Distribution-Free and Other Prediction Intervals

Konijn, H. S.

doi:10.2307/2684311

Cited by 3 publications

(4 citation statements)

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“…We show that classical KNN provide smaller confidence intervals which fail to guarantee the required level of inclusion percentage. For future works, we propose to build in the same way the possibility distributions encoding prediction intervals [8] [9]. We will also extend this approach to normal mixtures and distribution free sample sets.…”

Section: Resultsmentioning

confidence: 99%

Possibilistic KNN Regression Using Tolerance Intervals

Hamed

Serrurier

Durand

2012

Communications in Computer and Information Science

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Abstract. By employing regression methods minimizing predictive risk, we are usually looking for precise values which tends to their true response value. However, in some situations, it may be more reasonable to predict intervals rather than precise values. In this paper, we focus to find such intervals for the K-nearest neighbors (KNN) method with precise values for inputs and output. In KNN, the prediction intervals are usually built by considering the local probability distribution of the neighborhood. In situations where we do not dispose of enough data in the neighborhood to obtain statistically significant distributions, we would rather wish to build intervals which takes into account such distribution uncertainties. For this latter we suggest to use tolerance intervals to build the maximal specific possibility distribution that bounds each population quantiles of the true distribution (with a fixed confidence level) that might have generated our sample set. Next we propose a new interval regression method based on KNN which take advantage of our possibility distribution in order to choose, for each instance, the value of K which will be a good trade-off between precision and uncertainty due to the limited sample size. Finally we apply our method on an aircraft trajectory prediction problem.

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Section: Resultsmentioning

confidence: 99%

Possibilistic KNN Regression Using Tolerance Intervals

Hamed

Serrurier

Durand

2012

Communications in Computer and Information Science

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“…For distribution free prediction intervals, the reader can find more information in [16], [23] and [6].…”

Section: Possibility Distribution Encoding Prediction Intervalsmentioning

confidence: 99%

Representing Uncertainty by Possibility Distributions Encoding Confidence Bands, Tolerance and Prediction Intervals

Hamed

Serrurier

Durand

2012

Lecture Notes in Computer Science

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Representing uncertainty by possibility distributions encoding confidence bands, tolerance and prediction intervals.Abstract. For a given sample set, there are already different methods for building possibility distributions encoding the family of probability distributions that may have generated the sample set. Almost all the existing methods are based on parametric and distribution free confidence bands. In this work, we introduce some new possibility distributions which encode different kinds of uncertainties not treated before. Our possibility distributions encode statistical tolerance and prediction intervals (regions). We also propose a possibility distribution encoding the confidence band of the normal distribution which improves the existing one for all sample sizes. In this work we keep the idea of building possibility distributions based on intervals which are among the smallest intervals for small sample sizes. We also discuss the properties of the mentioned possibility distributions.

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“…In Konijn (1963) we considered maximum likelihood estimation. In Konijn (1966) we showed that the parameters are identifiable, but that u and p do not have consistent estimators (see Section 2 below). We now show that p does not have a consistent estimator, either.…”

Section: Introductionmentioning

confidence: 99%

“…, n}. In Konijn (1966) we mentioned some uses of this model. In Konijn (1963) we considered maximum likelihood estimation.…”

Section: Introductionmentioning

confidence: 99%