On the Choice of the Number of Class Intervals in the Application of the Chi Square Test

“…The papers were read as follows : papers 1-6 in the section for Analysis on Tuesday morning; papers 7-12 in the section for Algebra, Geometry, and Topology on Tuesday morning; papers [13][14][15][16][17][18][19][20][21][22] …”

mentioning

confidence: 99%

The Summer meeting in Poughkeepsie

Hollcroft¹

1942

Bull. Amer. Math. Soc.

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“…Both are hard problems and despite huge literature on the topic, there are no clear cut solutions. Some major references on this hard problem are Mann and Wald(1942), Oosterhoff(1985), and .…”

Section: Choice Of Kmentioning

confidence: 99%

“…We now present some results on selecting the number of cells k. Mann and Wald (1942) formulated the problem of selecting the value of k in a (somewhat complicated) paradigm and came out with an optimal rate of growth of k as n → ∞. The formulation of Mann and Wald was along the following lines.…”

Section: Choice Of Kmentioning

confidence: 99%

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Classical Nonparametrics

Dasgupta

Asymptotic Theory of Statistics and Probability

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The development of nonparametrics originated from a concern about the approximate validity of parametric procedures based on a specific narrow model when the model is questionable. Procedures which are reasonably insensitive to the exact assumptions that one makes are called robust. Such assumptions may be about a variety of things. They may be about an underlying common density assuming that the data are iid; they may be about the dependence structure of the data itself; in regression problems, they may be about the form of the regression function, etc. For example, if we assume that our data are iid from a certain N (θ, 1) density, then we have a specific parametric model for our data. Statistical models are always, at best, an approximation. We do not believe that the normal model is the correct model. There is a trade-off.As a simple example, consider the t-test for the mean µ of a normal distribution.If normality holds, then under the null hypothesis, H 0 : µ = µ 0 ,for all n, µ 0 , and σ. However, if the population is not normal, neither the size nor the power of the t-test remains the same as under the normal case. If these hange substantially, we have a robustness problem. However, as we will later see, by making a minimal number of assumptions (specifically, no parametric assumptions) we can develop procedures with some sort of a safety net. Such methods would qualify for being called nonparametric methods.

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On the Choice of the Number of Class Intervals in the Application of the Chi Square Test

Cited by 241 publications

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A Tale of Tails: An Empirical Analysis of Loss Distribution Models for Estimating Operational Risk Capital

A Tale of Tails: An Empirical Analysis of Loss Distribution Models for Estimating Operational Risk Capital

The Summer meeting in Poughkeepsie

Classical Nonparametrics

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