scholarly journals Efficient bootstrap estimates for tail statistics

2017 ◽  
Vol 17 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Øyvind Breivik ◽  
Ole Johan Aarnes
Keyword(s):  
Confidence Intervals ◽  
Distributed Model ◽  
Small Subset ◽  
High Temporal Resolution ◽  
Entire Sample ◽  
Empirical Distributions ◽  
Parametric Bootstrapping ◽  
Large Ensembles ◽  
Bootstrap Estimates ◽  
Return Value

Abstract. Bootstrap resamples can be used to investigate the tail of empirical distributions as well as return value estimates from the extremal behaviour of the sample. Specifically, the confidence intervals on return value estimates or bounds on in-sample tail statistics can be obtained using bootstrap techniques. However, non-parametric bootstrapping from the entire sample is expensive. It is shown here that it suffices to bootstrap from a small subset consisting of the highest entries in the sequence to make estimates that are essentially identical to bootstraps from the entire sample. Similarly, bootstrap estimates of confidence intervals of threshold return estimates are found to be well approximated by using a subset consisting of the highest entries. This has practical consequences in fields such as meteorology, oceanography and hydrology where return values are calculated from very large gridded model integrations spanning decades at high temporal resolution or from large ensembles of independent and identically distributed model fields. In such cases the computational savings are substantial.

scholarly journals Efficient Bootstrap Estimates for Tail Statistics

2016 ◽  
Author(s):  
Øyvind Breivik ◽  
Ole Johan Aarnes
Keyword(s):  
Confidence Intervals ◽  
Temporal Resolution ◽  
Small Subset ◽  
High Temporal Resolution ◽  
Data Set ◽  
Empirical Distributions ◽  
Bootstrap Techniques ◽  
Entire Sequence ◽  
Bootstrap Estimates ◽  
Return Value

Abstract. Bootstrap resamples can be used to investigate the tail of empirical distributions as well as return value estimates based on the extremal behaviour of the distribution. Specifically, the confidence intervals on return value estimates or bounds on in-sample tail statistics can be estimated using bootstrap techniques. However, bootstrapping from the entire data set is expensive. It is shown here that it suffices to bootstrap from a small subset consisting of the highest entries in the sequence to make estimates that are essentially identical to bootstraps from the entire sequence. Similarly, bootstrap estimates of confidence intervals of threshold return estimates are found to be well approximated by using a subset consisting of the highest entries. This has practical consequences in fields such as meteorology, oceanography and hydrology where return estimates are routinely made from very large gridded model integrations spanning decades at high temporal resolution. In such cases the computational savings are substantial.

scholarly journals Parametric Bootstrap Methods for Estimating Model Parameters of Non-homogeneous Gamma Process

2018 ◽  
Vol 3 (2) ◽  
pp. 167-176 ◽  
Author(s):  
Yasuhiro Saito ◽  
Tadashi Dohi
Keyword(s):  
Confidence Intervals ◽  
Bootstrap Method ◽  
Parametric Bootstrap ◽  
Gamma Process ◽  
Estimation Accuracy ◽  
Model Parameters ◽  
Trend Function ◽  
Bootstrap Methods ◽  
Parametric Bootstrapping ◽  
Simulation Based

Non-Homogeneous Gamma Process (NHGP) is characterized by an arbitrary trend function and a gamma renewal distribution. In this paper, we estimate the confidence intervals of model parameters of NHGP via two parametric bootstrap methods: simulation-based approach and re-sampling-based approach. For each bootstrap method, we apply three methods to construct the confidence intervals. Through simulation experiments, we investigate each parametric bootstrapping and each construction method of confidence intervals in terms of the estimation accuracy. Finally, we find the best combination to estimate the model parameters in trend function and gamma renewal distribution in NHGP.

scholarly journals Indirect downscaling of global circulation model data based on atmospheric circulation and temperature for projections of future precipitation in hourly resolution

2013 ◽  
Vol 10 (7) ◽  
pp. 8841-8874 ◽  
Author(s):  
F. Beck ◽  
A. Bárdossy
Keyword(s):  
Atmospheric Circulation ◽  
Regional Distribution ◽  
Circulation Model ◽  
High Temporal Resolution ◽  
Global Circulation Model ◽  
Hourly Precipitation ◽  
Atmospheric Circulation Patterns ◽  
Urban Sewage ◽  
Empirical Distributions ◽  
Global Circulation

Abstract. Many hydraulic applications like the design of urban sewage systems require projections of future precipitation in high temporal resolution. We developed a method to predict the regional distribution of hourly precipitation sums based on daily mean sea level pressure and temperature data from a Global Circulation Model. It is an indirect downscaling method avoiding uncertain precipitation data from the model. It is based on a fuzzy-logic classification of atmospheric circulation patterns (CPs) that is further subdivided by means of the average daily temperature. The observed empirical distributions at 30 rain gauges to each CP-temperature class are assumed as constant and used for projections of the hourly precipitation sums in the future. The method was applied to the CP-temperature sequence derived from the 20th century run and the scenario A1B run of ECHAM5. According to ECHAM5, the summers in southwest Germany will become progressively drier. Nevertheless, the frequency of the highest hourly precipitation sums will increase. According to the predictions, estival water stress and the risk of extreme hourly precipitation will both increase simultaneously during the next decades.

