THE DAGUM FAMILY OF ISOTROPIC COVARIANCE FUNCTIONS HAS TWO PARAMETERS THAT ALLOW FOR DECOUPLING OF THE FRACTAL DIMENSION AND THE HURST EFFECT FOR GAUSSIAN RANDOM FIELDS THAT ARE STATIONARY AND ISOTROPIC OVER EUCLIDEAN SPACES. SUFFICIENT CONDITIONS THAT ALLOW FOR POSITIVE DEFINITENESS IN RD OF THE DAGUM FAMILY HAVE BEEN PROPOSED ON THE BASIS OF THE FACT THAT THE DAGUM FAMILY ALLOWS FOR COMPLETE MONOTONICITY UNDER SOME PARAMETER RESTRICTIONS. THE SPECTRAL PROPERTIES OF THE DAGUM FAMILY HAVE BEEN INSPECTED TO A VERY LIMITED EXTENT ONLY, AND THIS PAPER GIVES INSIGHT INTO THIS DIRECTION. SPECIFICALLY, WE STUDY FINITE AND ASYMPTOTIC PROPERTIES OF THE ISOTROPIC SPECTRAL DENSITY (INTENDED AS THE HANKEL TRANSFORM) OF THE DAGUM MODEL. ALSO, WE ESTABLISH SOME CLOSED-FORM EXPRESSIONS FOR THE DAGUM SPECTRAL DENSITY IN TERMS OF THE FOX?WRIGHT FUNCTIONS. FINALLY, WE PROVIDE ASYMPTOTIC PROPERTIES FOR SUCH A CLASS OF SPECTRAL DENSITIES.

COKRIGING IS THE COMMON METHOD OF SPATIAL INTERPOLATION (BEST LINEAR UNBIASED PREDICTION) IN MULTIVARIATE GEOSTATISTICS. WHILE BEST LINEAR PREDICTION HAS BEEN WELL UNDERSTOOD IN UNIVARIATE SPATIAL STATISTICS, THE LITERATURE FOR THE MULTIVARIATE CASE HAS BEEN ELUSIVE SO FAR. THE NEW CHALLENGES PROVIDED BY MODERN SPATIAL DATASETS, BEING TYPICALLY MULTIVARIATE, CALL FOR A DEEPER STUDY OF COKRIGING. IN PARTICULAR, WE DEAL WITH THE PROBLEM OF MISSPECIFIED COKRIGING PREDICTION WITHIN THE FRAMEWORK OF FIXED DOMAIN ASYMPTOTICS. SPECIFICALLY, WE PROVIDE CONDITIONS FOR EQUIVALENCE OF MEASURES ASSOCIATED WITH MULTIVARIATE GAUSSIAN RANDOM FIELDS, WITH INDEX SET IN A COMPACT SET OF A D-DIMENSIONAL EUCLIDEAN SPACE. SUCH CONDITIONS HAVE BEEN ELUSIVE FOR OVER ABOUT 50 YEARS OF SPATIAL STATISTICS. WE THEN FOCUS ON THE MULTIVARIATE MATERN AND GENERALIZED WENDLAND CLASSES OF MATRIX VALUED COVARIANCE FUNCTIONS, THAT HAVE BEEN VERY POPULAR FOR HAVING PARAMETERS THAT ARE CRUCIAL TO SPATIAL INTERPOLATION, AND THAT CONTROL THE MEAN SQUARE DIFFERENTIABILITY OF THE ASSOCIATED GAUSSIAN PROCESS. WE PROVIDE SUFFICIENT CONDITIONS, FOR EQUIVALENCE OF GAUSSIAN MEASURES, RELYING ON THE COVARIANCE PARAMETERS OF THESE TWO CLASSES. THIS ENABLES TO IDENTIFY THE PARAMETERS THAT ARE CRUCIAL TO ASYMPTOTICALLY EQUIVALENT INTERPOLATION IN MULTIVARIATE GEOSTATISTICS. OUR FINDINGS ARE THEN ILLUSTRATED THROUGH SIMULATION STUDIES

