dataesr/scientific-paragraphs-categorization huggingface dataset:
We then run a Kolmogorov-Smirnov test for each of the models and obtain the results presented in Table  3. "Single Gaussian" refers to a simple Gaussian distribution fitted to each time series. The single Gaussian distribution is rejected for the four datasets, as it is neither asymmetric nor bimodal. The Gaussian bi-model distribution is rejected as well: it fails at capturing the tail behavior of the jumps' distribution. The Double exponential distribution is always rejected at a 5% risk level. Finally, the Cauchy and the scaled Student distributions are always accepted at a 5% risk level. However the acceptance probability are consistently higher for the Cauchy case: for this reason 9 , we will rely on this distribution throughout the forthcoming empirical analysis. Figure  3  displays the empirical distribution of the estimated models vs.
When p = 0 (and thus RM=RV), this model nests the so-called HAR-RV model developed in  Maheu and McCurdy (2011)  and for our empirical investigations ǫ t can either be Gaussian or a mixture of Gaussian distributions 19 , the later being able to span a very large scope of couples of kurtosis and skewness as presented in  Bertholon et al. (2006). In this case, using the independence hypothesis, we obtain the conditional joint density of the pair (r t , RV t ) and the bivariate model is estimated by conditional maximum-likelihood. When p = 0 (and thus RM=MedRV), even if the conditional joint density of the pair (r t , RV t ) is still available, we favor a two-steps estimation strategy that takes advantage of the jump detection presented in Section 2. In fact, the probability p is first estimated by the proportion of jumpy days in our datasets and the parameters of the jump density f J are obtained from the classical maximum-likelihood for independent observations.
Here, as proposed Amisano Giacomini (  2007 ), we use a Newey-West estimator that take into account heteroskedasticity and autocorrelation. One of the main interest of this approach comes from the fact that the two models can be nested or not 21 and can be estimated using very different techniques from the moment that they are based on a finite estimation window. Tables  4, 5 , 6 and 7 present the estimation results for the four datasets used in this article: the S&P 500, the WTI, the USDCAD and the the 10-year bond futures. The estimation has been performed over rolling windows of 1260 trading days, that is 5 years of data 22. The tables display the average values for each parameters across our rolling estimations, as well as the 5 and 95% quantiles. For most of the parameters, both quantiles across our estimates are of the same sign, pointing into the direction of statistically significant parameters.
Turning to the jump-to-volatility feedback parameter γ 2 , our results suggest that only in the case of the WTI is this parameter significantly different from zero. In the S&P 500 case, the estimates vary from -4. 807 to 58. 218: despite the negativity of the 5% quantile, this jump-tovolatility feedback might be playing a role as well. Turning finally to the jump parameters, our estimates depict distributions that are consistent with the descriptive statistics provided in Table  2 : the jump distributions exhibit a negative average for all datasets but one, as the λ parameter that is found to be greater than 0. 5 across all samples. Its lowest value is obtained for the USDCAD dataset for which λ is estimated to be equal to 0. 52 while the average value of the jumps is 0. 4. Then, the strongest asymmetry is found for the 10-year futures in Table  2 , and in Table  7  as it is the only dataset for which |µ a | < |µ b |.
RV -Gaussian ω φ 1 φ 2 φ 3 γ 1 Average value -1 The estimates presented in this table are obtained by maximizing the log-likelihood associated with of the models presented in Section 4 and using the S&P 500 data. The estimation has been performed over a 1260 days rolling period. "Average" presents the average value obtained across the estimation. The table also displays the associated 5 and 95% quantiles. Tables  8, 9 , 10 and 11 and Figure  4  display the results of the  Amisano and Giacomini (2007)  forecasting density test. From these tables and graphs, several conclusions can be raised. First, for forecast horizons ranging from 1 and 30 days, the models using the MedRV volatility measure as well as jumps based on the discontinuous distributions introduced earlier statistically dominate the rest of the models across the four datasets.
