An Examination of Some Signi cant Approaches to Statistical Deconvolution

We examine statistical approaches to two significant areas of deconvolution - Blind Deconvolution (BD) and Robust Deconvolution (RD) for stochastic stationary signals. For BD, we review some major classical and new methods in a unified framework of nonGaussian signals. The first class of algorithms we look at falls into the class of Minimum Entropy Deconvolution (MED) algorithms. We discuss the similarities between them despite differences in origins and motivations. We give new theoretical results concerning the behaviour and generality of these algorithms and give evidence of scenarios where they may fail. In some cases, we present new modifications to the algorithms to overcome these shortfalls. Following our discussion on the MED algorithms, we next look at a recently proposed BD algorithm based on the correntropy function, a function defined as a combination of the autocorrelation and the entropy functiosn. We examine its BD performance when compared with MED algorithms. We find that the BD carried out via correntropy-matching cannot be straightforwardly interpreted as simultaneous moment-matching due to the breakdown of the correntropy expansion in terms of moments. Other issues such as maximum/minimum phase ambiguity and computational complexity suggest that careful attention is required before establishing the correntropy algorithm as a superior alternative to the existing BD techniques. For the problem of RD, we give a categorisation of different kinds of uncertainties encountered in estimation and discuss techniques required to solve each individual case. Primarily, we tackle the overlooked cases of robustification of deconvolution filters based on estimated blurring response or estimated signal spectrum. We do this by utilising existing methods derived from criteria such as minimax MSE with imposed uncertainty bands and penalised MSE. In particular, we revisit the Modified Wiener Filter (MWF) which offers simplicity and flexibility in giving improved RDs to the standard plug-in Wiener Filter (WF)

A transfer function model for volatilities between water inflows and spot prices for Colombian electricity market

Abstract: The electricity generation mix in Colombia is predominantly hydroelectric. Phenomena that could generate extreme hydrology as El Niño or La Niña cause nervousness among electricity generators and therefore, the Electricity Spot Price increases the volatility. In this paper we propose a transfer function model between the volatilities of water inows and energy price based on models of SARFIMA-GARCH type. The model for Energy Prices incorporates seasonality and long memory. The transfer model confirms that the hydrology regimen influences the price and the GARCH part of the price model can incorporate the volatility of water inflows as an exogenous variable. It is important to note that, although the spot price volatility is influenced by other variables, we only analyze the influence of water inows.Resumen: La canasta de generación eléctrica en Colombia es predominantemente hidroeléctrica. Fenómenos que pudieran generar hidrologías extremas como El Niño o La Niña causan nerviosismo entre las empresas generadoras de electricidad y por lo tanto, aumenta la volatilidad del precio de bolsa de energía eléctrica. En este trabajo nosotros introducimos un modelo de función de transferencia entre las volatilidades de los aportes hidrológicos y el precio de la energía con base en modelos del tipo SARFIMA-GARCH. El modelo para el Precio de Energía incorpora estacionalidad y memoria larga. El modelo de transferencia confirma que el régimen hidrológico influencia el precio y la parte GARCH del modelo de Precios puede incorporar la volatilidad de los aportes hidrológicos como una variable exógena. Es importante hacer notar que aunque la volatilidad del precio de bolsa está influenciada por otras variables, aquí solo se analizará la influencia de los aportes hidrológicosMaestrí

Multi-Resolution Spatio-Temporal Change Analyses of Hydro-Climatological Variables in Association with Large-Scale Oceanic-Atmospheric Climate Signals

