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Sartore, Luca (2014) Quantile Regression and Bass Models in Hydrology. [Ph.D. thesis]

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Abstract (english)

Spatiotemporal phenomena related to the rainfall measurements can be characterised by statistical models grounded on physical concepts instead of being identified by spatiotemporal patterns based on standard correlations and related analytical tools. This perspective is useful in understanding if the relationships among neighbouring zones and consecutive years are attributable to latent physical mechanisms. Satellite data are used to examine this theory and provide evidence on empirical basis.
A recent hydrological theory, which is based on the concept of self-organisation, consists of simplified physical mechanisms that are essential for the explanation of local data relationships. The regression models inspired by the diffusion of innovation can approximate the evolution of the rainfall process within a year through a more straightforward perspective.
However, the multitude of collected data requires innovative techniques of data management and advanced analytical solutions, in order to achieve optimal results in reasonable time. Indeed, the nonlinear least squares and nonlinear quantile regression are considered to make inference on the response variable given some covariates.
A new quantile regression technique is developed in order to provide simultaneous estimates that do not violate the monotonicity property of quantiles. The nonlinear least squares highlight strong connections among rainfall and the salient features of the measurements areas. Furthermore, the quantile regression analyses quantify the intrinsic variability of the data.

Abstract (italian)

I fenomeni spazio-temporali relativi alle misurazioni di piovosità possono essere caratterizzati da modelli statistici fondati su concetti fisici invece di essere identificati da modelli standard basati su correlazioni spazio-temporali e i relativi strumenti analitici. Questa prospettiva è utile per capire se i rapporti tra zone confinanti e anni consecutivi sono attribuibili a meccanismi fisici latenti. Dati satellitari vengono utilizzati per esaminare questa teoria e fornire prove su base empirica.
Una recente teoria idrologica, basata sul concetto di auto-organizzazione, è caratterizzata da meccanismi fisici semplificati che sono essenziali per la spiegazione delle relazioni locali presenti nei dati osservati. I modelli di regressione, che si ispirano alla teoria della diffusione di innovazioni, sono in grado di approssimare l'evoluzione del processo di precipitazione di un singolo anno attraverso una più semplice prospettiva.
Tuttavia, la moltitudine di informazioni raccolte richiede tecniche innovative di gestione dei dati e soluzioni analitiche avanzate con lo scopo di ottenere risultati ottimali in tempi ragionevoli. Infatti, i minimi quadrati e la regressione quantilica per modelli non-lineari vengono utilizzati per fare inferenza sulla variabile risposta condizionatamente ad alcune covariate.
Una nuova tecnica di regressione quantilica è stata sviluppata ad hoc al fine di fornire stime simultanee che non vìolino la proprietà di monotonicità dei quantili. I minimi quadrati non lineari evidenziano un forte legame tra le precipitazioni e alcune caratteristiche salienti delle zone di misurazione. Inoltre, le analisi ottenute tramite la regressione quantilica quantificano la variabilità intrinseca nei dati.

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EPrint type:Ph.D. thesis
Tutor:Guseo, Renato
Supervisor:Furlan, Claudia
Ph.D. course:Ciclo 26 > Scuole 26 > SCIENZE STATISTICHE
Data di deposito della tesi:29 January 2014
Anno di Pubblicazione:31 January 2014
Key Words:rainfall constrained penalized regression Bemmaor innovation diffusion goodness fit test confidence interval region simulation empirical distribution nonlinear semi-parametric generalized Bass quantile sheet optimization Levenberg Marquardt
Settori scientifico-disciplinari MIUR:Area 13 - Scienze economiche e statistiche > SECS-S/01 Statistica
Struttura di riferimento:Dipartimenti > Dipartimento di Scienze Statistiche
Codice ID:6589
Depositato il:04 Nov 2014 13:58
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