IN THIS PAPER, WE PROPOSE A NEW CLASS OF NON-GAUSSIAN RANDOM FIELDS NAMED TWO-PIECE RANDOM FIELDS. THE PROPOSED CLASS ALLOWS TO GENERATE RANDOM FIELDS THAT HAVE FLEXIBLE MARGINAL DISTRIBUTIONS, POSSIBLY SKEWED AND/OR HEAVY-TAILED AND, AS A CONSEQUENCE, HAS A WIDE RANGE OF APPLICATIONS. WE STUDY THE SECOND-ORDER PROPERTIES OF THIS CLASS AND PROVIDE ANALYTICAL EXPRESSIONS FOR THE BIVARIATE DISTRIBUTION AND THE ASSOCIATED CORRELATION FUNCTIONS. WE EXEMPLIFY OUR GENERAL CONSTRUCTION BY STUDYING TWO EXAMPLES: TWO-PIECE GAUSSIAN AND TWO-PIECE TUKEY-H RANDOM FIELDS. AN INTERESTING FEATURE OF THE PROPOSED CLASS IS THAT IT OFFERS A SPECIFIC TYPE OF DEPENDENCE THAT CAN BE USEFUL WHEN MODELING DATA DISPLAYING SPATIAL OUTLIERS, A PROPERTY THAT HAS BEEN SOMEWHAT IGNORED FROM MODELING VIEWPOINT IN THE LITERATURE FOR SPATIAL POINT REFERENCED DATA. SINCE THE LIKELIHOOD FUNCTION INVOLVES ANALYTICALLY INTRACTABLE INTEGRALS, WE ADOPT THE WEIGHTED PAIRWISE LIKELIHOOD AS A METHOD OF ESTIMATION. THE EFFECTIVENESS OF OUR METHODOLOGY IS ILLUSTRATED WITH SIMULATION EXPERIMENTS AS WELL AS WITH THE ANALYSIS OF A GEOREFERENCED DATASET OF MEAN TEMPERATURES IN MIDDLE EAST.

THE GAUSSIAN COPULA IS A POWERFUL TOOL THAT HAS BEEN WIDELY USED TO MODEL SPATIAL AND/OR TEMPORAL CORRELATED DATA WITH ARBITRARY MARGINAL DISTRIBUTIONS. HOWEVER, THIS KIND OF MODEL CAN POTENTIALLY BE TOO RESTRICTIVE SINCE IT EXPRESSES A REFLECTION SYMMETRIC DEPENDENCE. IN THIS PAPER, WE PROPOSE A NEW SPATIAL COPULA MODEL THAT MAKES IT POSSIBLE TO OBTAIN RANDOM FIELDS WITH ARBITRARY MARGINAL DISTRIBUTIONS WITH A TYPE OF DEPENDENCE THAT CAN BE REFLECTION SYMMETRIC OR NOT.

IN THIS PAPER, WE PROVIDE A NEW BIVARIATE DISTRIBUTION OBTAINED FROM A KIBBLE-TYPE BIVARIATE GAMMA DISTRIBUTION. THE STOCHASTIC REPRESENTATION WAS OBTAINED BY THE SUM OF A KIBBLE-TYPE BIVARIATE RANDOM VECTOR AND A BIVARIATE RANDOM VECTOR BUILDED BY TWO INDEPENDENT GAMMA RANDOM VARIABLES. IN ADDITION, THE RESULTING BIVARIATE DENSITY CONSIDERS AN INFINITE SERIES OF PRODUCTS OF TWO CONFLUENT HYPERGEOMETRIC FUNCTIONS. IN PARTICULAR, WE DERIVE THE PROBABILITY AND CUMULATIVE DISTRIBUTION FUNCTIONS, THE MOMENT GENERATION AND CHARACTERISTIC FUNCTIONS, THE HAZARD, BONFERRONI AND LORENZ FUNCTIONS, AND AN APPROXIMATION FOR THE DIFFERENTIAL ENTROPY AND MUTUAL INFORMATION INDEX. NUMERICAL EXAMPLES SHOWED THE BEHAVIOR OF EXACT AND APPROXIMATED EXPRESSIONS.

