A Combinatorial Optimization Approach to the Selection of Statistical Units

In the case of some large statistical surveys, the set of units that will constitute the scope of the survey must be selected. We focus on the real case of a Census of Agriculture, where the units are farms. Surveying each unit has a cost and brings a different portion of the whole information. In this case, one wants to determine a subset of units producing the minimum total cost for being surveyed and representing at least a certain portion of the total information. Uncertainty aspects also occur, because the portion of information corresponding to each unit is not perfectly known before surveying it. The proposed approach is based on combinatorial optimization, and the arising decision problems are modeled as multidimensional binary knapsack problems. Experimental results show the effectiveness of the proposed approach

Applications of combinatorial optimization arising from large scale surveys

Many difficult statistical problems arising in censuses or in other large scale surveys have an underlying Combinatorial Optimization structure and can be solved with Combinatorial Optimization techniques. These techniques are often more efficient than the ad hoc solution techniques already developed in the field of Statistics. This thesis considers in detail two relevant cases of such statistical problems, and proposes solution approaches based on Combinatorial Optimization and Graph Theory. The first problem is the delineation of Functional Regions, the second one concerns the selection of the scope of a large survey, as briefly described below. The purpose of this work is therefore the innovative application of known techniques to very important and economically relevant practical problems that the "Censuses, Administrative and Statistical Registers Department" (DICA) of the Italian National Institute of Statistics (Istat), where I am senior researcher, has been dealing with. In several economical, statistical and geographical applications, a territory must be partitioned into Functional Regions. This operation is called Functional Regionalization. Functional Regions are areas that typically exceed administrative boundaries, and they are of interest for the evaluation of the social and economical phenomena under analysis. Functional Regions are not fixed and politically delimited, but are determined only by the interactions among all the localities of a territory. In this thesis, we focus on interactions represented by the daily journey-to-work flows between localities in which people live and/or work. Functional Regionalization of a territory often turns out to be computationally difficult, because of the size (that is, the number of localities constituting the territory under study) and the nature of the journey-to-work matrix (that is, the sparsity). In this thesis, we propose an innovative approach to Functional Regionalization based on the solution of graph partition problems over an undirected graph called transitions graph, which is generated by using the journey-to-work data. In this approach, the problem is solved by recursively partitioning the transition graph by using the min cut algorithms proposed by Stoer and Wagner and Brinkmeier. %In the second approach, the problem is solved maximizing a function of the sizes and interactions of subsets identified by successions of partitions obtained via Multilevel partitioning approach. This approach is applied to the determination of the Functional Regions for the Italian administrative regions. The target population of a statistical survey, also called scope, is the set of statistical units that should be surveyed. In the case of some large surveys or censuses, the scope cannot be the set of all available units, but it must be selected from this set. Surveying each unit has a cost and brings a different portion of the whole information. In this thesis, we focus on the case of Agricultural Census. In this case, the units are farms, and we want to determine a subset of units producing the minimum total cost and safeguarding at least a certain portion of the total information, according to the coverage levels assigned by the European regulations. Uncertainty aspects also occur, because the portion of information corresponding to each unit is not perfectly known before surveying it. The basic decision aspect is to establish the inclusion criteria before surveying each unit. We propose here to solve the described problem using multidimensional binary knapsack models

