Interval and band estimation for curves with jumps

2004 ◽  
Vol 41 (A) ◽  
pp. 65-79 ◽  
Author(s):  
Irène Gijbels ◽  
Peter Hall ◽  
Aloïs Kneip
Keyword(s):  
Normal Distribution ◽  
Confidence Intervals ◽  
Simulation Study ◽  
Sampling Error ◽  
Confidence Bands ◽  
Unusual Feature ◽  
Nile River ◽  
Flow Volume ◽  
Jump Point ◽  
Point Estimator

Jump points in curves arise when the conditions under which data are generated change suddenly, for example because of an unplanned change in a treatment. This paper suggests bootstrap methods for quantifying the error in estimates of jump points, and for constructing confidence intervals for jump points and confidence bands for the curve. These problems have the unusual feature that the sampling error of the jump-point estimator often has a highly non-normal distribution, which depends intimately on the distribution of regression errors. The methods are illustrated by a simulation study as well as by an application to data on the annual flow volume of the Nile river.

Interval and band estimation for curves with jumps

2004 ◽  
Vol 41 (A) ◽  
pp. 65-79 ◽  
Author(s):  
Irène Gijbels ◽  
Peter Hall ◽  
Aloïs Kneip
Keyword(s):  
Normal Distribution ◽  
Confidence Intervals ◽  
Simulation Study ◽  
Sampling Error ◽  
Confidence Bands ◽  
Unusual Feature ◽  
Nile River ◽  
Flow Volume ◽  
Jump Point ◽  
Point Estimator

Jump points in curves arise when the conditions under which data are generated change suddenly, for example because of an unplanned change in a treatment. This paper suggests bootstrap methods for quantifying the error in estimates of jump points, and for constructing confidence intervals for jump points and confidence bands for the curve. These problems have the unusual feature that the sampling error of the jump-point estimator often has a highly non-normal distribution, which depends intimately on the distribution of regression errors. The methods are illustrated by a simulation study as well as by an application to data on the annual flow volume of the Nile river.

Verification of the Calculation Assumptions Applied to Solutions of the Acoustic Measurements Uncertainty

2015 ◽  
Vol 39 (2) ◽  
pp. 199-202
Author(s):  
Wojciech Batko ◽  
Renata Bal
Keyword(s):  
Normal Distribution ◽  
Confidence Intervals ◽  
Uncertainty Of Measurement ◽  
Acoustic Measurements ◽  
Uncertainty In Measurement ◽  
Sound Levels ◽  
Measurement Results ◽  
Analysis Of Results ◽  
Essential Problem ◽  
Expression Of Uncertainty

Abstract The assessment of the uncertainty of measurement results, an essential problem in environmental acoustic investigations, is undertaken in the paper. An attention is drawn to the - usually omitted - problem of the verification of assumptions related to using the classic methods of the confidence intervals estimation, for the controlled measuring quantity. Especially the paper directs attention to the need of the verification of the assumption of the normal distribution of the measuring quantity set, being the base for the existing and binding procedures of the acoustic measurements assessment uncertainty. The essence of the undertaken problem concerns the binding legal and standard acts related to acoustic measurements and recommended in: 'Guide to the expression of uncertainty in measurement' (GUM) (OIML 1993), developed under the aegis of the International Bureau of Measures (BIPM). The model legitimacy of the hypothesis of the normal distribution of the measuring quantity set in acoustic measurements is discussed and supplemented by testing its likelihood on the environment acoustic results. The Jarque-Bery test based on skewness and flattening (curtosis) distribution measures was used for the analysis of results verifying the assumption. This test allows for the simultaneous analysis of the deviation from the normal distribution caused both by its skewness and flattening. The performed experiments concerned analyses of the distribution of sound levels: LD, LE, LN, LDWN, being the basic noise indicators in assessments of the environment acoustic hazards.

scholarly journals Test-Retest Reliability is not a Measure of Reliability or Stability: A Friendly Reminder

2020 ◽  
Author(s):  
Lukas Röseler ◽  
Daniel Wolf ◽  
Johannes Leder ◽  
Astrid Schütz
Keyword(s):  
Confidence Intervals ◽  
Simulation Study ◽  
Repeated Measurement ◽  
Reliability Coefficient ◽  
Diagnostic Instrument ◽  
Retest Reliability ◽  
Cronbach's Alpha ◽  
Correction For Attenuation ◽  
The Stability ◽  
Test Retest Reliability

We argue that the test-retest reliability coefficient, which is the correlation between a measurement and a repeated measurement using the same diagnostic instrument in the same sample (sometimes referred to as repeatability or falsely referred to as stability), is by itself not an appropriate measure of the reliability of the diagnostic instrument or of the stability of the construct in question. In combination with an actual coefficient of reliability such as Cronbach’s alpha, the test-retest reliability coefficient can be used to estimate and compare the stabilities of constructs using a procedure based on the correction for attenuation. However, results from a simulation study showed that classically constructed confidence intervals for the estimator exhibit under-coverage and thus cannot be interpreted correctly.

scholarly journals The Shortest Confidence Interval for the Mean of a Normal Distribution

2018 ◽  
Vol 7 (2) ◽  
pp. 33
Author(s):  
Traoré Boubakar ◽  
Diabaté Lassina ◽  
Touré Belco ◽  
Fané Abdou
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Mathematical Statistics ◽  
Standard Normal Distribution ◽  
Pivotal Quantity ◽  
Construction Technique ◽  
Standard Normal ◽  
The Mean ◽  
Shortest Confidence Intervals

An interesting topic in mathematical statistics is that of the construction of the confidence intervals. Two kinds of intervals which are both based on the method of pivotal quantity are the shortest confidence interval and the equal tail confidence intervals. The aim of this paper is to clarify and comment on the finding of such intervals and to investigation the relation between the two kinds of intervals. In particular, we will give a construction technique of the shortest confidence intervals for the mean of the standard normal distribution. Examples illustrating the use of this technique are given.

scholarly journals Overlap coefficients based on Kullback-Leibler divergence: Exponential populations case

2017 ◽  
Vol 6 (4) ◽  
pp. 135
Author(s):  
Hamza Dhaker ◽  
Papa Ngom ◽  
Malick Mbodj
Keyword(s):  
Statistical Inference ◽  
Mean Square Error ◽  
Confidence Intervals ◽  
Taylor Series ◽  
Simulation Study ◽  
Invariance Property ◽  
Mean Square ◽  
Taylor Series Approximation ◽  
Leibler Divergence ◽  
Exponential Populations

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita’s measure ρ, Morisita’s measure λ and Weitzman’s measure ∆. A new overlap measure Λ based on Kullback-Leibler measure is proposed. The invariance property and a method of statistical inference of these coefficients also are presented. Taylor series approximation are used to construct confidence intervals for the overlap measures. The bias and mean square error properties of the estimators are studied through a simulation study.

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