THIS ARTICLE GIVES A NARRATIVE OVERVIEW OF WHAT CONSTITUTES CLIMATOLOGICAL DATA AND THEIR TYPICAL FEATURES, WITH A FOCUS ON ASPECTS RELEVANT TO STATISTICAL MODELING. WE RESTRICT THE DISCUSSION TO UNIVARIATE SPATIAL FIELDS AND FOCUS ON MAXIMUM LIKELIHOOD ESTIMATION. TO ADDRESS THE PROBLEM OF ENORMOUS DATASETS, WE STUDY THREE COMMON APPROXIMATION SCHEMES: TAPERING, DIRECT MISSPECIFICATION, AND COMPOSITE LIKELIHOOD FOR GAUSSIAN AND NONGAUSSIAN DISTRIBUTIONS. WE FOCUS PARTICULARLY ON THE SO-CALLED SINH-ARCSINH DISTRIBUTION, OBTAINED THROUGH A SPECIFIC TRANSFORMATION OF THE GAUSSIAN DISTRIBUTION. BECAUSE IT HAS FLEXIBLE MARGINAL DISTRIBUTIONS - POSSIBLY SKEWED AND/OR HEAVY-TAILED - IT HAS A WIDE RANGE OF APPLICATIONS. ONE APPEALING PROPERTY OF THE TRANSFORMATION INVOLVED IS THE EXISTENCE OF AN EXPLICIT INVERSE TRANSFORMATION THAT MAKES LIKELIHOOD-BASED METHODS STRAIGHTFORWARD. WE DESCRIBE A SIMULATION STUDY ILLUSTRATING THE EFFECTS OF THE DIFFERENT APPROXIMATION SCHEMES. TO THE BEST OF OUR KNOWLEDGE, A DIRECT COMPARISON OF TAPERING, DIRECT MISSPECIFICATION, AND COMPOSITE LIKELIHOOD HAS NEVER BEEN MADE PREVIOUSLY, AND WE SHOW THAT DIRECT MISSPECIFICATION IS INFERIOR. IN SOME METRICS, COMPOSITE LIKELIHOOD HAS A MINOR ADVANTAGE OVER TAPERING. WE USE THE ESTIMATION APPROACHES TO MODEL A HIGH-RESOLUTION GLOBAL CLIMATE CHANGE FIELD. ALL SIMULATION CODE IS AVAILABLE AS A DOCKER CONTAINER AND IS THUS FULLY REPRODUCIBLE. ADDITIONALLY, THE PRESENT ARTICLE DESCRIBES WHERE AND HOW TO GET VARIOUS CLIMATE DATASETS. (C) 2022 THE AUTHOR(S). PUBLISHED BY ELSEVIER B.V. THIS IS AN OPEN ACCESS ARTICLE UNDER THE CC BY-NC-ND LICENSE.

THE UNIVARIATE GAMMA (CHI-SQUARED) SUPERSTATISTICS HAS BEEN USED IN SEVERAL APPLICATIONS BY ASSUMING INDEPENDENCE BETWEEN SYSTEMS. HOWEVER, IN SOME CASES IT SEEMS MORE REASONABLE TO CONSIDER A DEPENDENCE STRUCTURE. THIS FACT MOTIVATES THE INTRODUCTION OF A FAMILY OF BIVARIATE SUPERSTATISTICS BASED ON AN EXTENSION OF THE GAMMA DISTRIBUTION, DEFINED BY GENERALIZED HYPERGEOMETRIC FUNCTIONS. THE PARTICULAR CASES INCLUDE BOLTZMANN AND OTHER STATISTICAL WEIGHTING FACTORS IN THE LITERATURE. NUMERICAL ILLUSTRATIONS SHOW THE BEHAVIOUR OF THE PROPOSED SUPERSTATISTICS.

