Resample-smoothing of Voronoi intensity estimators

Moradi, Mehdi; Cronie, Ottmar; Rubak, Ege; Lachièze-Rey, Raphaël; Mateu, Jorge; Baddeley, Adrian

doi:10.1007/s11222-018-09850-0

Cited by 37 publications

(38 citation statements)

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“…The spatiotemporal intensity functions of the drought events and the anomalous wet conditions are estimated with a resample‐smoothed Voronoi estimator (Moradi et al, ). Let Y ={ x 1 ,…, x N }⊂[0, T ] be the collection of random time points associated to the events occurring in the time interval [0, T ], and denoting the associated spatial extents with

\underline{s} \leq s_{i} \leq \overset{s}{true}

, i =1,…, N , we obtain the spatiotemporal point process

X = false{false(x_{1}, s_{1} false), ⋯, false(x_{N}, s_{N} false) false} \subset false[0, T false] \times false[\underline{s}, \overset{s}{true} false]

.…”

Section: Methodsmentioning

confidence: 99%

“…Then, the resample‐smoothed Voronoi estimator (Moradi et al, ) is given by

{\overset{ρ}{true}}_{p, m} false(t, v false) = \frac{1}{m p} true \sum_{i = 1}^{m} {\overset{ρ}{true}}_{i} false(t, v false) = true \sum_{i = 1}^{m} \sum_{false(x, s false) \in X_{i, p}} \frac{double-struck1 false{false(t, v false) \in V_{false(x, s false)} false(X_{i, p} false) false}}{m p false| V_{false(x, s false)} false(X_{i, p} false) false|}, false(t, v false) \in false[0, T false] \times false[\underline{s}, \overset{s}{true} false],

where for any ( x , s )∈ X i , p ,

false| V_{false(x, s false)} false(X_{i, p} false) false|

is the size of

V_{false(x, s false)} false(X_{i, p} false) = false{u \in false[0, T false] \times false[\underline{s}, \overset{s}{true} false] : false‖ u - false(x, s false) false‖ \leq false‖ u - false(x^{'}, s^{'} false) false‖ for any false(x^{'}, s^{'} false) \in X_{i, p} ∖ false{false(x, s false) false} false},

which is the Voronoi cell consisting of all points

u \in false[0, T false] \times false[\underline{s}, \overset{s}{true} false]

closer to ( x , s ) tha...…”

Section: Methodsmentioning

confidence: 99%

“…Let further X 1,p , … , X m,p be m ≥ 1 independent p-thinnings of X, 0 ≤ p ≤ 1; we obtain each collection X i,p by running through the points of X and independently 10.1029/2019EF001170 throwing out each of its points with probability 1 − p. Then, the resample-smoothed Voronoi estimator (Moradi et al, 2019) is given bŷ…”

Section: 1029/2019ef001170mentioning

confidence: 99%

“…which is the Voronoi cell consisting of all points u ∈ [0, T]× [s,s] closer to (x, s) than any (x ′ , s ′ ) ∈ X i,p ⧵{(x, s)} in terms of the Euclidean distance. It has been suggested (Moradi et al, 2019) to choose p and m such that 0 < p ≤ 0.2 and m ≥ 400. The interval [0, T] is here chosen empirically by letting 0 represent the first observed event time minus half its distance to the second smallest observed event time.…”

Section: 1029/2019ef001170mentioning

confidence: 99%

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The Exceptional 2018 European Water Seesaw Calls for Action on Adaptation

et al. 2019

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Temperature and precipitation are the most important factors responsible for agricultural productivity variations. In 2018 spring/summer growing season, Europe experienced concurrent anomalies of both. Drought conditions in central and northern Europe caused yield reductions up to 50% for the main crops, yet wet conditions in southern Europe saw yield gains up to 34%, both with respect to the previous 5‐year mean. Based on the analysis of documentary and natural proxy‐based seasonal paleoclimate reconstructions for the past half millennium, we show that the 2018 combination of climatic anomalies in Europe was unique. The water seesaw, a marked dipole of negative water anomalies in central Europe and positive ones in southern Europe, distinguished 2018 from the five previous similar droughts since 1976. Model simulations reproduce the 2018 European water seesaw in only 4 years out of 875 years in historical runs and projections. Future projections under the RCP8.5 scenario show that 2018‐like temperature and rainfall conditions, favorable to crop growth, will occur less frequent in southern Europe. In contrast, in central Europe high‐end emission scenario climate projections show that droughts as intense as 2018 could become a common occurrence as early as 2043. While integrated European and global agricultural markets limited agro‐economic shocks caused by 2018's extremes, there is an urgent need for adaptation strategies for European agriculture to consider futures without the benefits of any water seesaw.

