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We study the distribution of phases and amplitudes for the spectral representation of weighted moving averages of a general noise measure. The simple independent structure, known for the Gaussian case, and involving Rayleigh amplitude and uniform phase distributions, is lost for the non Gaussian noise case. We show that the amplitude/phase distributions exhibit a rich and more complex structure depending not just on the covariance of the process but specifically on the form of the kernel and the noise distribution. We present a theoretical tool for studying these distributions that follows from a proof of the spectral theorem that yields an explicit expression for the spectral measure. The main interest is in noise measures based on second-order Lévy motions since such measures are easily available through independent sampling. We approximate the spectral stochastic measure by independent noise increments which allows us to obtain amplitude/phase distributions that is of fundamental interest for analyzing processes in the frequency domain. For the purpose of approximating the moving average process through sums of trigonometric functions, we assess the mean square error of discretization of the spectral representation. For a specified accuracy, the approximation is explicitly given. We illustrate the method for the moving averages driven by the Laplace motion. © 2017 Taylor & Francis Group, LLC 1 15 Article in Press

The surface of the ocean, and so such quantities as the significant wave height, $H-s$, can be thought of as a random surface that develops over time. In this paper, we explore certain types of random fields in space and time, with and without dynamics that may or may not be driven by a physical law, as models for the significant wave height. Reanalysis data is used to estimate the sea-state motion which is modeled as a hidden Markov chain in a state space framework by means of an AR(1) process or in the presence of the dispersion relation. Parametric covariance models with and without dynamics are fitted to reanalysis and satellite data and compared to the empirical covariance functions. The derived models have been validated against satellite and buoy data. © 2010 John Wiley & Sons, Ltd. 22 3 354 369 Cited By :7

1 online ID: 885 In: Water resources research, Vol. 51, no. 6 (June 2015), p.4338-4358. Summary: AbstractA daily stochastic spatiotemporal precipitation generator that yields precipitation realizations that are quantitatively consistent is described. The methodology relies on a latent Gaussian field that drives both the occurrence and intensity of the precipitation process. For the precipitation intensity, the marginal distributions, which are space and time dependent, are described by a composite model of a gamma distribution for observations below some threshold with a generalized Pareto distribution modeling the excesses above the threshold. Model parameters are estimated from data and extrapolated to locations and times with no direct observations using linear regression of position covariates. One advantage of such a model is that stochastic generator parameters are readily available at any location and time of the year inside the stationarity regions. The methodology is illustrated for a network of 12 locations in Sweden. Performance of the model is judged through its ability to accurately reproduce a series of spatial dependence measures and weather indices.

The spectral representation of a moving average process obtained as a convolution of a kernel with a general noise measure is studied. A proof of the spectral theorem that yields explicit expression for the spectral measure in terms of the noise measure is presented. The main interest is in noise measures generated by second order Lévy motions. For practical considerations, such measures are easily available through independent sampling. On the other hand spectral measures are not since their increments are dependent, with the notable exception of the Gaussian noise case. For this reason the issue of approximating the spectral measure by independent increments of the noise is also addressed. For the purpose of approximating the moving average process through sums of trigonometric functions, the mean square error of discretization of the spectral representation is assessed. For a specified accuracy, the coefficients of approximation are explicitly given. The method is illustrated for moving averages processes driven by Laplace motion.

In this paper, we construct a homogeneous spatio-temporal model to describe the variability of significant wave height over small regions of the sea and over short periods of time. Then, the model is extended to a nonhomogeneous one that is valid over larger areas of the sea and for time periods of up to 10 h. To validate the proposed model, we reconstruct the significant wave height surface under different scenarios and then compare it to satellite measurements and the C-ERA-40 field. Copyright © 2008 John Wiley & Sons, Ltd. 20 1 14 31 Cited By :29