FROM A BIVARIATE SUPERSTATISTICS, WE SHOW THAT IT IS POSSIBLE TO OBTAIN A GENERALIZED KAPPA DISTRIBUTION, CURRENTLY KNOWN FOR THEIR GREAT PERFORMANCE DESCRIBING MANY ANISOTROPIC HIGH-ENERGY TAIL PLASMAS. SOME PARTICULAR CASES OBTAINED THROUGH THIS PROCEDURE ARE SHOWN IN THIS PAPER, AND, ON THE OTHER HAND, THE BIMODALITY EFFECT OF MARGINAL ON THE STATIONARY SUPERSTATISTICAL DISTRIBUTION IS EXPLORED.

WITH THE AIM OF MITIGATING THE DAMAGE CAUSED BY THE CORONAVIRUS DISEASE 2019 (COVID-19) PANDEMIC, IT IS IMPORTANT TO USE MODELS THAT ALLOW FORECASTING POSSIBLE NEW INFECTIONS ACCURATELY IN ORDER TO FACE THE PANDEMIC IN SPECIFIC SOCIOCULTURAL CONTEXTS IN THE BEST POSSIBLE WAY. OUR FIRST CONTRIBUTION IS EMPIRICAL. WE USE AN EXTENSIVE COVID-19 DATASET FROM NINE LATIN AMERICAN COUNTRIES FOR THE PERIOD OF 1 APRIL 2020 TO 31 DECEMBER 2021. OUR SECOND AND THIRD CONTRIBUTIONS ARE METHODOLOGICAL. WE EXTEND RELEVANT (I) STATE-SPACE MODELS WITH SCORE-DRIVEN DYNAMICS AND (II) NONLINEAR STATE-SPACE MODELS WITH UNOBSERVED COMPONENTS, RESPECTIVELY. WE USE WEEKLY SEASONAL EFFECTS, IN ADDITION TO THE LOCAL-LEVEL AND TREND FILTERS OF THE LITERATURE, FOR (I) AND (II), AND THE NEGATIVE BINOMIAL DISTRIBUTION FOR (II). WE FIND THAT THE STATISTICAL AND FORECASTING PERFORMANCES OF THE NOVEL SCORE-DRIVEN SPECIFICATIONS ARE SUPERIOR TO THOSE OF THE NONLINEAR STATE-SPACE MODELS WITH UNOBSERVED COMPONENTS MODEL, PROVIDING A POTENTIAL VALID ALTERNATIVE TO FORECASTING THE NUMBER OF POSSIBLE NEW COVID-19 INFECTIONS.

THIS ARTICLE WILL DISCUSS TWO IMPORTANT SUBJECTS. THE FIRST IS THE MODEL OF THE IMPACT OF EDUCATIONAL RESEARCH ON TEACHING PRACTICE. THE SECOND IS THE CREATION OF AN INDEX THAT MEASURES THE IMPACT OF EDUCATIONAL RESEARCH ON TEACHING PRACTICE, USING STRUCTURAL EQUATION MODELING. THIS STUDY LOOKED AT A SAMPLE OF 179 INDIVIDUALS, OF WHICH 62 WERE UNIVERSITY TEACHERS AND 117 WERE NON-?UNIVERSITY TEACHERS. THROUGH A SECONDARY ANALYSIS OF THE DATA, THE DIFFERENT STAGES OF CONSTRUCT VALIDITY WERE DEVELOPED AND STRUCTURAL EQUATION MODELING, OBTAINING A MODEL COVERED BY THREE CONSTRUCTS REPRESENTED BY 15 ITEMS. THE MODEL SHOWED THAT THE PERCEPTION OF THE DIAGNOSIS OF THE IMPACT OF EDUCATIONAL RESEARCH ON THE PRACTICE OF TEACHERS DIRECTLY EXPLAINED THE UNDERSTANDING OF THE IMPACT PHENOMENON. THE IMPACT INDEX EI-?PD WAS 60.23%, SHOWING THAT TEACHERS DO NOT SUBSTANTIALLY CONSIDER THE CONTRIBUTION OF EDUCATIONAL RESEARCH ON TEACHING PRACTICE.