LOS ENTORNOS DE ENSEÑANZA EN LÍNEA REQUIEREN PROMOVER EFICAZMENTE LA AUTONOMÍA DEL APRENDIZAJE, EL COMPROMISO ACTIVO Y EL DESARROLLO DE COMPETENCIAS DIGITALES EN ESTUDIANTES DE EDUCACIÓN SUPERIOR. ESTE TRABAJO INDAGA LA RELACIÓN ENTRE ESTAS VARIABLES A TRAVÉS DE UNA REVISIÓN SISTEMÁTICA DE LITERATURA SOBRE EL VÍNCULO ENTRE MOTIVACIÓN, AUTORREGULACIÓN DEL APRENDIZAJE Y COMPETENCIA DIGITAL. SE REALIZÓ UNA BÚSQUEDA DE ARTÍCULOS EN WEB OF SCIENCE Y SCOPUS, Y LUEGO SE ANALIZARON CUALITATIVAMENTE CON UN ENFOQUE TEMÁTICO. SE OBSERVARON PERSPECTIVAS TEÓRICAS SEMINALES EN COMÚN; SIN EMBARGO, POCAS EXPERIENCIAS ABORDARON ESTAS DIMENSIONES DE MANERA INTEGRADA. LOS RESULTADOS MUESTRAN UN DESARROLLO INICIAL DEL ESTUDIO DEL TEMA EN CONTEXTOS DE ENSEÑANZA CON APOYO DE PLATAFORMAS EDUCATIVAS, RECONOCIENDO RELACIONES BILATERALES ENTRE LOS CONSTRUCTOS, CON UNA REPERCUSIÓN RELEVANTE EN EL DESEMPEÑO ACADÉMICO Y LA DISPOSICIÓN PARA EL APRENDIZAJE.

THE MATÉRN AND THE GENERALIZED CAUCHY FAMILIES OF COVARIANCE FUNCTIONS HAVE A PROMINENT ROLE IN SPATIAL STATISTICS AS WELL AS IN A WEALTH OF STATISTICAL APPLICATIONS. THE MATÉRN FAMILY IS CRUCIAL TO INDEX MEAN-SQUARE DIFFERENTIABILITY OF THE ASSOCIATED GAUSSIAN RANDOM FIELD; THE CAUCHY FAMILY IS A DECOUPLER OF THE FRACTAL DIMENSION AND HURST EFFECT FOR GAUSSIAN RANDOM FIELDS THAT ARE NOT SELF-SIMILAR. OUR EFFORT IS DEVOTED TO PROVE THAT A SCALE-DEPENDENT FAMILY OF COVARIANCE FUNCTIONS, OBTAINED AS A REPARAMETERIZATION OF THE GENERALIZED CAUCHY FAMILY, CONVERGES TO A PARTICULAR CASE OF THE MATÉRN FAMILY, PROVIDING A SOMEWHAT SURPRISING BRIDGE BETWEEN COVARIANCE MODELS WITH LIGHT TAILS AND COVARIANCE MODELS THAT ALLOW FOR LONG MEMORY EFFECT.