The Lamperti transformation of a self-similar process is a stationary process. In particular, the fractional Brownian motion transforms to the second order stationary Gaussian process. This process is represented as a series of independent processes. The terms of this series are Ornstein-Uhlenbeck processes if H1/2. From the representation effective approximations of the process are derived. The corresponding results for the fractional Brownian motion are obtained by applying the inverse Lamperti transformation. Implications for simulating the fractional Brownian motion are discussed. 40 5 1395 1435 Cited By :2

In this paper, we propose a new method for modelling precipitation in Sweden. We consider a chain dependent stochastic model that consists of a component that models the probability of occurrence of precipitation at a weather station and a component that models the amount of precipitation at the station when precipitation does occur. For the first component, we show that for most of the weather stations in Sweden a Markov chain of an order higher than one is required. For the second component, which is a Gaussian process with transformed marginals, we use a composite of the empirical distribution of the amount of precipitation below a given threshold and the generalized Pareto distribution for the excesses in the amount of precipitation above the given threshold. The derived models are then used to compute different weather indices. The distribution of the modelled indices and the empirical ones show good agreement, which supports the choice of the model. © 2008 Elsevier B.V. All rights reserved. 363 1-4 42 59 Cited By :23

Significant wave height (Hs) is a measure of the variability of the ocean surface. Benefits from knowing the spatial and temporal characteristics of this field are multiple: It is useful to size offshore structures, to foresee the fatigue of the ship's hull depending on its route and season, to compute probabilities of risks associated with marine operations. In this paper, we describe a method for modeling the Hs in space. The method is based on the Gaussian hypothesis for the logarithms of Hs and consists of estimating the mean and the covariance structure of log(Hs) using the information provided by the total variation. We then use the estimated parameters of every area in the world to construct maps of the median and the correlation structure. These maps are used to compute the probability of Hs exceeding a predefined level, and the distribution of the length of a storm. The data used are those of the TOPEX-Poseidon satellite. Copyright © by The International Society of Offshore and Polar Engineers. 18 1 1 7 Cited By :7

Significant wave height (Hs) is a measure of the variability of the ocean surface. Knowledge of the spatial and temporal characteristics of this field are multiple: it is useful to dimension offshore structures, to foresee the fatigue of the ship's hull depending on its route and season, or to compute probabilities of risks associated with marine operations. In this paper, we describe a method for modelling the Hs in space. The method is based on the Gaussian hypothesis for the logarithms of Hs and consists of estimating the mean and the covariance structure of log(Hs) using the information provided by the total variation. We then use the estimated parameters of every area in the world to construct maps of the median and the correlation structure. These maps are then used to compute the probability the Hs exceeds a pre-defined level, and the distribution of the length of a storm. The data used are that of the TOPEX-Poseidon satellite. Copyright ©2007 by The International Society of Offshore and Polar Engineers(ISOPE). 1822 1829 Sponsors: International Society of Offshore and Polar Engineers (ISOPE) Conference code: 70675 Cited By :2

The sea elevation at a fixed point is modelled by means of a second order model, which is a smooth algebraic function of a vector valued Gaussian process. Asymptotic methods, presented first in [1], are used to estimate the mean upcrossing intensity µ+(h). The intensity is then used to determine the density of crest height in a second order sea. Numerical examples illustrate the method. The proposed approximation is used to estimate the design crest height for a specified return period. Copyright © 2005 by ASME. 2 295 309 Sponsors: ASME Ocean, Offshore, and Arctic Engineering Division Conference code: 66012 Cited By :8

2004,3 ID: 886 Anastassia Baxevani Getr. Zählung graph. Darst Enth. 6 Aufsätze Zugl.: Lund, Univ., Diss., 2004 (DE-601)353619310 2004,3$92004000003

We study the probability distribution of the height of global maximum for a Gaussian random field evolving in time. Particularly, we discuss the role of the wave kinematics. It is observed that taking into account time dynamics of spatial characteristics results in distributions different from those obtained for the static case. We show how different characteristics of the sea surface like significant wave height, wave period and wave length along different directions, affect the distribution of the height of high crests. We demonstrate the results by computing the derived distribution for different Gaussian seas. Copyright © 2004 by The International Society of Offshore and Polar Engineers. 47 54 Sponsors: International Society of Offshore and Polar Engineers, ISOPE Conference code: 65480

