academy of Arts and Sciences 2006 Commander of the Order of Orange-Nassau 2013 R. A. Fisher Lectureship 2014 Honorary Doctorate degree from ETH Zurich

References

Further reading Ritov, Y. A. (2011). "A Random Walk with Drift: Interview with Peter J. Bickel". Statistical Science. 26: 150–159. arXiv:1106.2881. doi:10.1214/09-STS300. S2CID 62621269. Fan, Jianqing; Ritov, Ya'acov; Wu, Chien-Fu, eds. (2012). "Biography of Peter J. Bickel". Selected Works of Peter J. Bickel. Springer Science+Business Media. ISBN 9781461455448.

External links Homepage Peter John Bickel at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Peter J. Bickel

Start with the simplest possible case. Write down what Peter J. Bickel claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Peter J. Bickel before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Peter J. Bickel ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Peter J. Bickel

In research: Peter J. Bickel appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Peter J. Bickel in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Peter J. Bickel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1940 births, American statisticians, California Institute of Technology alumni, so understanding it makes those chapters shorter.
In everyday life: Look for Peter J. Bickel outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Peter J. Bickel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Peter J. Bickel means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Peter J. Bickel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Peter J. Bickel in simple terms?

Why does Peter J. Bickel matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Peter J. Bickel?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Peter J. Bickel.