INE building
NIPO 096-22-006-0
ISSN 2695-9070

Spanish Journal of Statistics (SJS)

The Spanish Journal of Statistics (SJS) is the official journal of the National Statistics Institute of Spain (INE). The journal replaces Estadística Española, edited and published in Spanish by the INE for more than 60 years, which has long been highly influential in the Spanish scientific community.

The journal seeks papers containing original theoretical contributions of direct or potential value in applications, but the practical implications of methodological aspects are also welcome. The levels of innovation and impact are crucial in the papers published in SJS.

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    SJS aims to publish original sound papers on either well-established or emerging areas in the scope of the journal. The objective of papers should be to contribute to the understanding of official statistics and statistical methodology and/or to develop and improve statistical methods; any mathematical theory should be directed towards these aims. Within these parameters, the kinds of contribution considered include:

    • Official Statistics.
    • Theory and methods.
    • Computation and simulation studies that develop an original methodology.
    • Critical evaluations and new applications
    • Development, evaluation, review, and validation of statistical software and algorithms.
    • Reviews of methodological techniques.
    • Letters to the editor.

    One volume is published annually in two issues, but special issues covering up-to-date challenging topics may occasionally be published.

Issue 4. 2022

 Full issue DOI: https://doi.org//10.37830/SJS.2022.1

Presentation of Volume 4, 1, 2022

José María Sarabia

DOI: https://doi.org/10.37830/SJS.2022.1.01   Nº SJS/004

A review on specification tests for models with functional data

Wenceslao González-Manteiga

DOI: https://doi.org/10.37830/SJS.2022.1.02   Nº SJS/004

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    Nowadays, due to the progress in technological advances, massive amounts of data are generated. As a result, new statistical methodology is needed to properly manage this information. The functional data are an example of special importance. These are mainly obtained by means of high-frequency measurements (spectrometric curves, stock prices recording, etc.). Since the beginning of this century, this type of data has achieved great popularity. This fact has generated new distribution or regression models, among others, appropriate to the functional context. In the last 10 years, novel specification tests are proposed for those models. These are generalizations of methodologies developed for the vectorial framework over the last century. Besides, innovative procedures based on distance correlation ideas have been proposed as well. This article reviews the most notable developments in this context, providing some illustrations from real data sets.

Testing Benford’s law: from small to very large data sets

Leonardo Campanelli

DOI: https://doi.org/10.37830/SJS.2022.1.03   Nº SJS/004

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    We discuss some limitations of the use of generic tests, such as the Pearson’s 2, for testing Benford’s law. Statistics with known distribution and constructed under the specific null hypothesis that Benford’s law holds, such as the Euclidean distance, are more appropriate when assessing the goodness-of-fit to Benford’s law, and should be preferred over generic tests in quantitative analyses. The rule of thumb proposed by Goodman for compliance checking to Benford’s law, instead, is shown to be statistically unfounded. For very large sample sizes (N > 1000), all existing statistical tests are inappropriate for testing Benford’s law due to its empirical nature. We propose a new statistic whose sample values are asymptotically independent on the sample size making it a natural candidate for testing Benford’s law in very large data sets.

The gamma flexibleWeibull distribution: Properties and Applications

Alexsandro A. Ferreira, Gauss M. Cordeiro

DOI: https://doi.org/10.37830/SJS.2022.1.04   Nº SJS/004

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    A new gamma flexibleWeibull distribution is introduced, which presents a bathtub-shaped hazard rate, and some of its properties are obtained. The parameters are estimated via máximum likelihood, and a simulation study is performed to examine the consistency of the estimates. The utility of the proposed model is shown using three real applications.

On moments and entropy of the gamma-Gompertz distribution

Fredy Castellares, Artur J. Lemonte

DOI: https://doi.org/10.37830/SJS.2022.1.05   Nº SJS/004

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    The three-parameter gamma-Gompertz family of distributions was introduced recently in the literature. We verify that the analytical expressions provided for the ordinary moments and Shannon entropy are not correct and hence cannot be used for computing such quantities. We derive two closed-form expressions for the mean and a closed-form expression for the Shannon entropy in terms of the Whittaker function.

