Small-Sample Quantile Estimators in a Large Nonparametric Model

2006 ◽  
Vol 35 (7) ◽  
pp. 1223-1241 ◽  
Author(s):  
Ryszard Zieliński
Keyword(s):  
Small Sample ◽  
Nonparametric Model ◽  
Sample Quantile ◽  
Quantile Estimators

scholarly journals The comparison of the scores obtained by Bayesian nonparametric model and classical test theory methods

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110283
Author(s):  
Meltem Yurtcu ◽  
Hülya Kelecioglu ◽  
Edward L Boone
Keyword(s):  
Classical Test Theory ◽  
Small Sample ◽  
Test Theory ◽  
Nonparametric Model ◽  
Bayesian Nonparametric ◽  
Test Equating ◽  
Classical Test ◽  
A Value ◽  
Item Functioning ◽  
The Individual

Bayesian Nonparametric (BNP) modelling can be used to obtain more detailed information in test equating studies and to increase the accuracy of equating by accounting for covariates. In this study, two covariates are included in the equating under the Bayes nonparametric model, one is continuous, and the other is discrete. Scores equated with this model were obtained for a single group design for a small group in the study. The equated scores obtained with the model were compared with the mean and linear equating methods in the Classical Test Theory. Considering the equated scores obtained from three different methods, it was found that the equated scores obtained with the BNP model produced a distribution closer to the target test. Even the classical methods will give a good result with the smallest error when using a small sample, making equating studies valuable. The inclusion of the covariates in the model in the classical test equating process is based on some assumptions and cannot be achieved especially using small groups. The BNP model will be more beneficial than using frequentist methods, regardless of this limitation. Information about booklets and variables can be obtained from the distributors and equated scores that obtained with the BNP model. In this case, it makes it possible to compare sub-categories. This can be expressed as indicating the presence of differential item functioning (DIF). Therefore, the BNP model can be used actively in test equating studies, and it provides an opportunity to examine the characteristics of the individual participants at the same time. Thus, it allows test equating even in a small sample and offers the opportunity to reach a value closer to the scores in the target test.

scholarly journals Scaling of High-Quantile Estimators

2011 ◽  
Vol 48 (04) ◽  
pp. 968-983 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts
Keyword(s):  
Heavy Tails ◽  
Global Financial Crisis ◽  
Financial Institution ◽  
Small Sample ◽  
Accurate Estimation ◽  
Risk Capital ◽  
High Quantile ◽  
Quantile Estimators ◽  
Small Sample Sizes ◽  
The Global Financial Crisis

Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

scholarly journals Conditional Quantile Estimators: A Small Sample Theory

2021 ◽  
Author(s):  
Grigory Franguridi ◽  
Bulat Gafarov ◽  
Kaspar Wuthrich
Keyword(s):  
Small Sample ◽  
Conditional Quantile ◽  
Quantile Estimators

scholarly journals Scaling of High-Quantile Estimators

2011 ◽  
Vol 48 (4) ◽  
pp. 968-983 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts
Keyword(s):  
Heavy Tails ◽  
Global Financial Crisis ◽  
Financial Institution ◽  
Small Sample ◽  
Accurate Estimation ◽  
Risk Capital ◽  
High Quantile ◽  
Quantile Estimators ◽  
Small Sample Sizes ◽  
The Global Financial Crisis

Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

scholarly journals Nonparametric Limits of Agreement for Small to Moderate Sample Sizes: A Simulation Study

Stats ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 343-355 ◽  
Author(s):  
Maria E. Frey ◽  
Hans C. Petersen ◽  
Oke Gerke
Keyword(s):  
Simulation Study ◽  
Method Comparison ◽  
Quantile Estimation ◽  
Observer Variability ◽  
Sample Quantile ◽  
Sample Sizes ◽  
Limits Of Agreement ◽  
Variability Analysis ◽  
Quantitative Measurements ◽  
Quantile Estimators

The assessment of agreement in method comparison and observer variability analysis of quantitative measurements is usually done by the Bland–Altman Limits of Agreement, where the paired differences are implicitly assumed to follow a normal distribution. Whenever this assumption does not hold, the 2.5% and 97.5% percentiles are obtained by quantile estimation. In the literature, empirical quantiles have been used for this purpose. In this simulation study, we applied both sample, subsampling, and kernel quantile estimators, as well as other methods for quantile estimation to sample sizes between 30 and 150 and different distributions of the paired differences. The performance of 15 estimators in generating prediction intervals was measured by their respective coverage probability for one newly generated observation. Our results indicated that sample quantile estimators based on one or two order statistics outperformed all of the other estimators and they can be used for deriving nonparametric Limits of Agreement. For sample sizes exceeding 80 observations, more advanced quantile estimators, such as the Harrell–Davis and estimators of Sfakianakis–Verginis type, which use all of the observed differences, performed likewise well, but may be considered intuitively more appealing than simple sample quantile estimators that are based on only two observations per quantile.

scholarly journals TESTING FOR STRUCTURAL CHANGE IN TIME-VARYING NONPARAMETRIC REGRESSION MODELS

2014 ◽  
Vol 31 (4) ◽  
pp. 811-859 ◽  
Author(s):  
Michael Vogt
Keyword(s):  
Regression Models ◽  
Asymptotic Properties ◽  
Regression Function ◽  
Real Data ◽  
Small Sample ◽  
Time Span ◽  
Nonparametric Model ◽  
Time Varying ◽  
Test Statistic ◽  
Set Up

In this paper, we consider a nonparametric model with a time-varying regression function and locally stationary regressors. We are interested in the question whether the regression function has the same shape over a given time span. To tackle this testing problem, we propose a kernel-based L2-test statistic. We derive the asymptotic distribution of the statistic both under the null and under fixed and local alternatives. To improve the small sample behavior of the test, we set up a wild bootstrap procedure and derive the asymptotic properties thereof. The theoretical analysis of the paper is complemented by a simulation study and a real data example.

Probing the ultrastructure of the mitotic and meiotic spindle in eggs: An expeditious approach based on semi-thin (0.25 μm) serial sections

1983 ◽  
Vol 41 ◽  
pp. 552-555
Author(s):  
Conly L. Rieder ◽  
S. Bowser ◽  
R. Nowogrodzki ◽  
K. Ross ◽  
G. Sluder
Keyword(s):  
Small Sample Size ◽  
Small Sample ◽  
Meiotic Spindle ◽  
Serial Sections ◽  
Mitotic Apparatus ◽  
Thin Sections ◽  
Cell Cycles ◽  
Ultrastructural Studies

Eggs have long been a favorite material for studying the mechanism of karyokinesis in-vivo and in-vitro. They can be obtained in great numbers and, when fertilized, divide synchronously over many cell cycles. However, they are not considered to be a practical system for ultrastructural studies on the mitotic apparatus (MA) for several reasons, the most obvious of which is that sectioning them is a formidable task: over 1000 ultra-thin sections need to be cut from a single 80-100 μm diameter egg and of these sections only a small percentage will contain the area or structure of interest. Thus it is difficult and time consuming to obtain reliable ultrastructural data concerning the MA of eggs; and when it is obtained it is necessarily based on a small sample size.We have recently developed a procedure which will facilitate many studies concerned with the ultrastructure of the MA in eggs. It is based on the availability of biological HVEM's and on the observation that 0.25 μm thick serial sections can be screened at high resolution for content (after mounting on slot grids and staining with uranyl and lead) by phase contrast light microscopy (LM; Figs 1-2).

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