The surface of the ocean, and so such quantities as the significant wave height, can be thought of as a random surface in space which develops over time. In this paper, we explore certain types of random fields (in space and time) as models for the significant wave height and fit these models to data obtained from the TOPEX-Poseidon satellite. The data consist of observations along different one-dimensional tracks over time. It is assumed that, for the region of ocean considered and for a fixed time, the data can be considered stationary. Further-more, the shape of the data suggests that it is reasonable to use a lognormal distribution. As the covariance function may change over time, the model chosen is fitted to the data for each time separately. The data over space exhibit variation at different scales and hence the covariance function needs to reflect this property. Consequently, a mixture of Gaussian functions is assumed for the covariance function. To fit the model to the data, the theoretical variogram is fitted to the empirical variogram using weighted least squares. Stochastic models for the variation of the parameter values were investigated. The results of fitting these models are discussed and interpreted. 1375 1382 Conference code: 62122 Cited By :3

For a stationary two-dimensional random field evolving in time, we derive the intensity distributions of appropriately defined velocities of crossing contours. The results are based on a generalization of the Rice formula. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. We study dynamical aspects of deep sea waves by applying the derived results to Gaussian fields modeling irregular sea surfaces. In doing so, we obtain distributions of velocities for the sea surface as well as for the envelope field based on this surface. Examples of wave and wave group velocities are computed numerically and illustrated graphically. 12 18 25 Sponsors: ISOPE Kyushu University Conference code: 62589