Boudt et al. 's (2011) the variations in trading activity over the all week. Jumps detected for the four series are plotted in Figures A. 1 to A. 4. From the all Figures, it is clear that jumps tend to cluster in more volatile periods. Table2provides descriptive statistics for jumps detected using theBoudt et al. 's (2011)methodology. The number of days where a jump occurs is in line with the estimates inAndersen et al. (2007a)as it is in a range of 4 to 8%. Descriptive statistics of the jump dataset.
* For the first two authors, this work was achieved through the  Laboratory of Excellence on Financial Regulation (Labex ReFi ) supported by  PRES heSam  under the reference  ANR10LABX0095. It benefited from a French government support managed by the  National Research Agency (ANR)  within the  project Investissements d'Avenir Paris Nouveaux Mondes  (investments for the future Paris New Worlds) under the reference  ANR11IDEX000602.
Background: The availability of big data in healthcare and the intensive development of data reuse and georeferencing have opened up perspectives for health spatial analysis. However, fine-scale spatial studies of ecological and medical databases are limited by the change of support problem and thus a lack of spatial unit interoperability. The use of spatial disaggregation methods to solve this problem introduces errors into the spatial estimations. Here, we present a generic, two-step method for merging medical and ecological databases that avoids the use of spatial disaggregation methods, while maximizing the spatial resolution. Methods: Firstly, a mapping table is created after one or more transition matrices have been defined. The latter link the spatial units of the original databases to the spatial units of the final database.
Results: We used our novel method to merge a medical database (the French national diagnosis-related group database, containing 5644 spatial units) with an ecological database (produced by the French National Institute of Statistics and Economic Studies, and containing with 36,594 spatial units). The mapping table yielded 5632 final spatial units. The mapping table's validity was evaluated by comparing the number of births in the medical database and the ecological databases in each final spatial unit. The median [interquartile range] relative difference was 2. 3% [0; 5. 7]. The spatial continuity criterion was low (2. 4%), and the spatial resolution index was greater than for most French administrative areas.
Background In the field of epidemiology, the term "spatial analysis" refers to the description and analysis of the spatial distribution of healthcare phenomena, such as the incidence or prevalence of disease or healthcare consumption across geographic areas  [1] [2] [3] [4] [5]. Although spatial analysis can be applied to point data, geostatistical data and aggregated data, most of the data for spatial analysis in the field of health are aggregated because they ensure that the patients' data remain confidential. By definition, these so-called ecological studies use data that have been aggregated into administrative spatial units, such as counties, provinces and states. These analyses require two categories of aggregated data. The first category is related to how the events (e. g. the cases of disease or surgical acts) are counted within each spatial unit in the study area.
The second category is related to the descriptive ecological data on the source population and the living environment within these spatial units, such as the socio-economic level, the employment rate, housing conditions and environmental quality. For example, a spatial analysis of the incidence of Crohn's disease in northern France examined correlations between two data sources: all new cases of Crohn's disease recorded in the EPIMAD register for each district (canton), and the characteristics of each of these districts in terms of the underlying population and the living environment. By combining these two sources, the investigators were able to (1) calculate the incidence of Crohn's disease for each canton, and (2) evaluate the influence of the living environment and the population's socio-economic level  [6, 7].
Spatial analysis in healthcare is attracting growing interest because of improvements in statistical analysis, the development of information technology tools, and the emergence of disease registries  [8] [9] [10] [11] [12] [13] [14]. More recently, the availability of big data in healthcare  [15] [16] [17]  and the intensive development of data reuse  [18, 19]  and georeferencing  [20, 21]  have opened up new perspectives for describing healthcare consumption or disease prevalence/incidence over large geographical areas-even whole countries-and analyzing their ecological determinants (such as socio-economic factors)  [22, 23]. However, the correlation of big data and ecological data over large areas is complicated by the problem of database interoperability  [24] [25] [26]. In the specific setting of spatial analysis, interoperability is based on the smallest possible spatial reference unit, which acts as a link between the medical database and the ecological database.