The primary objective of the work presented in this dissertation was to evaluate the change patterns, i.e., a gradual change known as the trend, and an abrupt change known as the shift, of multiple hydro-climatological variables, namely, streamflow, snow water equivalent (SWE), temperature, precipitation, and potential evapotranspiration (PET), in association with the large-scale oceanic-atmospheric climate signals. Moreover, both observed datasets and modeled simulations were used to evaluate such change patterns to assess the efficacy of the modeled datasets in emulating the observed trends and shifts under the influence of uncertainties and inconsistencies. A secondary objective of this study was to utilize the detected change patterns in designing data-driven prediction models, e.g., artificial neural networks (ANNs), support vector machines (SVMs), and Gaussian process regression (GPR) models, coupled with data pre-processing techniques, e.g., principal component analysis (PCA) and wavelet transforms (WTs). The study was not solely limited to the hydrologic regions of the conterminous United States (U.S.); rather it was extended to include an analysis of northern India to appraise the differences in the spatiotemporal variation on a broader scale. A task was designed to investigate the significant spatiotemporal variations in continental US streamflow patterns as a response to large-scale climate signals across multiple spectral bands (SBs). Using non-parametric (long-term) trend and (abrupt) shift detection tests, coupled with discrete wavelet transform, 237 unimpaired streamflow stations were analyzed over a study period of 62 years (1951 to 2012), looking at the water year and seasonal data, along with three discrete SBs of two, four, and eight years. Wavelet coherence analysis, derived from continuous wavelet transform, determined the association between the regional streamflow patterns and three large-scale climate signals, i.e., El Niño Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and Atlantic Multi-decadal Oscillation (AMO), across continuous SBs ranging from two to 16 years. The results indicated significant positive (negative) trends and shifts in the northeastern and north-central (northwestern) regions with an increase in the number of stations as the SB durations increased. The spatiotemporal association between regional streamflow and climate signals varied significantly (from no correlation, Rn2 ~ 0, to perfect correlation, Rn2 ~ 1.0) even amongst adjacent regions. Among the climate signals, ENSO showed the highest association (Rn2 ~ 1.0), having a consistent phase relationship with regional streamflow patterns, especially in the higher SBs. PDO (with the least influence among the three signals) and AMO showed stronger associations, in the lower SBs. These results may help explain the teleconnections between the climate signals and the US streamflow variations across multiple SBs, which may lead to improved regional flow regulations. The comparison among several data-driven models, e.g., ANN, SVM, and GPR models, preceded by PCA and WT, produced comparable results with significant accuracy (with R2 above 0.90) in short-term prediction of streamflow. Later, the correlations between the western U.S. snow water equivalent (SWE) and the two major oceanic-atmospheric indices originating from the Pacific Ocean, namely, ENSO and PDO, were evaluated using continuous wavelet transform and its derivatives. Snow Telemetry (SNOTEL) data for 1 April SWE from 323 sites (out of which 258 are in six hydrologic regions) were obtained for a study period of 56 years (1961–2016). The results showed that ENSO had a much higher influence than PDO throughout the western U.S. SWE across the study period. Both ENSO and PDO showed a higher correlation with SWE at multiple timescale bands across different time intervals, although significant intervals in the higher timescales were of longer duration. ENSO showed a higher correlation in the 10-to-16-year band across the entire study period as well as in the lower timescales. PDO showed a higher correlation below the 4-year band. The relative phase relationship suggested that ENSO led SWE, with certain lags, while both were moving in the same direction in many instances. The lag-response behavior of