Includes bibliography. Number of sources in the bibliography: 224 Thesis (Ph. D.) -- University of Cyprus, Faculty of Pure and Applied Sciences, Department of Mathematics and Statistics, 2022. The University of Cyprus Library holds the printed form of the thesis. Precipitation modelling is important because it has a great impact in hydrology, ecology, agriculture, weather derivatives, drought and flood management. One difficulty in modelling phenomena like precipitation is that they are best described by a mixture of discrete and continuous distributions consisting of a continuous part and an atom at zero. These distributions are in most cases either skewed or have heavy tails or both. In this thesis, we investigate the compound Poisson-Gamma model that has the ability to model simultaneously the occurrence and intensity of precipitation. We investigate its properties, its relation to the Tweedie distribution and the convergence of its infinite sum. We propose various methods of estimating its parameters and we evaluate the performance of the estimators on simulated and real precipitation data in different temporal scales. In the spatial framework, we investigate the extension of the compound Poisson-Gamma model in multiple locations with spatial dependence. For this purpose we adapt the methodology of effective distribution models using univariate effective compound Poisson-Gamma probability density functions with spatially dependent parameters. We use two methods to estimate the compound Poisson-Gamma parameters at the unobserved locations. The first one is to apply the kernel regression technique directly to the compound Poisson-Gamma parameters, while for the second one we use the kriging formulas. Then, we generate realizations conditionally on the precipitation values using computationally efficient simulation algorithms. These values are correlated, to ensure spatial continuity of the generated precipitation field. Finally, we evaluate the efficiency of the reconstruction. We also investigate the construction of a temporal model that will be able to model correlated data since in reality there is a serial correlation between daily precipitation series. We propose a model that is useful in the sense that it can simplify the compound Poisson-Gamma model and can be used to generate uncorrelated precipitation data. In addition, we propose a method termed as Multivariate Poisson approach to model the temporal evolution of precipitation and can be used for the construction of correlated precipitation series that have the same statistical characteristics with historical precipitation series and reproduce accurately the most precipitation indices as well as the dry/wet spells. The covariance function of the censored and transformed Gaussian random field is also investigated. We perform a comparison of the different methods for covariance estimation, we prove some of their properties and we compare them theoretically and numerically in the sense of their performance in the spatial interpolation using kriging formulas. Η μοντελοποίηση της κατακρήμνισης είναι σημαντική επειδή έχει μεγάλο αντίκτυπο στην υδρολογία, τη γεωργία, τα παράγωγα καιρού, τη διαχείριση της ξηρασίας και των πλημμύρων. Μία δυσκολία στη μοντελοποίηση φαινομένων όπως η κατακρήμνιση είναι ότι περιγράφονται καλύτερα από μια μεικτή κατανομή που αποτελείται από ένα συνεχές μέρος και μια μάζα στο μηδέν. Αυτές οι κατανομές είναι στις περισσότερες περιπτώσεις είτε ασύμμετρες ή έχουν βαριές ουρές ή και τα δύο. Στην παρούσα διατριβή, μελετάμε το σύνθετο Πουασόν-Γάμμα μοντέλο το οποίο έχει την ικανότητα να μοντελοποιεί ταυτόχρονα την εμφάνιση και την ένταση της κατακρήμνισης. Ερευνούμε τις ιδιότητες του και τη σύγκλιση του άπειρου αθροίσματος του. Προτείνουμε διάφορες μεθόδους εκτίμησης των παραμέτρων του και αξιολογούμε την επίδοση τους σε δεδομένα προσομοίωσης και πραγματικά δεδομένα σε διαφορετικές χρονικές κλίμακες. Στο χωρικό πλαίσιο, ερευvνούμε την επέκταση του σύνθετου Πουασόν-Γάμμα μοντέλου σε πολλαπλές τοποθεσίες με χωρική εξάρτηση. Για το σκοπό αυτό προσαρμόζουμε τη μεθοδολογία των ενεργών μοντέλων κατανομής χρησιμοποιώντας μονομεταβλητά σύνθετα Πουασόν-Γάμμα μοντέλα συνάρτησης πυκνότητας πιθανότητας με χωρικά εξαρτώμενες παραμέτρους. Χρησιμοποιούμε δύο μεθόδους για να εκτιμήσουμε τις παραμέτρους του σύνθετου Πουασόν-Γάμμα μοντέλου σε τοποθεσίες όπου δεν υπάρχουν παρατηρήσεις. Η πρώτη μέθοδος είναι η εφαρμογή της τεχνικής παλινδρόμησης συναρτήσεων πυρήνα, ενώ στη δεύτερη χρησιμοποιούμε εξισώσεις kriging. Στη συνέχεια, παράγουμε δεσμευμένες υλοποιήσεις στις τιμές της κατακρήμνισης χρησιμοποιώντας υπολογιστικά αποδοτικούς αλγόριθμους προσομοίωσης. Αυτές οι τιμές συσχετίζονται για να διασφαλιστεί η χωρική συνέχεια του παραγόμενου πεδίου κατακρήμνισης. Τελειώνοντας αξιολογούμε την αποτελεσματικότητα της ανακατασκευής. Επιπρόσθετα, ερευvνούμε την κατασκευή ενός χρονικού μοντέλου το οποίο να είναι ικανό να μοντελοποιεί συσχετισμένα δεδομένα αφού στην πραγματικότητα υπάρχει μία σειριακή συσχέτιση ανάμεσα στις ημερήσιες σειρές κατακρήμνισης. Προτείνουμε ένα μοντέλο το οποίο είναι χρήσιμο με την έννοια ότι απλοποιεί το σύνθετο Πουασόν-Γάμμα μοντέλο και μπορεί να χρησιμοποιηθεί για την κατασκευή ασυσχέτιστων δεδομένων κατακρήμνισης. Επιπλέον, προτείνουμε μία μέθοδο που ονομάσαμε ως πολυμεταβλητή προσέγγιση Πουασόν για τη μοντελοποίηση της χρονικής εξέλιξης της κατακρήμνισης και η οποία μπορεί να χρησιμοποιηθεί για την κατασκευή συσχετισμένων δεδομένων σειρών κατακρήμνισης οι οποίες έχουν τα ίδια στατιστικά χαρακτηριστικά με τα ιστορικά δεδομένα σειρών κατακρήμνισης και αναπαράγουν με ακρίβεια τους περισσότερους δείκτες κατακρήμνισης όπως επίσης τις ξηρές/υγρές περιόδους. Μελετούμε επίσης τη συνάρτηση συνδιακύμανσης του περικομμένου και μετασχηματισμένου κανονικού τυχαίου πεδίου. Διεξάγουμε μία συγκριτική έρευνα για τις διαφορετικές μεθόδους εκτίμησης της συνάρτησης συνδιακύμανσης, αποδεικνύουμε μερικές από τις ιδιότητες τους και τις συγκρίνουμε θεωρητικά και αριθμητικά με την έννοια της επίδοσης τους στη χωρική παρεμβολή χρησιμοποιώντας εξισώσεις kriging.