Poor interoperability between medical databases and ecological databases thus appears to be a major limitation for fine-scale spatial analyses of large geographical areas. However, the interoperability problem should not limit the choice of the most appropriate scale. This interoperability problem has been highlighted (for example) for National Health Service data in the UK, Statewide Planning and Research Cooperative System data from New York State in the USA, and the French national diagnosisrelated group database (Programme Médicalisé des Systèmes d'Information, PMSI)  [27, 32, 33]. Two ways of tackling the interoperability problem have been suggested: spatial disaggregation and spatial aggregation. The first approach consists in creating a mapping table that adopts the finest scale; consequently, the data aggregated on a larger scale are disaggregated into spatial units at the finest scale.
However, this necessitates the use of complex statistical models for spatial disaggregation (such as areal interpolation models) to estimate the variables' values on a smaller scale. Hence, these procedures can lead to errors in the spatial estimation, which are especially large because the spatial units of origin are considered on very different scales (e. g. by going from the state scale to the town scale)  [26, 34]. The second approach (aggregation methods) consists in creating a mapping table that links the spatial units of one or both databases to a larger scale. In a simple, particular case, the data from one of the two databases are aggregated to the spatial scale of the other database. However, in the most frequent case, the spatial units of the two databases are aggregated into a larger spatial unit that covers them both.
Although most studies use administrative spatial units as a larger spatial unit, this is not necessarily the finest and/or most appropriate scale for use. Consequently, aggregation methods markedly decrease spatial resolution (e. g. by going from the town scale to the county scale), and may lead to an increase in the ecological bias  [27] [28] [29]. The primary objective of the present study was to develop and characterize a generic method for building a mapping table between a medical database and an ecological database while maximizing the spatial resolution and avoiding the use of spatial disaggregation techniques and thus enabling the choice of most appropriate scale for the phenomenon being studied. By way of an illustrative example, we applied this method to the interoperability of the above-mentioned PMSI medical database and the socio-economic data produced by the French National Institute of Statistics and Economic Studies (Institut National de la Statistique et des Études Économiques, INSEE).
Data and objectives Let us consider two distinct databases: a medical database that describes patients and healthcare events, and an ecological database that describes the population. The present method considers the following conditions of application: 1. The medical database is organized on the scale of the individual. Each individual is attached to a spatial ID Spatial_Id_Medical, which corresponds to the spatial unit SU_medical. A variable characterizes each healthcare event. 2. The ecological database is organized on the scale of the spatial unit SU_eco, which has a unique spatial ID Spatial_Id_Eco. 3. The spatial units SU_medical and SU_eco differ, as do the spatial IDs Spatial_Id_Eco and Spatial_Id_Medical. The objective of our method is to build a mapping table that enables the creation of a final database comprising both medical and ecological data from the above-mentioned databases on the scale of the spatial unit SU_analysis and with a unique spatial ID called Spatial_Id_Analysis.
Construction rules 1. The direction of the relationship. When spatial units differ in size (i. e. SU_medical ≠ SU_eco), the two databases can only be aligned after the data have been aggregated. Count data are aggregated by calculating a sum, whereas continuous variables or proportions can be aggregated by calculating a median, mean or weighted mean. The larger of the two spatial units is then chosen as SU_analysis. The reverse process requires the use of a disaggregation method, leading to a loss of precision  [34, 35].
For example, the spatial resolution decreases if (for a given geographical zone) the data for a town are aggregated with data for the region as a whole. The decline in spatial resolution can initially be evaluated visually. The background map for SU_analysis is compared with the background map for the smallest spatial unit in the initial databases, in order to identify any obviously aberrant aggregates. The decline in spatial resolution can then be measured by calculating the ratio between the median surface area of SU_analysis and that of the smallest spatial unit in the initial databases (SU_initial = SU_eco or SU_med). This ratio must also be calculated for other administrative reference units whose surface area is known. These ratios are then compared: a lower index of decline corresponds to a spatial unit with a higher spatial resolution.