A first interim assessment of the third round of peer review of the European statistical system

Agustín Cañada

DOI: https://doi.org/10.37830/SJS.2022.1.06   Nº SJS/004

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    Peer Reviews are exercises to assess compliance with the principles and indicators of the European Statistics Code of Practice by the members of the European Statistical System: Eurostat and the national statistical systems (composed of statistical offices and other institutions). Peer Reviews are carried out periodically (every 5/6 years), by agreement of the European Union. To date, three rounds have been carried out: in 2006-2008, in 2013-2015, and a third round is underway between 2021 and 2023. Although the third round is still ongoing at the time of writing (December 2022), based on the experience of a representative group (14) of the countries already reviewed, a first assessment can already be made of the degree of achievement of the objectives pursued. The aim of this document is to provide a first input for a future comprehensive "lessons learned exercise" and to contribute to the debate on aspects to be taken into account in future peer reviews.

Use of death statistics according to cause of death in health research

Gregorio Barrio

DOI: https://doi.org/10.37830/SJS.2022.1.07   Nº SJS/004

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    Estimates of total and cause-specific mortality rates require information on the number of deaths (numerator) and the population at risk (denominator). In unlinked mortality studies, the numerator and denominator come from different sources, so there may be a numerator/denominator bias when estimating mortality rates according to certain individual attributes. This bias does not occur in linked mortality studies, in which data from the census or general population surveys are linked to vital records, and in the case of death, to the date and cause of death. However, regulations to protect individuals’ confidentiality greatly limit the use of linked and unlinked mortality statistics for scientific research, whether due to the regulations themselves or because of the restrictive interpretations thereof by some statistical offices not always sufficiently argued. On the other hand, some methodological developments by these offices are of enormous relevance, for example, the linkage between socioeconomic indicators and mortality by the National Statistics Institute of Spain, which enables the study of the relationship between socioeconomic factors and mortality and its variation over time.

The Statistics on Causes of Death: characteristics and improvements

Margarita García Ferruelo, M. Rosario González García

DOI: https://doi.org/10.37830/SJS.2022.1.08   Nº SJS/004

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    The Statistics on Causes of Death is a key tool for the Public Health. This article describes the complex process of the statistics, the advances achieved in recent years, such as the implementation of an international automatic system for coding multiple causes of death and for the selection of the underlying cause (IRIS) or the improvement in obtaining the external causes of death, as well as its usefulness for the epidemiological studies and health research. It is also discussed some of the lessons learned during the worst pandemic period, that, without any doubt, have highlighted the need of a more efficient method to get information through the implementation of an Electronic Death Certificate. And, finally, it is proposed to collect other variables of interest for the analysis of the causes of death using available administrative sources.

Mortality statistics

Enrique Regidor

DOI: https://doi.org/10.37830/SJS.2022.1.09   Nº SJS/004

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    The creation of civil registries, together with the obligation to report information on the deceased from the death certificate, have enabled the monitoring of various population health indicators. Data from death certificates, as compiled and disseminated by central statistics offices, are used to estimate different measures, most classically infant mortality and life expectancy. However, in high-income countries, infant mortality is no longer considered an appropriate measure of population health due to its low magnitude. From the health system perspective, the adoption of the International Classification of Diseases and Causes of Death was a crucial milestone in population health statistics, shedding light on the diseases responsible for most deaths and the trends in causes of death over time. Morbidity statistics and public health surveillance systems have important objectives, but they do not allow adequate monitoring of the frequency of diseases and other health problems, nor can they quantify diseases’ impact on population health. On the other hand, statistics on cause of death do provide this information thanks to the combination of two features: the exhaustiveness of the data they collect and the objective nature of the phenomenon they quantify.