Includes bibliography. Number of sources in the bibliography: 86 Thesis (Ph. D.) -- University of Cyprus, Faculty of Pure and Applied Sciences, Department of Mathematics and Statistics, 2022. The University of Cyprus Library holds the printed form of the thesis. Οι Τεχνικές ΄Εμμεσης Ερώτησης εμφανίστηκαν λόγω της αδυναμίας συλλογής αξι-όπιστων δεδομένων για ανθρώπινους πληθυσμούς, όταν σε αυτούς πραγματοποιούνται δειγματοληπτικές έρευνες για ευαίσθητα σε περιεχόμενο θέματα (π.χ. σεξουαλική συ-μπεριφορά, χρήση ναρκωτικών ουσιών κ.λπ.). Σε διάφορες δειγματοληπτικές έρευνες σε ομάδες πληθυσμών, οι ερευνητές αντιμετωπίζουν ποικίλες δυσκολίες στη συλλογή αξιόπι-στων δεδομένων λόγω της προκατάληψης και της μεροληψίας απάντησης (answer-bias) και γενικά λόγω των μη δειγματοληπτικών σφαλμάτων (non-sampling errors). Σε πε-ρίπτωση που το υπό διερεύνηση ζήτημα είναι ευαίσθητο ή στιγματιστικό, οι άνθρωποι διστάζουν να συμμετάσχουν ή να απαντήσουν ειλικρινά σε ερωτήσεις που παραβιάζουν την ιδιωτικότητά τους, επομένως δίνονται ψευδείς ή παραπλανητικές απαντήσεις εάν εφαρ-μοστεί Τεχνική ΄Αμεσης Ερώτησης. Μία διέξοδος από αυτή τη δυσκολία παρέχεται από τις περίφημες Τεχνικές ΄Εμμεσης Ερώτησης. Η έμμεση ερώτηση έχει χρησιμοποιηθεί από ψυχολόγους και εμπόρους από τη δεκαετία του 1950 (Matarazzo et al. (1956), Westfall et al. (1957), Dalton et al. (1994)). Ωστόσο, ο Warner (1965) ήταν ο πρώτος ερευνητής που δημοσίευσε μια ερευνητική εργασία σχετικά με τις Τεχνικές ΄Εμμεσης Ερώτησης. Είναι γεγονός ότι η τεχνική του Warner έχει δημιουργήσει ένα νέο πεδίο ερευνητικής δρα-στηριότητας. Ο Fisher (1993) πραγματοποίησε μια λεπτομερή μελέτη για να διερευνήσει την εγκυρότητα της μεθόδου αυτής. Οι Fisher and Katz (2008) διεξήγαγαν αρκετές μελέτες οι οποίες επιβεβαίωσαν ότι ενώ οι άμεσες ερωτήσεις επηρεάζονται από την προ-κατάληψη της κοινωνικής επιθυμίας (social desirability bias), οι έμμεσες ερωτήσεις δεν επηρεάζονται. Κατά τη διάρκεια των ετών, πολλοί άλλοι ερευνητές πρότειναν διάφορες επεκτάσεις και γενικεύσεις με βάση την τεχνική του Warner. Σκοπός των επεκτάσεων και γενικεύσεων είναι η βελτίωση και η διαφοροποίηση της «πρωτότυπης» μεθόδου για την καλύτερη προστασία της ιδιωτικότητας των συμμετεχόντων. Οι Τεχνικές ΄Εμμεσης Ερώτησης καλύπτονται λεπτομερώς στην πρόσφατη μονογρα-φία των Chaudhuri and Christofides (2013) καθώς και στη μονογραφία των Chaudhuri (2011), Chaudhuri and Mukerjee (1988), Fox and Tracy (1986). Σε αυτή τη διατριβή, εξετάζουμε εν συντομία μερικές από τις Τεχνικές ΄Εμμεσης Ερώτησης. Αν και οι πε-ρισσότερες από τις τεχνικές εμπίπτουν στην κατηγορία των Τεχνικών Τυχαιοποιημένης Απάντησης, μια άλλη προσέγγιση, η Τεχνική Καταμέτρησης Δηλώσεων, αποτελεί μια εναλλακτική λύση. Η Τεχνική Τυχαιοποιημένης Απάντησης του Warner (1965), το Μο-ντέλο τυχαιοποιημένης απάντησης άσχετων ερωτήσεων των Greenberg et al. (1969) και η Τεχνική Καταμέτρησης Δηλώσεων στην οποία επικεντρώνεται η έρευνά μας, περι-γράφονται και εξηγούνται αναλυτικά σε επόμενα κεφάλαια. Ο κύριος στόχος της παρούσας έρευνας ήταν η εύρεση νέων εκδοχών που θα προ-στατεύουν πλήρως την ιδιωτικότητα των συμμετεχόντων. Από όσο γνωρίζουμε, μέχρι τώρα όλες οι προτεινόμενες μεθοδολογίες δεν διασφαλίζουν