Spatial_Id_INSEE Zip_code Spatial_Id_PMSI data partition is not necessary because the transition matrix M2 aggregates exactly the same units. Lastly, a Spatial_Id_analysis ID is attributed to each of the Spatial_Id_PMSI (situations 1 to 4). The combination of transition matrix M1 and transition matrix M2 can, however, generate a small number of particular cases (< 1% of cases). In situation 5, several Spatial_Id_PMSI IDs have at least one Spatial_Id_INSEE ID in common. It is then impossible to obtain an exact correlation between the spatial ID from the PMSI and the spatial ID from the INSEE. In this situation, the Spatial_Id_PMSI IDs are aggregated into a single Spatial_Id_Analysis ID. Thus, 23 Spatial_Id_PMSI IDs were grouped into 11 Spatial_Id_ Analysis IDs. In total, there were 5632 Spatial_Id_Analysis IDs in the final database.
Validation of the mapping table In order to evaluate the quality of the match between the PMSI database and the INSEE database, the annual number of live births was used as the common variable. The number of births associated with each Spatial_ Id_INSEE ID was provided by the INSEE. The number of births associated with each Spatial_Id_PMSI ID was obtained by extracting the PMSI database. For each Spatial_Id_Analysis ID, the indicators were compared by calculating the relative difference (i. e. the difference between the number of births in the INSEE data and the number of births in the PMSI data, divided by the number of births in the PMSI data). These relative differences are quoted as the median  [IQR]. The total number of births was 785,742 in the INSEE database and 737,545 in the PMSI database, giving a difference of 48,197.
The median [IQR] relative difference was 2. 3% [0-5. 7] (a boxplot is available in the Additional file 4). In 2012, the ATIH performed an extensive study of the number of inhabitants in each SU_PMSI spatial unit, based on the INSEE data. The data on the number of inhabitants are available online for each Spatial_Id_PMSI  [45]. We therefore transformed these data on the scale of the Spatial_Id_Analysis and compared the population data provided by the ATIH and the population data provided for SU_INSEE, as aggregated by our mapping table. For each of the Spatial_Id_Analysis IDs, the correlation was perfect (difference = 0). Hence, the resulting mapping table automatically performs the task described by the ATIH, regardless of the INSEE variable.
Spatial validation A background map of the SU_analysis spatial unit was created using data from the French National Geographic Institute (Institut National de l'Information Géographique et Forestière, IGN) (Fig. 4 ). Spatial continuity was evaluated by calculating the fragmentation index; this was 2. 4% (n = 134) for the 5632 SU_analysis spatial units. This value is within the range of fragmentation indices (2-40%) reported for public use microdata areas (PUMAs) in the USA  [37]. A possible decline in the spatial resolution was evaluated first by visual comparison of the respective background maps for SU_INSEE and SU_analysis (Fig. 4 ). The SU_analysis spatial unit appeared to be regularly distributed over the geographical zone, with no aberrant aggregations. In a second step, we calculated the decline index for the spatial resolution required to obtain data on the surface area and the number of inhabitants in the French communes, cantons and départements.
The surface area data came from the IGN, whereas the data on the number of inhabitants came from the INSEE database. The comparison of the spatial resolution index for SU_analysis with the French administrative units is described in Table  2. The SU_analysis unit has a lower decline index than the cantons and départements for the surface area (6. 5, 13. 6 and 555. 3, respectively) and the number of inhabitants (14. 6, 24 and 1249. 2, respectively). On average, the spatial unit for analysis is therefore 6 times larger than the smallest available unit, testifying to a loss of spatial resolution. However, our method minimizes this loss; for the surface area, the scale is twice as fine as the first reference unit (the canton) and nearly 100 times finer than for the département (the second reference unit).