RANDOM FIELDS ARE USEFUL MATHEMATICAL TOOLS FOR REPRESENTING NATURAL PHENOMENA WITH COMPLEX DEPENDENCE STRUCTURES IN SPACE AND/OR TIME. IN PARTICULAR, THE GAUSSIAN RANDOM FIELD IS COMMONLY USED DUE TO ITS ATTRACTIVE PROPERTIES AND MATHEMATICAL TRACTABILITY. HOWEVER, THIS ASSUMPTION SEEMS TO BE RESTRICTIVE WHEN DEALING WITH COUNTING DATA. TO DEAL WITH THIS SITUATION, WE PROPOSE A RANDOM FIELD WITH A POISSON MARGINAL DISTRIBUTION BY CONSIDERING A SEQUENCE OF INDEPENDENT COPIES OF A RANDOM FIELD WITH AN EXPONENTIAL MARGINAL DISTRIBUTION AS 'INTER-ARRIVAL TIMES' IN THE COUNTING RENEWAL PROCESSES FRAMEWORK. OUR PROPOSAL CAN BE VIEWED AS A SPATIAL GENERALIZATION OF THE POISSON PROCESS. UNLIKE THE CLASSICAL HIERARCHICAL POISSON LOG-GAUSSIAN MODEL, OUR PROPOSAL GENERATES A (NON)-STATIONARY RANDOM FIELD THAT IS MEAN SQUARE CONTINUOUS AND WITH POISSON MARGINAL DISTRIBUTIONS. FOR THE PROPOSED POISSON SPATIAL RANDOM FIELD, ANALYTIC EXPRESSIONS FOR THE COVARIANCE FUNCTION AND THE BIVARIATE DISTRIBUTION ARE PROVIDED. IN AN EXTENSIVE SIMULATION STUDY, WE INVESTIGATE THE WEIGHTED PAIRWISE LIKELIHOOD AS A METHOD FOR ESTIMATING THE POISSON RANDOM FIELD PARAMETERS. FINALLY, THE EFFECTIVENESS OF OUR METHODOLOGY IS ILLUSTRATED BY AN ANALYSIS OF REINDEER PELLET-GROUP SURVEY DATA, WHERE A ZERO-INFLATED VERSION OF THE PROPOSED MODEL IS COMPARED WITH ZERO-INFLATED POISSON LOG-GAUSSIAN AND POISSON GAUSSIAN COPULA MODELS. SUPPLEMENTARY MATERIALS FOR THIS ARTICLE, INCLUDE TECHNICAL PROOFS AND R CODE FOR REPRODUCING THE WORK, ARE AVAILABLE AS AN ONLINE SUPPLEMENT.

A HIGHLY SCALABLE METHOD FOR (NON-)GAUSSIAN RANDOM FIELDS ESTIMATION IS PROPOSED. IN PARTICULAR, A NOVEL (A) SYMMETRIC WEIGHT FUNCTION BASED ON NEAREST NEIGHBORS FOR THE METHOD OF MAXIMUM WEIGHTED COMPOSITE LIKELIHOOD BASED ON PAIRS (WCLP) IS STUDIED. THE NEW WEIGHT FUNCTION ALLOWS ESTIMATING MASSIVE (UP TO MILLIONS) SPATIAL DATASETS AND IMPROVES THE STATISTICAL EFFICIENCY OF THE WCLP METHOD USING SYMMETRIC WEIGHTS BASED ON DISTANCES, AS SHOWN IN THE NUMERICAL EXAMPLES. AS AN APPLICATION OF THE PROPOSED METHOD, THE ESTIMATION OF A NOVEL NON-GAUSSIAN RANDOM FIELD NAMED TUKEY-HH RANDOM FIELD THAT HAS FLEXIBLE MARGINAL DISTRIBUTIONS (POSSIBLY SKEWED AND/OR HEAVY-TAILED) IS CONSIDERED. IN AN EXTENSIVE SIMULATION STUDY THE STATISTICAL EFFICIENCY OF THE PROPOSED NEAREST NEIGHBORS WCLP METHOD WITH RESPECT TO THE WCLP METHOD USING WEIGHTS BASED ON DISTANCES IS EXPLORED WHEN ESTIMATING THE PARAMETERS OF THE TUKEY-HH RANDOM FIELD. IN THE GAUSSIAN CASE THE PROPOSED METHOD IS COMPARED WITH THE VECCHIA APPROXIMATION FROM COMPUTATIONAL AND STATISTICAL VIEWPOINTS. FINALLY, THE EFFECTIVENESS OF THE PROPOSED METHODOLOGY IS ILLUSTRATED BY ESTIMATING A LARGE DATASET OF MEAN TEMPERATURES IN SOUTH -AMERICA. THE PROPOSED METHODOLOGY HAS BEEN IMPLEMENTED IN AN OPEN-SOURCE PACKAGE FOR THE R STATISTICAL ENVIRONMENT.