scholarly journals Significance of spatial variability in precipitation for process-oriented modelling: results from two nested catchments using radar and ground station data

2005 ◽  
Vol 9 (1/2) ◽  
pp. 29-41 ◽  
Author(s):  
D. Tetzlaff ◽  
S. Uhlenbrook
Keyword(s):  
High Resolution ◽  
Input Data ◽  
Radar Data ◽  
West Germany ◽  
Distributed Model ◽  
High Temporal Resolution ◽  
Ground Station ◽  
Station Data ◽  
Process Oriented ◽  
Catchment Model

Abstract. The importance of considering the spatial distribution of rainfall for process-oriented hydrological modelling is well-known. However, the application of rainfall radar data to provide such detailed spatial resolution is still under debate. In this study the process-oriented TACD (Tracer Aided Catchment model, Distributed) model had been used to investigate the effects of different spatially distributed rainfall input on simulated discharge and runoff components on an event base. TACD is fully distributed (50x50m2 raster cells) and was applied on an hourly base. As model input rainfall data from up to 7 ground stations and high resolution rainfall radar data from operational C-band radar were used. For seven rainfall events the discharge simulations were investigated in further detail for the mountainous Brugga catchment (40km2) and the St. Wilhelmer Talbach (15.2km2) sub-basin, which are located in the Southern Black Forest Mountains, south-west Germany. The significance of spatial variable precipitation data was clearly demonstrated. Dependent on event characteristics, localized rain cells were occasionally poorly captured even by a dense ground station network, and this resulted in inadequate model results. For such events, radar data can provide better input data. However, an extensive data adjustment using ground station data is required. For this purpose a method was developed that considers the temporal variability in rainfall intensity in high temporal resolution in combination with the total rainfall amount of both data sets. The use of the distributed catchment model allowed further insights into spatially variable impacts of different rainfall estimates. Impacts for discharge predictions are the largest in areas that are dominated by the production of fast runoff components. The improvements for distributed runoff simulation using high resolution rainfall radar input data are strongly dependent on the investigated scale, the event characteristics and the existing monitoring network.

scholarly journals Wave Extremes in the Northeast Atlantic

2012 ◽  
Vol 25 (5) ◽  
pp. 1529-1543 ◽  
Author(s):  
Ole Johan Aarnes ◽  
Øyvind Breivik ◽  
Magnar Reistad
Keyword(s):  
Confidence Intervals ◽  
Order Statistic ◽  
Significant Wave Height ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Gev Distribution ◽  
Northeast Atlantic ◽  
Generalized Pareto ◽  
Return Value ◽  
Meteorological Institute

The objective of this study is to compute 100-yr return value estimates of significant wave height using a new hindcast developed by the Norwegian Meteorological Institute. This regional hindcast covers the northeast Atlantic and spans the period 1958–2009. The return value estimates are based upon three different stationary models commonly applied in extreme value statistics: the generalized extreme value (GEV) distribution, the joint GEV distribution for the r largest-order statistic (rLOS), and the generalized Pareto (GP) distribution. Here, the qualitative differences between the models and their corresponding confidence intervals are investigated.

Accurate Calculation of Confidence Intervals on Predicted Extreme Met-Ocean Conditions When Using Small Datasets

2004 ◽  
Author(s):  
Daniel C. Brooker ◽  
Geoffrey K. Cole
Keyword(s):  
Confidence Intervals ◽  
Profile Likelihood ◽  
Parametric Bootstrap ◽  
Likelihood Method ◽  
Finite Sample ◽  
Likelihood Methods ◽  
Finite Sample Size ◽  
Design Values ◽  
Asymptotic Normal ◽  
Return Value

Estimation of high return period values of wind and wave conditions is usually done using a limited sample of data from measurement or hindcast studies. Because a finite sample size is used, the reliability of estimates is usually evaluated by constructing confidence intervals around design values such as the 100 year return value. In this paper, a numerical simulation study is used to compare the accuracy of calculated confidence intervals using several different calculation methods: the asymptotic normal, parametric bootstrap and profile likelihood methods. The accuracy of each method for different sample sizes is assessed for the truncated Weibull distribution. Based on these results, a profile likelihood method for estimation of confidence intervals is suggested for use when dealing with small datasets.

Rate of Sublimation of Ice by Radiative Heating in Freeze-Etching

1980 ◽  
Vol 38 ◽  
pp. 618-619
Author(s):  
Yeshayahu Talmon
Keyword(s):  
Heat Flux ◽  
Freeze Fracture ◽  
Constant Heat Flux ◽  
Radiative Heating ◽  
Constant Heat ◽  
Entire Sample ◽  
Simplified Method ◽  
Freeze Etching ◽  
Sublimation Rates ◽  
Fractured Surface

To bring out details in the fractured surface of a frozen sample in the freeze fracture/freeze-etch technique,the sample or part of it is warmed to enhance water sublimation.One way to do this is to raise the temperature of the entire sample to about -100°C to -90°C. In this case sublimation rates can be calculated by using plots such as Fig.1 (Talmon and Thomas),or by simplified formulae such as that given by Menold and Liittge. To achieve higher rates of sublimation without heating the entire sample a radiative heater can be used (Echlin et al.). In the present paper a simplified method for the calculation of the rates of sublimation under a constant heat flux F [W/m2] at the surface of the sample from a heater placed directly above the sample is described.

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