πλήρως την προστασία της ιδιωτικότητας και σε περιπτώσεις που προστατεύεται πλήρως η ιδιωτικότητα η τεχνική δεν μπορεί να εφαρμοστεί εύκολα. Σε αυτή τη διατριβή, παρουσιάζουμε μερικές αναθεωρη-μένες τεχνικές της Τεχνικής Καταμέτρησης Δηλώσεων χωρίς floor and ceiling e ects. Επίσης, μια άλλη προσέγγιση θα μπορούσε να είναι μια μεθοδολογία που συνδυάζει την Τεχνική Τυχαιοποιημένης Απάντησης και την Τεχνική Καταμέτρησης Δηλώσεων, αλλά χωρίς τη χρήση συσκευής τυχαιοποίησης. Μια τέτοια προσέγγιση περιλαμβάνει την Τε-χνική Τυχαιοποιημένης Απάντησης και την κλασική Τεχνική Καταμέτρησης Δηλώσεων ως ειδικές περιπτώσεις. Ο συντριπτικός όγκος της έρευνας για τις Τεχνικές ΄Εμμεσης Ερώτησης επικεντρώνε-ται σε αμερόληπτες εκτιμήτριες σε βάρος άλλων παραγόντων, όπως η ακρίβεια της εκτι-μήτριας και η προστασία της ιδιωτικότητας. Σε αυτήν την έρευνα δώσαμε μεγαλύτερη έμφαση στην κατασκευή εκτιμητριών που μπορεί να μην είναι απαραίτητα αμερόληπτες, αλλά που προστατεύουν καλύτερα την ιδιωτικότητα των συμμετεχόντων. Για τον λόγο αυτό, προτείνουμε διάφορες επεκτάσεις της Τεχνικής Καταμέτρησης Δηλώσεων και σε ο-ρισμένες περιπτώσεις συζητάμε τα σχετικά μέτρα προστασίας της ιδιωτικότητας. Επίσης, διερευνούμε και προσπαθούμε να βρούμε τον βέλτιστο αριθμό των μη ευαίσθητων σε περιεχόμενο στοιχείων που μπορούν να χρησιμοποιηθούν, ώστε να έχουμε την μέγιστη δυνατή ακρίβεια της εκτιμήτριας και ταυτόχρονα να μην τίθεται σε κίνδυνο η προστασία της ιδιωτικότητας. Τέλος, επιθυμούμε να ελέγξουμε εάν τα αποτελέσματα που λαμβάνονται χρησιμοποι-ώντας διάφορες Τεχνικές ΄Εμμεσης Ερώτησης (π.χ. την μέθοδος του Warner, το Μο-ντέλο τυχαιοποιημένης απάντησης ασυσχέτιστων ερωτήσεων, την Τεχνική Καταμέτρησης Δηλώσεων κλπ.) έναντι της μεθόδου άμεσης απάντησης είναι πιο ακριβής ή όχι. Για κάθε τεχνική, χτίζουμε ένα σενάριο και υποθέτουμε ότι έχουμε ένα δείγμα μεγέθους n με επανάθεση από τον πληθυσμό και κάθε συμμετέχων δίνει μια άμεση απάντηση για το ευα-ίσθητο σε περιεχόμενο στοιχείο και μια έμμεση απάντηση. Από τα αποτελέσματα που παρουσιάζονται μπορούμε εύκολα να συμπεράνουμε ότι αξίζει η εφαρμογή και η χρήση των Τεχνικών ΄Εμμεσης Ερώτησης. Indirect Questioning Techniques have appeared due to the inability to gather reliable data on human populations when sample surveys on sensitive items (e.g. sexual behavior, drug abuse etc.) are carried out. In sample surveys of human populations, researchers are faced with various difficulties in gathering reliable data such as evasive answer-bias and non-sampling errors in general. In case the issue under investigation is sensitive or stigmatizing, people are reluctant to participate or to honestly answer questions that violate their privacy, so false or misleading answers are given if a direct questioning technique is applied. One way out of this difficulty is provided by the celebrated techniques of indirect response. Indirect questioning has been used by psychologists and merchants since the 1950s (Matarazzo et al. (1956), Westfall et al. (1957), Dalton et al. (1994)). However, Warner (1965) was the first researcher to publish a research paper concerning Indirect Questioning Techniques. It is a fact that Warner's paper has created a