Applications of combinatorial optimization arising from large scale surveys

Many difficult statistical problems arising in censuses or in other large scale surveys have an underlying Combinatorial Optimization structure and can be solved with Combinatorial Optimization techniques. These techniques are often more efficient than the ad hoc solution techniques already developed in the field of Statistics. This thesis considers in detail two relevant cases of such statistical problems, and proposes solution approaches based on Combinatorial Optimization and Graph Theory. The first problem is the delineation of Functional Regions, the second one concerns the selection of the scope of a large survey, as briefly described below. The purpose of this work is therefore the innovative application of known techniques to very important and economically relevant practical problems that the "Censuses, Administrative and Statistical Registers Department" (DICA) of the Italian National Institute of Statistics (Istat), where I am senior researcher, has been dealing with. In several economical, statistical and geographical applications, a territory must be partitioned into Functional Regions. This operation is called Functional Regionalization. Functional Regions are areas that typically exceed administrative boundaries, and they are of interest for the evaluation of the social and economical phenomena under analysis. Functional Regions are not fixed and politically delimited, but are determined only by the interactions among all the localities of a territory. In this thesis, we focus on interactions represented by the daily journey-to-work flows between localities in which people live and/or work. Functional Regionalization of a territory often turns out to be computationally difficult, because of the size (that is, the number of localities constituting the territory under study) and the nature of the journey-to-work matrix (that is, the sparsity). In this thesis, we propose an innovative approach to Functional Regionalization based on the solution of graph partition problems over an undirected graph called transitions graph, which is generated by using the journey-to-work data. In this approach, the problem is solved by recursively partitioning the transition graph by using the min cut algorithms proposed by Stoer and Wagner and Brinkmeier. %In the second approach, the problem is solved maximizing a function of the sizes and interactions of subsets identified by successions of partitions obtained via Multilevel partitioning approach. This approach is applied to the determination of the Functional Regions for the Italian administrative regions. The target population of a statistical survey, also called scope, is the set of statistical units that should be surveyed. In the case of some large surveys or censuses, the scope cannot be the set of all available units, but it must be selected from this set. Surveying each unit has a cost and brings a different portion of the whole information. In this thesis, we focus on the case of Agricultural Census. In this case, the units are farms, and we want to determine a subset of units producing the minimum total cost and safeguarding at least a certain portion of the total information, according to the coverage levels assigned by the European regulations. Uncertainty aspects also occur, because the portion of information corresponding to each unit is not perfectly known before surveying it. The basic decision aspect is to establish the inclusion criteria before surveying each unit. We propose here to solve the described problem using multidimensional binary knapsack models

The Variance Profile

The variance profile is defined as the power mean of the spectral density function of a stationary stochastic process. It is a continuous and non-decreasing function of the power parameter, p, which returns the minimum of the spectrum (p → −∞), the interpolation error variance (harmonic mean, p = −1), the prediction error variance (geometric mean, p = 0), the unconditional variance (arithmetic mean, p = 1) and the maximum of the spectrum (p → ∞). The variance profile provides a useful characterisation of a stochastic processes; we focus in particular on the class of fractionally integrated processes. Moreover, it enables a direct and immediate derivation of the Szego-Kolmogorov formula and the interpolation error variance formula. The paper proposes a non-parametric estimator of the variance profile based on the power mean of the smoothed sample spectrum, and proves its consistency and its asymptotic normality. From the empirical standpoint, we propose and illustrate the use of the variance profile for estimating the long memory parameter in climatological and financial time series and for assessing structural change.Predictability; Interpolation; Non-parametric spectral estimation; Long memory.

A min-cut approach to functional regionalization, with a case study of the Italian local labour market areas

In several economical, statistical and geographical applications, a territory must be subdivided into functional regions. Such regions are not fixed and politically delimited, but should be identified by analyzing the interactions among all its constituent localities. This is a very delicate and important task, that often turns out to be computationally difficult. In this work we propose an innovative approach to this problem based on the solution of minimum cut problems over an undirected graph called here transitions graph. The proposed procedure guarantees that the obtained regions satisfy all the statistical conditions required when considering this type of problems. Results on real-world instances show the effectiveness of the proposed approach

The Variance Profile

The variance profile is defined as the power mean of the spectral density function of a stationary stochastic process. It is a continuous and non-decreasing function of the power parameter, p, which returns the minimum of the spectrum (p → −∞), the interpolation error variance (harmonic mean, p = −1), the prediction error variance (geometric mean, p = 0), the unconditional variance (arithmetic mean, p = 1) and the maximum of the spectrum (p → ∞). The variance profile provides a useful characterisation of a stochastic processes; we focus in particular on the class of fractionally integrated processes. Moreover, it enables a direct and immediate derivation of the Szego-Kolmogorov formula and the interpolation error variance formula. The paper proposes a non-parametric estimator of the variance profile based on the power mean of the smoothed sample spectrum, and proves its consistency and its asymptotic normality. From the empirical standpoint, we propose and illustrate the use of the variance profile for estimating the long memory parameter in climatological and financial time series and for assessing structural change