SWE and PDO was not found to be uniform. Regional analyses, based on the western U.S. hydrologic regions, suggested significant variation across adjacent regions in terms of their correlation with ENSO/PDO. Association with ENSO was also observed to be higher compared to PDO among the regions. Regions close to the ocean and at lower elevation showed higher correlation compared to the inland regions with higher elevation. The influence of ENSO on the north Indian temperature, precipitation, and PET change patterns was evaluated during the monsoon season across the last century. Trends and shifts in 146 districts were assessed using non-parametric statistical tests. To quantify their temporal variation, the concept of apportionment entropy was applied to both the annual and seasonal scales. Results suggest that the El Niño years played a greater role in causing hydro-climatological changes compared to the La Niña or neutral years. El Niño was more influential in causing shifts compared to trends. For certain districts, a phase change in ENSO reversed the trend/shift direction. The all-year (century-wide) analysis suggested that the vast majority of the districts experienced significant decreasing trends/shifts in temperature and PET. However, precipitation experienced both increasing and decreasing trends/shifts based on the location of the districts. Entropy results suggested a lower apportionment of precipitation compared to the other variables, indicating an intermittent deviation of precipitation pattern from the generic trend. The findings may help understand the effects of ENSO on hydro-climatological variables during the monsoon season. Practitioners may find the results useful, as monsoon, among the Indian seasons, experience the largest climate extremes. A final task was designed that evaluated Coupled Model Intercomparison Project 5 (CMIP5) simulation models’ ability to capture the observed trends under the influence of shifts and persistence in their data distributions. A total of 41 temperature and 25 precipitation CMIP5 simulation models across 22 grid cells (2.5° x 2.5° squares) within the Colorado River Basin were analyzed and compared against the Climate Research Unit Time Series (CRU-TS) observed datasets over a study period of 104 years (from 1901 to 2004). Both the model simulations and observations were tested for shifts, and the time series before and after the shifts were analyzed separately for trend detection and quantification. Effects of several types of persistence were accounted for prior to both the trend and shift detection tests. The mean significant shift points (SPs) of the CMIP5 temperature models across the grid cells were found to be within a narrower range (between 1960 and 1970) compared to the CRU-TS observed SPs (between 1930 and 1980). Precipitation time series, especially the CRU-TS dataset, had a lack of significant SPs, which led to an inconsistency between the models and observations since the numbers of grid cells with a significant SP were not comparable. The modeled CMIP5 temperature trends, under the influence of shifts and persistence, were able to match the observed trends quite satisfactorily (within the same order and consistent direction). Unlike the temperature models, the CMIP5 precipitation models detected the SPs earlier than the observed SPs found in the CRU-TS data. The direction (as well as the magnitude) of trends, before and after significant shifts, were found to be inconsistent between the modeled simulations and observed precipitation data. Shifts, based on their direction, were found to either strengthen or neutralize pre-existing trends both in the model simulations as well as in the observations. The results also suggest that the temperature and precipitation data distributions were sensitive to different types of persistence. Such sensitivity was found to be consistent between the modeled and observed datasets. The study detected certain biases in the CMIP5 models in detecting the SPs (a tendency of detecting shifts earlier or later than the observed shifts) and also in quantifying the trends (overestimating the trend slopes). Such insights may be helpful in evaluating the efficacy of the simulation models in capturing observed trends under uncertainties and natural variabilities