Discussion The method presented here addresses the interoperability problem for ecological and medical databases in a context of the spatial analysis of healthcare events. The loss of spatial resolution was minimized, and we did not have to resort to the use of spatial disaggregation techniques. The method's application to French national data enabled us to correlate medical data from the PMSI database with ecological data from the INSEE databaseresulting in the creation of a final database for fine-scale spatial analysis. This method may be of value for correlating ecological and medical big data in spatial analyses. This type of data is increasingly available and is opening up new perspectives in epidemiology. However, the use of medical big data in the field of spatial analysis is restrained by interoperability problems, known as the change-of-support problem and the misaligned data problem  [26].
In Rossheim et al. 's study of alcohol sales and the socio-economic environment, the data were available on the scale of the zip code, the census block or the zip code tabulation area. To perform analyses on the zip code scale, the researchers were obliged to use spatial disaggregation and aggregation methods; this decreased the quality of the final spatial analysis database  [46]. A similar problem was encountered in Sundmacher and Busse's study of the link between physician supply and avoidable cancer deaths in Germany. The lack of interoperability and the broad range of ecological databases prompted the researchers to use spatial interpolation methods on the district level and to not integrate certain environmental data-thus placing limitations on their analyses  [47]. Spatial resolution is a major issue in the spatial analysis of healthcare data because it is easier to detect local phenomena when the resolution is high  [30].
Furthermore, validation of the mapping table results in a high-quality final database for spatial analysis. The spatial validation process ensures that the greatest possible spatial resolution is achieved. Lastly, validation ensured that the spatial units' fragmentation index remains low. By way of an example, Siordia et al. 's studies of the American PUMA database featured a high fragmentation index and thus encountered theoretical difficulties in the application of statistical models; the spatial position of a healthcare event was no longer coherent with that of a spatial unit  [37, 38]. This generic method may provide a structural framework so that researchers can provide a standardized description of the methods used to aggregate ecological and medical spatial data. Nevertheless, our present method has a number of limitations, most of which are inherent to all spatial analyses.
Mutually exclusive equivalence situations for a transition matrix M k. M k is a transition matrix from among M 1 …M p transition matrices. M k describes the relationship between a Spatial_Id j and a Spatial_Id j+1 and therefore links them. n > 1, corresponds to the number of spatial IDs Spatial_Id, where Spatial_Id 1 corresponds to the Spatial_Id_Eco and Spatial_Id p+1 corresponds to the Spatial_Id_Medical. The transition matrices are based on a detailed assessment of the Spatial_Id_Medical and Spa-tial_Id_Eco IDs. It is then necessary to describe all the equivalence situations for each transition matrix. One or several Spatial_Id j can correspond to one or several Spa-tial_Id Ecological database Medical database ID patient Spatial_Id_Medical Events* Spatial_Id_Eco Number of inhabitants Var 2 Var 3 Spatial_Id_Medical Number of events Mapping table Spatial_Id_Eco Spatial_Id_Medical Spatial_Id_Analyse Spatial analysis final database Spatial_Id_Analyse Number of events Number of inhabitants Var 2 Var 3 Spatial_Id 1 = Spatial_Id_Eco 1*Spatial_Id j n*Spatial_Id j 1*Spatial_Id j n*Spatial_Id j , Spatial_Id j+1 … Fig.
3 M 1 M k … Spatial_Id j Spatial_Id_Temp M p 1*Spatial_Id j+1 1*Spatial_Id j+1 n*Spatial_Id j+1 n*Spatial_Id j+1 Spatial_Id p+1 = Spatial_Id_Medical Mk Mk Mk Mk AggregationFig. 2A generic method for building a final database for spatial analysis. Asterisk a variable characterizing the healthcare event studied (e. g. cases of disease, length of hospital stay, surgical acts, etc. )A mapping table for the IDs Spatial_Id_Medical and Spatial_Id_Eco IDs can be built by using p transition matrices (p ≥ 1). For example, a transition matrix makes it possible to associate each town's spatial ID with the spatial ID of the state to which it belongs. However, in more complex situations, there may be no direct way of linking the two spatial IDs. Thus, two or more matrices are required, leading to the creation of at least one temporary spatial ID Spatial_Id_Temp.