separate field of research activity. Fisher (1993) carried out a detailed study to investigate the validity of the method. Fisher and Katz (2008) conducted several studies which confirmed that while direct questions are affected by social desirability bias, indirect questions are not. During the years, many other researchers proposed various extensions and generalizations based on Warner's technique. The purpose of the extensions and generalizations is the improvement and the diversification of the "original" method in order to better protect the privacy of the participants. Indirect Questioning Techniques are covered in detail in the recent monograph of Chaudhuri and Christofides (2013) as well as in the monographs of Chaudhuri (2011), Chaudhuri and Mukerjee (1988) and Fox and Tracy (1986). In this thesis, we review some of the Indirect Questioning Techniques. Although most of the techniques fall in the category of Randomized Response, one approach, the Item Count Technique is an alternative. The Randomized Response Technique of Warner (1965), the Unrelated Characteristic Model of Greenberg et al. (1969) and the Item Count Technique on which our research is focused, are fully described and explained. The main objective of this research was to find new versions which will fully protect the privacy of the participants. To the best of our knowledge, until now all the proposed methodologies do not fully ensure the protection of privacy and in cases their privacy is protected the technique can not be easily applied. In this thesis, we introduce some revised designs of the Item Count Technique with no floor and ceiling effects. Also, another approach is a methodology which combines the Randomized Response Technique and the Item Count Technique, but without the use of a randomizing device. Such an approach includes Randomized Response Technique and the Classical Item Count Technique as special cases. The overwhelming amount of research on Indirect Questioning Techniques focuses on unbiased estimators at the expense of other aspects such as the accuracy and the protection of privacy. In this research we put more emphasis on producing estimators which may not necessarily be unbiased but which better protect the privacy of the participants. For this reason, we propose various revised versions of the Item Count Technique and in some cases, we discuss the related measures of the protection of privacy. Also, we investigate and try to find the optimal number of nonsensitive items used so that the accuracy of the estimator is improved and at the same time the protection of privacy is not jeopardized. Finally, we wish to check whether the results received using various Indirect Questioning Techniques (e.g. Warner’s technique, Unrelated Question Model, ICT etc.) versus the direct questioning method are more accurate or not. For each technique, we build a scenario and we assume that we have a sample of size n drawn with replacement from the population and each participant provides a direct response for the sensitive item and an indirect response. From the results generated we can easily conclude that the Indirect Questioning Techniques are worth applying.