Determinazione di aree economiche per la valutazione dell’impatto sul sistema produttivo italiano delle misure di contrasto all’epidemia da Covid-19

The paper proposes a new geography of nested economic areas that shape the Italian economy. These economic areas, named economic regions and economic macro-regions, are an upper tier integration of Local Labour Systems (LLS) obtained using a Community Detection algorithm called INFOMAP. This approachdetermines the optimal number of regions and the assignment of LLS to them, minimizing a function known as MAP Equation. In the paper, these economic areas are the unit of analysis for impact assessment on the Italian economy of control measures implemented by the government to counteract the epidemic from Covid-19. Moreover, if the purpose is to contain new epidemic hotbeds of Covid-19, these areas are the most suitable tool for doing so, because of their extremely high self-containment, much higher than that of LLSs. Finally, the paper suggests their utility for both epidemiological and socio-economic monitoring

Lifestyle Modifications to Help Prevent Headache at a Developmental Age

Headache is the world’s seventh most significant cause of disability-adjusted-life in people aged between 10 and 14 years. Therapeutic management is based on pharmacological approaches and lifestyle recommendations. Many studies show associations between each migraine-promoting lifestyle, behavioral triggers, frequency, and intensity of headaches. Nevertheless, the overall aspects of this topic lack any definitive evidence. Educational programs advise that pediatric patients who suffer from migraines follow a correct lifestyle and that this is of the utmost importance in childhood, as it will improve quality of life and assist adult patients in avoiding headache chronicity, increasing general well-being. These data are important due to the scarcity of scientific evidence on drug therapy for prophylaxis during the developmental age. The “lifestyle recommendations” described in the literature include a perfect balance between regular sleep and meal, adequate hydration, limited consumption of caffeine, tobacco, and alcohol, regular physical activity to avoid being overweight as well as any other elements causing stress. The ketogenic diet is a possible new therapeutic strategy for the control of headache in adults, however, the possible role of dietary factors requires more specific studies among children and adolescents. Educational programs advise that the improvement of lifestyle as a central element in the management of pediatric headache will be of particular importance in the future to improve the quality of life of these patients and reduce the severity of cephalalgic episodes and increase their well-being in adulthood. The present review highlights how changes in different aspects of daily life may determine significant improvements in the management of headaches in people of developmental age

Some Like it Hot: The X-Ray Emission of The Giant Star YY Mensae

(Abridged abstract) We present an analysis of the X-ray emission of the rapidly rotating giant star YY Mensae observed by Chandra HETGS and XMM-Newton. Although no obvious flare was detected, the X-ray luminosity changed by a factor of two between the XMM-Newton and Chandra observations taken 4 months apart. The coronal abundances and the emission measure distribution have been derived from three different methods using optically thin collisional ionization equilibrium models. The abundances show an inverse first ionization potential (FIP) effect. We further find a high N abundance which we interpret as a signature of material processed in the CNO cycle. The corona is dominated by a very high temperature (20-40 MK) plasma, which places YY Men among the magnetically active stars with the hottest coronae. Lower temperature plasma also coexists, albeit with much lower emission measure. Line broadening is reported, which we interpret as Doppler thermal broadening, although rotational broadening due to X-ray emitting material high above the surface could be present as well. We use two different formalisms to discuss the shape of the emission measure distribution. The first one infers the properties of coronal loops, whereas the second formalism uses flares as a statistical ensemble. We find that most of the loops in the corona of YY Men have their maximum temperature equal to or slightly larger than about 30 MK. We also find that small flares could contribute significantly to the coronal heating in YY Men. Although there is no evidence of flare variability in the X-ray light curves, we argue that YY Men's distance and X-ray brightness does not allow us to detect flares with peak luminosities Lx <= 10^{31} erg/s with current detectors.Comment: Accepted paper to appear in Astrophysical Journal, issue Nov 10, 2004 (v615). This a revised version. Small typos are corrected. Figure 7 and its caption and some related text in Sct 7.2 are changed, without incidence for the conclusion