New contributions to algorithms and tools for the analysis of photometric and spectroscopic time-series in exoplanet searches

[eng] The current trend in exoplanet research focuses on the detection and characterisation of Earth-sized planets, and the study of their potential subtle and tenuous atmospheres. The aim of this thesis is the development of tools and simulation codes for the detection and characterisation of exoplanets by means of the indirect methods of radial velocities and transits. The structure of the thesis is two-fold. Firstly, we present a multidimensional extension to the well-known period search GLS code, which we dub MGLS (Multidimensional Generalized Lomb-Scargle periodogram). The analysis of a time-series periodogram of radial velocity data is the usual starting point to seek for periodic signals which then can be associated with the reflex Keplerian motion of a star caused by orbiting exoplanets. In the case of multiplanetary systems such analysis is usually carried out in an iterative fashion, known as prewhitening. This approach can diminish the significance and distort the parameters of periodic signals, and we aim to solve those limitations by introducing a multidimensional approach. Additionally, a robust criterion to determine the number of signals (dimensionality) in a time-series is presented. The new approach is more flexible and enhances the significance of multisignal detections and their multiplicity. It is further better capable to pinpoint the fit parameters and is able to compare models of different dimensionality. The MGLS code has been tested with real multiplanetary systems, showing its excellent performance in detectability. The code is publicly available to the community. The second part addresses the effects of rotationally-induced stellar activity on the photometric and spectroscopic observables. The properties, distribution, and evolution of inhomogeneities on the surface of active stars, such as dark spots and bright faculae, significantly influence the determination of the parameters of an orbiting exoplanet. The chromatic effect they have on transmission spectroscopy, for example, could affect the analysis of data from future space missions such as James Webb Space Telescope (JWST) and Ariel. To quantify and mitigate the effects of those surface phenomena, we developed a fast modelling approach to derive the surface distribution and properties of active regions by modelling simultaneous multi-wavelength time-series observables. We present an upgraded version of the StarSim code, now featuring the capability to solve the inverse problem and derive the properties of the stars and their active regions by modelling time-series data. The multiband photometric inverse problem is both analytically and numerically discussed, as well as a broad analysis of the degeneracies found in the inversion process. As a test case, we analyse a BVRI multiband ground photometry dataset of the exoplanet host star WASP-52. From the results, we further simulated the chromatic contribution of surface phenomena on the observables of its transiting planet. We demonstrate that by using contemporaneous ground-based multiband photometry of an active star, it is possible to reconstruct the parameters and distribution of active regions over time, thus making it feasible to quantify the chromatic effects on the planetary radii measured with transit spectroscopy and mitigate them by about an order of magnitude. The obtained results show it is possible to accurately characterise the heterogeneous stellar surface up to a precision of a few parts in 10^5 and validate the scientific case of space missions like Ariel, designed for exoplanetary transmission spectroscopy.[cat] L'interès actual en la recerca en exoplanetes rau en la detecció de planetes cada cop més petits on els senyals són estadísticament poc significatius, particularment en l'estudi de les seves atmosferes. La tesi té com a objectiu el disseny i desenvolupament d'eines i codis sofisticats per a la detecció i caracterització de les propietats d'exoplanetes mitjançant l'ús de les tècniques de velocitat radial i trànsits, i es compon de dues parts diferenciades: la primera, tracta la generalització d'una eina de detecció de periodicitats molt popular en aquest camp (GLS). S'ha desenvolupat una versió multidimensional, que anomenem MGLS (Multidimensional Generalized Lomb-Scargle periodogram), que permet l'ajust simultani d'un nombre arbitrari de senyals, de manera que millora notablement la detectabilitat de senyals compostos, i evita els problemes derivats del filtratge quan es fa servir el procediment seqüencial, com falsos positius/negatius. Addicionalment es presenta un procediment robust per a la determinació del nombre de senyals (dimensionalitat). La segona part, tracta els efectes de l'activitat estel·lar sobre les mesures de velocitat radial i fotometria. L'activitat magnètica superficial en forma de taques i fàcules constitueix superfícies heterogènies, que amb la rotació de l'estrella, produeixen variacions d'intensitat i cromàtiques en els observables. S'ha desenvolupat un codi ràpid per a la modelització física de l'activitat induïda per rotació de taques, prenent com a base una versió de codi preexistent. En la versió StarSim 2, permet dur a terme el problema invers per determinar l'estat de la superfície més probable donades unes observacions fotomètriques. També es desenvolupa una formulació analítica per al problema invers multibanda i s'analitzen detalladament les degeneracions existents en el problema. L'esquema d'inversió i el codi s'aplica a un conjunt de dades multifiltre (BVRI) de l'estrella WASP-52, i es simulen els efectes cromàtics del model d'activitat ajustat sobre els seus trànsits, com procedir per corregir-los per assolir una precisió d'unes poques parts en cent mil, i per tant validar el cas científic que sustenta la missió Ariel per a l'anàlisi d'atmosferes exoplanetàries per espectroscòpia de transmissió

"Empirical Likelihood Methods in Econometrics: Theory and Practice"

Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method inperspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator(GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related estimators. Second, EL is shown to have various advantages over other methods. The theory of large deviations demonstrates that EL emerges naturally in achieving asymptotic optimality both for estimation and testing. Interestingly, higher order asymptotic analysis also suggests that EL is generally a preferred method. Third, extensions of EL are discussed in various settings, including estimation of conditional moment restriction models, nonparametric specification testing and time series models. Finally, practical issues in applying EL to real data, such as computational algorithms for EL, are discussed. Numerical examples to illustrate the efficacy of the method are presented.

Semiparametric sieve-type generalized least squares inference

This article considers the problem of statistical inference in linear regression models with dependent errors. A sieve-type generalized least squares (GLS) procedure is proposed based on an autoregressive approximation to the generating mechanism of the errors. The asymptotic properties of the sieve-type GLS estimator are established under general conditions, including mixingale-type conditions as well as conditions which allow for long-range dependence in the stochastic regressors and/or the errors. A Monte Carlo study examines the finite-sample properties of the method for testing regression hypotheses