WE PROPOSE A NEW MODEL FOR REGRESSION AND DEPENDENCE ANALYSIS WHEN ADDRESSING SPATIAL DATA WITH POSSIBLY HEAVY TAILS AND AN ASYMMETRIC MARGINAL DISTRIBUTION. WE FIRST PROPOSE A STATIONARY PROCESS WITH T MARGINALS OBTAINED THROUGH SCALE MIXING OF A GAUSSIAN PROCESS WITH AN INVERSE SQUARE ROOT PROCESS WITH GAMMA MARGINALS. WE THEN GENERALIZE THIS CONSTRUCTION BY CONSIDERING A SKEW-GAUSSIAN PROCESS, THUS OBTAINING A PROCESS WITH SKEW-T MARGINAL DISTRIBUTIONS. FOR THE PROPOSED (SKEW) T PROCESS, WE STUDY THE SECOND-ORDER AND GEOMETRICAL PROPERTIES AND IN THE T CASE, WE PROVIDE ANALYTIC EXPRESSIONS FOR THE BIVARIATE DISTRIBUTION. IN AN EXTENSIVE SIMULATION STUDY, WE INVESTIGATE THE USE OF THE WEIGHTED PAIRWISE LIKELIHOOD AS A METHOD OF ESTIMATION FOR THE T PROCESS. MOREOVER WE COMPARE THE PERFORMANCE OF THE OPTIMAL LINEAR PREDICTOR OF THE T PROCESS VERSUS THE OPTIMAL GAUSSIAN PREDICTOR. FINALLY, THE EFFECTIVENESS OF OUR METHODOLOGY IS ILLUSTRATED BY ANALYZING A GEOREFERENCED DATASET ON MAXIMUM TEMPERATURES IN AUSTRALIA.

IN THIS PAPER, WE CONCENTRATE ON AN ALTERNATIVE MODELING STRATEGY FOR POSITIVE DATA THAT EXHIBIT SPATIAL OR SPATIOTEMPORAL DEPENDENCE. SPECIFICALLY, WE PROPOSE TO CONSIDER STOCHASTIC PROCESSES OBTAINED THROUGH A MONOTONE TRANSFORMATION OF SCALED VERSION OF ? ² RANDOM PROCESSES. THE LATTER IS WELL KNOWN IN THE SPECIALIZED LITERATURE AND ORIGINATES BY SUMMING INDEPENDENT COPIES OF A SQUARED GAUSSIAN PROCESS. HOWEVER, THEIR USE AS STOCHASTIC MODELS AND RELATED INFERENCE HAS NOT BEEN MUCH CONSIDERED. MOTIVATED BY A SPATIOTEMPORAL ANALYSIS OF WIND SPEED DATA FROM A NETWORK OF METEOROLOGICAL STATIONS IN THE NETHERLANDS, WE EXEMPLIFY OUR MODELING STRATEGY BY MEANS OF A NONSTATIONARY PROCESS WITH WEIBULL MARGINAL DISTRIBUTIONS. FOR THE PROPOSED WEIBULL PROCESS WE STUDY THE SECOND?ORDER AND GEOMETRICAL PROPERTIES AND WE PROVIDE ANALYTIC EXPRESSIONS FOR THE BIVARIATE DISTRIBUTION. SINCE THE LIKELIHOOD IS INTRACTABLE, EVEN FOR A RELATIVELY SMALL DATA SET, WE SUGGEST ADOPTING THE PAIRWISE LIKELIHOOD AS A TOOL FOR INFERENCE. MOREOVER, WE TACKLE THE PREDICTION PROBLEM AND WE PROPOSE TO USE A LINEAR PREDICTION. THE EFFECTIVENESS OF OUR MODELING STRATEGY IS ILLUSTRATED BY ANALYZING THE AFOREMENTIONED NETHERLAND WIND SPEED DATA THAT WE INTEGRATE WITH A SIMULATION STUDY. THE PROPOSED METHOD IS IMPLEMENTED IN THE R PACKAGE GEOMODELS.

