Nonparametric estimation of residual variance revisited

Seifert, Burkhardt; Gasser, Théo

doi:10.1093/biomet/80.2.373

Cited by 48 publications

(25 citation statements)

References 24 publications

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“…where l denotes the difference operator applied l subsequent times (Rice, 1984;Hall et al, 1990;Seifert et al, 1993;Dette et al, 1998). This estimator was introduced in Vrugt et al (2005) and was shown to work well for daily and hourly discharge data.…”

Section: Case Studies: Hydrologic Modelingmentioning

confidence: 99%

Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

Sadegh

Vrugt

2013

Hydrol. Earth Syst. Sci.

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Abstract. In recent years, a strong debate has emerged in the hydrologic literature regarding how to properly treat nontraditional error residual distributions and quantify parameter and predictive uncertainty. Particularly, there is strong disagreement whether such uncertainty framework should have its roots within a proper statistical (Bayesian) context using Markov chain Monte Carlo (MCMC) simulation techniques, or whether such a framework should be based on a quite different philosophy and implement informal likelihood functions and simplistic search methods to summarize parameter and predictive distributions. This paper is a follow-up of our previous work published in Vrugt and Sadegh (2013) and demonstrates that approximate Bayesian computation (ABC) bridges the gap between formal and informal statistical model-data fitting approaches. The ABC methodology has recently emerged in the fields of biology and population genetics and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics that measure the distance of each model simulation to the data. This paper further studies the theoretical and numerical equivalence of formal and informal Bayesian approaches using discharge and forcing data from different watersheds in the United States, in particular generalized likelihood uncertainty estimation (GLUE). We demonstrate that the limits of acceptability approach of GLUE is a special variant of ABC if each discharge observation of the calibration data set is used as a summary diagnostic.

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Section: Case Studies: Hydrologic Modelingmentioning

confidence: 99%

Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

Sadegh

Vrugt

2013

Hydrol. Earth Syst. Sci.

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“…For the estimation of variance σ 2 , usually one fits the regression function m first by smoothing spline or kernel regression (Müller and Stadtmüller 1987;Hall and Carroll 1989;Neumann 1994), and then estimate variance σ 2 from residual sum of squares. However, the regression function estimation depends on the amount of smoothing (Dette et al 1998), which requires knowledge about some unknown quantities such as 1 0 {m (1) (x)} 2 dx (Hall and Marron 1990), 1 0 {m (2) (x)} 2 dx (Buckley et al 1988), and even 1 0 {m (l) (x)} 2 dx where l is a derivative order (Seifert et al 1993;Eubank 1999;Wang 2011). Moreover, few methods are proposed to estimate the amount of smoothness 1 0 {m (l) (x)} 2 dx.…”

Section: Introductionmentioning

confidence: 99%

“…With respect to the Rice-type estimator, Müller and Stadtmüller (1999) proposed the lagged Rice estimator; Müller et al (2003) proposed a covariate-matched U-statistic; Tong and Wang (2005) further improved the lagged Rice estimator via estimating the variance as the intercept in a linear regression model, and the asymptotic optimal rate is discussed in Tong et al (2013), Dai and Tong (2014) proposed a pairwise regression for models with jump discontinuities. As for the Gasser-type estimator, Seifert et al (1993) generalized to a higher-order version, and Du and Schick (2009) proposed a covariate-matched U-statistic. For the differenced estimators above, there exist the following problems.…”

Section: Introductionmentioning

confidence: 99%

Optimal variance estimation based on lagged second-order difference in nonparametric regression

Wang

Yu³

2016

Comput Stat

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Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only n 1/2 -consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample.

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“…However, because of input, state, and structural errors the statistics of the model residual will not necessarily behave in a fashion similar to the statistics of the streamflow measurement error. In this paper, we use an alternative nonparametric approach for estimating the properties of the measurement error in a data series (e.g., Rice 1984;Hall et al 1990;Seifert et al 1993;Dette et al 1998). This method assumes that the measurement errors are random in nature, and involves taking the time difference of the original time series, z t , and estimating the error deviation as…”

Section: Experimental Design and Data Usedmentioning

confidence: 99%

Real-Time Data Assimilation for Operational Ensemble Streamflow Forecasting

Vrugt

Gupta

Nualláin

et al. 2006

Journal of Hydrometeorology

147

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Operational flood forecasting requires that accurate estimates of the uncertainty associated with modelgenerated streamflow forecasts be provided along with the probable flow levels. This paper demonstrates a stochastic ensemble implementation of the Sacramento model used routinely by the National Weather Service for deterministic streamflow forecasting. The approach, the simultaneous optimization and data assimilation method (SODA), uses an ensemble Kalman filter (EnKF) for recursive state estimation allowing for treatment of streamflow data error, model structural error, and parameter uncertainty, while enabling implementation of the Sacramento model without major modification to its current structural form. Model parameters are estimated in batch using the shuffled complex evolution metropolis stochasticensemble optimization approach (SCEM-UA). The SODA approach was implemented using parallel computing to handle the increased computational requirements. Studies using data from the Leaf River, Mississippi, indicate that forecast performance improvements on the order of 30% to 50% can be realized even with a suboptimal implementation of the filter. Further, the SODA parameter estimates appear to be less biased, which may increase the prospects for finding useful regionalization relationships.

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Nonparametric estimation of residual variance revisited

Cited by 48 publications

References 24 publications

Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

Optimal variance estimation based on lagged second-order difference in nonparametric regression

Real-Time Data Assimilation for Operational Ensemble Streamflow Forecasting

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