Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data

Bouezmarni, Taoufik; Ghouch, Anouar El; Mesfioui, Mhamed

doi:10.1155/2011/937574

Cited by 18 publications

(15 citation statements)

References 21 publications

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“…As shown in many studies (Schuster, 1985;Marron and Ruppert, 1994;Chen, 2000;Bouezmarni et al, 2011), since the normal KDE is symmetric, it could have a significant boundary bias for bounded data as, for example the ECV SM, which can only take values on the interval (0, 1), i.e. f(x) = 0 for x / ∈ (0, 1).…”

Section: The Empirical Standardized Soil Moisture Indexmentioning

confidence: 99%

“…(1) it avoids having to assume the existence of representative parametric distributions (Farahmand and AghaKouchak, 2015); (2) it avoids the bias problems associated with relatively small sample data sets (Sienz et al, 2012); (3) it allows for boundary bias correction of statistical data distributions supported on a finite interval (Bouezmarni et al, 2011). The ESSMI standardizes the observed soil moisture at a particular location during a period of time (e.g.…”

Section: Introductionmentioning

confidence: 99%

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An empirical standardized soil moisture index for agricultural drought assessment from remotely sensed data

Carrão

Russo

Sepulcre-Cantó

et al. 2016

International Journal of Applied Earth Observation and Geoinfor

126

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a b s t r a c tWe propose a simple, spatially invariant and probabilistic year-round Empirical Standardized Soil Moisture Index (ESSMI) that is designed to classify soil moisture anomalies from harmonized multi-satellite surface data into categories of agricultural drought intensity. The ESSMI is computed by fitting a nonparametric empirical probability density function (ePDF) to historical time-series of soil moisture observations and then transforming it into a normal distribution with a mean of zero and standard deviation of one. Negative standard normal values indicate dry soil conditions, whereas positive values indicate wet soil conditions. Drought intensity is defined as the number of negative standard deviations between the observed soil moisture value and the respective normal climatological conditions. To evaluate the performance of the ESSMI, we fitted the ePDF to the Essential Climate Variable Soil Moisture (ECV SM) v02.0 data values collected in the period between January 1981 and December 2010 at South-Central America, and compared the root-mean-square-errors (RMSE) of residuals with those of beta and normal probability density functions (bPDF and nPDF, respectively). Goodness-of-fit results attained with time-series of ECV SM values averaged at monthly, seasonal, half-yearly and yearly timescales suggest that the ePDF provides triggers of agricultural drought onset and intensity that are more accurate and precise than the bPDF and nPDF. Furthermore, by accurately mapping the occurrence of major drought events over the last three decades, the ESSMI proved to be spatio-temporal consistent and the ECV SM data to provide a well calibrated and homogenized soil moisture climatology for the region. Maize, soybean and wheat crop yields in the region are highly correlated (r > 0.82) with cumulative ESSMI values computed during the months of critical crop growing, indicating that the nonparametric index of soil moisture anomalies can be used for agricultural drought assessment.

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Section: The Empirical Standardized Soil Moisture Indexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An empirical standardized soil moisture index for agricultural drought assessment from remotely sensed data

Carrão

Russo

Sepulcre-Cantó

et al. 2016

International Journal of Applied Earth Observation and Geoinfor

126

View full text Add to dashboard Cite

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“…We use Kernel Density Estimate to calculate the PDFs on the empirical data. Mathematically, a kernel is a positive function K(x; h) controlled by the bandwidth parameter h [23]. With this kernel function, the density estimate to a point x within a group of points x i ; i = 1...N is defined as:…”

Section: Definition 3 (Activity Sequence) An Activity Sequence Is Timentioning

confidence: 99%

A Stochastic Model for Residential User Activity Simulation

Liu

Yang

et al. 2019

Energies

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User activities is an important input to energy modelling, simulation and performance studies of residential buildings. However, it is often difficult to obtain detailed data on user activities and related energy consumption data. This paper presents a stochastic model based on Markov chain to simulate user activities of the households with one or more family members, and formalizes the simulation processes under different conditions. A data generator is implemented to create fine-grained activity sequences that require only a small sample of time-use survey data as a seed. This paper evaluates the data generator by comparing the generated synthetic data with real data, and comparing other related work. The results show the effectiveness of the proposed modelling approach and the efficiency of generating realistic residential user activities.

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“…Liang et al ([4], 2005) obtained the optimal convergence rates of the nonlinear wavelet estimators of the hazard rate function when the survival times form a stationary strong mixing sequence. Bouezmarni et al ([5], 2011) proposed new estimators based on the gamma kernels for density and hazard rate functions which are free of bias, and achieved the optimal rate of convergence in terms of integrated mean squared error, and so on.…”

Section: Introductionmentioning

confidence: 99%