IN THIS PAPER, WE DEVELOP TWO FULLY PARAMETRIC QUANTILE REGRESSION MODELS, BASED ON THE POWER JOHNSON SB DISTRIBUTION FOR MODELING UNIT INTERVAL RESPONSE IN DIFFERENT QUANTILES. IN PARTICULAR, THE CONDITIONAL DISTRIBUTION IS MODELED BY THE POWER JOHNSON SB DISTRIBUTION. THE MAXIMUM LIKELIHOOD (ML) ESTIMATION METHOD IS EMPLOYED TO ESTIMATE THE MODEL PARAMETERS. SIMULATION STUDIES ARE CONDUCTED TO EVALUATE THE PERFORMANCE OF THE ML ESTIMATORS IN FINITE SAMPLES. FURTHERMORE, WE DISCUSS INFLUENCE DIAGNOSTIC TOOLS AND RESIDUALS. THE EFFECTIVENESS OF OUR PROPOSALS IS ILLUSTRATED WITH A DATA SET OF THE MORTALITY RATE OF COVID-19 IN DIFFERENT COUNTRIES. THE RESULTS OF OUR MODELS WITH THIS DATA SET SHOW THE POTENTIAL OF USING THE NEW METHODOLOGY. THUS, WE CONCLUDE THAT THE RESULTS ARE FAVORABLE TO THE USE OF PROPOSED QUANTILE REGRESSION MODELS FOR FITTING DOUBLE BOUNDED DATA.

THE EVALUATION OF PRODUCTIVITY IN OFFICE BUILDINGS IS PARTICULARLY COMPLEX; STUDIES INDICATE THAT OCCUPANTS? PERCEPTIONS REFLECT THERMAL CONDITIONS AND ARE THEREFORE AN IMPORTANT ELEMENT TO CONSIDER. THIS RESEARCH REVEALS THE INTERRELATIONSHIPS AND RELATIVE INFLUENCES OF THE THERMAL ENVIRONMENTAL FACTORS OF OFFICES ON THE PERCEIVED PRODUCTIVITY OF WORKERS. THROUGH FIELDWORK CONDUCTED IN WINTER AND SUMMER IN 18 CHILEAN OFFICE BUILDINGS, INFORMATION WAS COLLECTED FROM 940 OCCUPANTS ON 32 VARIABLES RELATED TO THE THERMAL ENVIRONMENT AND SELF-PERCEIVED PRODUCTIVITY. A TOTAL OF 3551 RESPONSES WERE USED TOGETHER WITH ENVIRONMENTAL AND PHYSICAL DATA ON THE INDOOR BUILT SPACE TO FORMULATE A MODEL THAT RECOGNIZES THE EFFECT OF THE THERMAL ENVIRONMENT ON PRODUCTIVITY. IN THIS MODEL, THE CONSTRUCTS OF INDIVIDUAL THERMAL SENSATION, THERMAL PREFERENCE, AND THERMAL ACCEPTABILITY ARE MEDIATING VARIABLES THAT ORIGINATE IN DIFFERENT OFFICE PARAMETERS AND INFLUENCE PERCEIVED PRODUCTIVITY. SUBSEQUENTLY, THE MODEL WAS VALIDATED AND SPECIFIED FOLLOWING THE SEM METHODOLOGY, THEREBY RESULTING IN A REDUCED MODEL OF 10 SIGNIFICANT VARIABLES. AN ANALYSIS OF THE INTERRELATIONSHIPS ESTABLISHED THE IMPORTANCE OF THESE VARIABLES ASSOCIATED WITH THE DESIGN OF BUILT SPACE AND THE MANAGEMENT OF COMFORT STRATEGIES CONSIDERING WORK PRODUCTIVITY.