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\underline{s} \leq s_{i} \leq \overset{s}{true}

, i =1,…, N , we obtain the spatiotemporal point process

X = false{false(x_{1}, s_{1} false), ⋯, false(x_{N}, s_{N} false) false} \subset false[0, T false] \times false[\underline{s}, \overset{s}{true} false]

.…”

Section: Methodsmentioning

confidence: 99%

“…Then, the resample‐smoothed Voronoi estimator (Moradi et al, ) is given by

{\overset{ρ}{true}}_{p, m} false(t, v false) = \frac{1}{m p} true \sum_{i = 1}^{m} {\overset{ρ}{true}}_{i} false(t, v false) = true \sum_{i = 1}^{m} \sum_{false(x, s false) \in X_{i, p}} \frac{double-struck1 false{false(t, v false) \in V_{false(x, s false)} false(X_{i, p} false) false}}{m p false| V_{false(x, s false)} false(X_{i, p} false) false|}, false(t, v false) \in false[0, T false] \times false[\underline{s}, \overset{s}{true} false],

where for any ( x , s )∈ X i , p ,

false| V_{false(x, s false)} false(X_{i, p} false) false|

is the size of

V_{false(x, s false)} false(X_{i, p} false) = false{u \in false[0, T false] \times false[\underline{s}, \overset{s}{true} false] : false‖ u - false(x, s false) false‖ \leq false‖ u - false(x^{'}, s^{'} false) false‖ for any false(x^{'}, s^{'} false) \in X_{i, p} ∖ false{false(x, s false) false} false},

which is the Voronoi cell consisting of all points

u \in false[0, T false] \times false[\underline{s}, \overset{s}{true} false]

closer to ( x , s ) tha...…”

Section: Methodsmentioning

confidence: 99%

Section: 1029/2019ef001170mentioning

confidence: 99%

Section: 1029/2019ef001170mentioning

confidence: 99%

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The Exceptional 2018 European Water Seesaw Calls for Action on Adaptation

et al. 2019

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“…A lo largo del mismo capítulo, y utilizando los métodos propuestos, también se analizan varios conjuntos de datos reales como datos del crimen de Castellón, (España) y Chicago (EEUU) y los accidentes de tráfico de Medellín (Colombia) y Western Australia (Australia). vii El Capítulo 3 propone una nueva técnica para proporcionar un estimador de intensidad adaptativo para procesos de puntos espaciales independientemente del state space (Moradi et al, 2018a). La técnica es introducida y aplicada a los estimadores de intensidad de Voronoi.…”

Section: Introductionunclassified

Spatial and spatio-temporal point patterns on linear networks

Moradi¹

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Partial characteristics for marked spatial point processes

Eckardt

Mateu

2019

Environmetrics

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This paper introduces a new class of partial summary characteristics for two types of marked planar point processes. We consider purely qualitatively marked spatial point processes and multitype spatial point processes with quantitative marks. After a survey of classical functional summary characteristics for qualitatively and quantitatively marked point processes, the class of partial characteristics is presented. These characteristics are defined through the periodogram, which makes the computations efficient. We demonstrate the application of our method in the analysis of a multispecies tree data recorded in the City of Melbourne.

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Resample-smoothing of Voronoi intensity estimators

Cited by 37 publications

References 47 publications

The Exceptional 2018 European Water Seesaw Calls for Action on Adaptation

The Exceptional 2018 European Water Seesaw Calls for Action on Adaptation

Spatial and spatio-temporal point patterns on linear networks

Partial characteristics for marked spatial point processes

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