Διδακτορική Διατριβή που υποβλήθηκε στη σχολή ΜηχΟΠ του Πολ. Κρήτης για την πλήρωση προϋποθέσεων λήψης του Διδακτορικού Διπλώματος Ειδίκευσης. Summarization: Technological advancements have increased the availability of spatiotemporal data. However, meteorological data are usually non-Gaussian and correlated in space and time. In this dissertation, state-of-the-art geostatistical and machine-learning methodologies were utilized to analyze large-scale non-Gaussian meteorological space-time data. We carried out a series of numerical investigations utilizing 26 surface variables from the ERA5 reanalysis data sets collected for 65 grid locations on the island of Crete, Greece. The data sets correspond to multiple temporal scales (hourly to annually) and span the period from 1979 until 2019. Four distinct approaches were implemented for the analysis of the meteorological parameters: 1. The ERA5 data set was used for the estimation of the standardized precipitation index (SPI) and the standardized precipitation evapotranspiration index (SPEI) to reveal the spatiotemporal patterns of drought in Crete. 2. Gaussian Anamorphosis with Hermite polynomials (GAH) was employed to transform non-Gaussian precipitation data into normally distributed variables. Ten processing scenarios were investigated and their performance with respect to spatial interpolation (based on Ordinary kriging) was evaluated. The scenarios include the application or exclusion of GAH with varying polynomial degrees, the utilization of either the exponential or Spartan variogram models, and the incorporation or omission of Monte Carlo simulations. 3. Twelve machine learning (ML) techniques were compared for the classification of precipitation data into eight classes. Twenty-six (26) numerical and categorical variables were used in a spatiotemporal predictive framework for precipitation. Due to pronounce class imbalance (dominance of ``no rain'' events), we first divided the data into two classes that represent the absence or occurrence of precipitation events. Then, the occurrence data set was split in five different classes to characterize the intensity of precipitation events. 4. Finally, we applied the Stochastic Local Interaction (SLI) model to perform temporal (precipitation, temperature and solar radiation) and spatiotemporal (precipitation and temperature) estimation of missing values (data gaps). The most important conclusions derived in this dissertation are as follows: 1. The dry climate of Crete was confirmed by the estimation of the SPI and SPEI drought indices. It was found that the eastern part of the island is more prone to desertification than the north-western part. Moreover, a temperature-inclusive drought index was shown to be more appropriate than a purely precipitation-based index for the study area. 2. Using higher-order (35 versus 20) polynomials in GAH has little effect on the cross-validation results for the monthly total precipitation data. In addition, the incorporation of Monte Carlo simulations does not universally improve the statistical measures. 3. With respect to the classification of hourly precipitation data, the method of Random Forests (Bagged Ensemble Trees) performs best for both the ``Binary'' (``rain'' versus ``no rain'') and the ``Only Rain'' classification cases. 4. SLI is a competitive method for interpolating large temporal and spatiotemporal data since it is fast and it performed very well (compared to nearest-neighbor interpolation) across all the different hourly data sets (temperature, precipitation, and solar radiation). The present study investigates a variety of methodological approaches for the analysis of non-Gaussian, large-scale meteorological variables. It provides an extensive analysis of precipitation, temperature, and solar radiation for the island of Crete using the ERA5 reanalysis data set. The meteorological data used involve multiple timescales. Two drought indices are evaluated and compared in order to assess the effect of warming trends on drought events. Various data processing scenarios that combine GAH, kriging interpolation and bootstrapping are studied and assessed. In addition, a comparison of twelve machine learning methods for the classification of precipitation data supported by 26 meteorological variables is conducted. Lastly, the computationally efficient SLI models are herein applied for the first time to spatiotemporal precipitation and solar radiation data.