IN THIS WORK, WE USE A COINTEGRATION STATE SPACE APPROACH TO ESTIMATE THE QUARTERLY SERIES OF THE CHILEAN GROSS DOMESTIC PRODUCT (GDP) IN THE PERIOD 1965?2009. FIRST, THE EQUATION OF ENGLE?GRANGER IS ESTIMATED USING THE DATA OF THE YEARLY GPD AND SOME RELATED VARIABLES, SUCH AS THE PRICE OF COPPER, THE EXPORTS OF GOODS AND SERVICES, AND THE MINING PRODUCTION INDEX. THE ESTIMATED COEFFICIENTS OF THIS REGRESSION ARE THEN USED TO OBTAIN A FIRST ESTIMATION OF THE QUARTERLY GDP SERIES WITH MEASUREMENT ERRORS. A STATE SPACE MODEL IS THEN APPLIED TO IMPROVE THE PRELIMINARY ESTIMATION OF THE GDP WITH THE MAIN PURPOSE OF ELIMINATING THE MAXIMUM ERROR OF MEASUREMENT SUCH THAT THE SUM OF THE THREE-MONTH VALUES COINCIDE SWITH THE YEARLY GDP. THE RESULTS ARE THEN COMPARED WITH THE TRADITIONAL DISAGGREGATION METHODS. THE RESULTING QUARTERLY GDP SERIES REFLECTS THE MAJOR EVENTS OF THE HISTORICAL CHILEAN ECONOMY.

THE MATÉRN FAMILY OF COVARIANCE FUNCTIONS HAS PLAYED A CENTRAL ROLE IN SPATIAL STATISTICS FOR DECADES, BEING A FLEXIBLE PARAMETRIC CLASS WITH ONE PARAMETER DETERMINING THE SMOOTHNESS OF THE PATHS OF THE UNDERLYING SPATIAL FIELD. THIS PAPER PROPOSES A FAMILY OF SPATIAL COVARIANCE FUNCTIONS, WHICH STEMS FROM A REPARAMETERIZATION OF THE GENERALIZED WENDLAND FAMILY. AS FOR THE MATÉRN CASE, THE PROPOSED FAMILY ALLOWS FOR A CONTINUOUS PARAMETERIZATION OF THE SMOOTHNESS OF THE UNDERLYING GAUSSIAN RANDOM FIELD, BEING ADDITIONALLY COMPACTLY SUPPORTED. MORE IMPORTANTLY, WE SHOW THAT THE PROPOSED COVARIANCE FAMILY GENERALIZES THE MATÉRN MODEL WHICH IS ATTAINED AS A SPECIAL LIMIT CASE. THIS IMPLIES THAT THE (REPARAMETRIZED) GENERALIZED WENDLAND MODEL IS MORE FLEXIBLE THAN THE MATÉRN MODEL WITH AN EXTRA-PARAMETER THAT ALLOWS FOR SWITCHING FROM COMPACTLY TO GLOBALLY SUPPORTED COVARIANCE FUNCTIONS. OUR NUMERICAL EXPERIMENTS ELUCIDATE THE SPEED OF CONVERGENCE OF THE PROPOSED MODEL TO THE MATÉRN MODEL. WE ALSO INSPECT THE ASYMPTOTIC DISTRIBUTION OF THE MAXIMUM LIKELIHOOD METHOD WHEN ESTIMATING THE PARAMETERS OF THE PROPOSED COVARIANCE MODELS UNDER BOTH INCREASING AND FIXED DOMAIN ASYMPTOTICS. THE EFFECTIVENESS OF OUR PROPOSAL IS ILLUSTRATED BY ANALYZING A GEOREFERENCED DATASET OF MEAN TEMPERATURES OVER A REGION OF FRENCH, AND PERFORMING A RE-ANALYSIS OF A LARGE SPATIAL POINT REFERENCED DATASET OF YEARLY TOTAL PRECIPITATION ANOMALIES.