WE STUDY ESTIMATION AND PREDICTION OF GAUSSIAN PROCESSES WITH COVARIANCE MODEL BELONGING TO THE GENERALIZED CAUCHY (GC) FAMILY, UNDER FIXED DOMAIN ASYMPTOTICS. GAUSSIAN PROCESSES WITH THIS KIND OF COVARIANCE FUNCTION PROVIDE SEPARATE CHARACTERIZATION OF FRACTAL DIMENSION AND LONG RANGE DEPENDENCE, AN APPEALING FEATURE IN MANY PHYSICAL, BIOLOGICAL OR GEOLOGICAL SYSTEMS. THE RESULTS OF THE PAPER ARE CLASSIFIED INTO THREE PARTS. IN THE FIRST PART, WE CHARACTERIZE THE EQUIVALENCE OF TWO GAUSSIAN MEASURES WITH GC COVARIANCE FUNCTION. THEN WE PROVIDE SUFFICIENT CONDITIONS FOR THE EQUIVALENCE OF TWO GAUSSIAN MEASURES WITH MAT{É}RN (MT) AND GC COVARIANCE FUNCTIONS AND TWO GAUSSIAN MEASURES WITH GENERALIZED WENDLAND (GW) AND GC COVARIANCE FUNCTIONS. IN THE SECOND PART, WE ESTABLISH STRONG CONSISTENCY AND ASYMPTOTIC DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE MICROERGODIC PARAMETER ASSOCIATED TO GC COVARIANCE MODEL, UNDER FIXED DOMAIN ASYMPTOTICS. THE LAST PART FOCUSES ON OPTIMAL PREDICTION WITH GC MODEL AND SPECIFICALLY, WE GIVE CONDITIONS FOR ASYMPTOTIC EFFICIENCY PREDICTION AND ASYMPTOTICALLY CORRECT ESTIMATION OF MEAN SQUARE ERROR USING A MISSPECIFIED GC, MT OR GW MODEL, UNDER FIXED DOMAIN ASYMPTOTICS. OUR FINDINGS ARE ILLUSTRATED THROUGH A SIMULATION STUDY: THE FIRST COMPARES THE FINITE SAMPLE BEHAVIOR OF THE MAXIMUM LIKELIHOOD ESTIMATION OF THE MICROERGODIC PARAMETER OF THE GC MODEL WITH THE GIVEN ASYMPTOTIC DISTRIBUTION. WE THEN COMPARE THE FINITE-SAMPLE BEHAVIOR OF THE PREDICTION AND ITS ASSOCIATED MEAN SQUARE ERROR WHEN THE TRUE MODEL IS GC AND THE PREDICTION IS PERFORMED USING THE TRUE MODEL AND A MISSPECIFIED GW MODEL.

WE STUDY ESTIMATION AND PREDICTION OF GAUSSIAN RANDOM FIELDS WITH COVARIANCE MODELS BELONGING TO THE GENERALIZED WENDLAND (GW) CLASS, UNDER FIXED DOMAIN ASYMPTOTICS. AS FOR THE MATÉRN CASE, THIS CLASS ALLOWS FOR A CONTINUOUS PARAMETERIZATION OF SMOOTHNESS OF THE UNDERLYING GAUSSIAN RANDOM FIELD, BEING ADDITIONALLY COMPACTLY SUPPORTED. THE PAPER IS DIVIDED INTO THREE PARTS: FIRST, WE CHARACTERIZE THE EQUIVALENCE OF TWO GAUSSIAN MEASURES WITH GW COVARIANCE FUNCTION, AND WE PROVIDE SUFFICIENT CONDITIONS FOR THE EQUIVALENCE OF TWO GAUSSIAN MEASURES WITH MATÉRN AND GW COVARIANCE FUNCTIONS. IN THE SECOND PART, WE ESTABLISH STRONG CONSISTENCY AND ASYMPTOTIC DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE MICROERGODIC PARAMETER ASSOCIATED TO GW COVARIANCE MODEL, UNDER FIXED DOMAIN ASYMPTOTICS. THE THIRD PART ELUCIDATES THE CONSEQUENCES OF OUR RESULTS IN TERMS OF (MISSPECIFIED) BEST LINEAR UNBIASED PREDICTOR, UNDER FIXED DOMAIN ASYMPTOTICS. OUR FINDINGS ARE ILLUSTRATED THROUGH A SIMULATION STUDY: THE FORMER COMPARES THE FINITE SAMPLE BEHAVIOR OF THE MAXIMUM LIKELIHOOD ESTIMATION OF THE MICROERGODIC PARAMETER WITH THE GIVEN ASYMPTOTIC DISTRIBUTION. THE LATTER COMPARES THE FINITE-SAMPLE BEHAVIOR OF THE PREDICTION AND ITS ASSOCIATED MEAN SQUARE ERROR WHEN USING TWO EQUIVALENT GAUSSIAN MEASURES WITH MATÉRN AND GW COVARIANCE MODELS, USING COVARIANCE TAPERING AS BENCHMARK.

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.

THIS RESEARCH DELVES INTO THE PEDAGOGICAL COMPETENCIES OFTECHNICIAN-TEACHERS WITH NO PEDAGOGICAL FORMATION WHO WILLSUPPORT THE WORKING AND EDUCATIVE TRAJECTORY OF STUDENTSWHO DECIDED TO STUDY THE TECHNICAL-PROFESSIONAL INTERMEDIATEEDUCATION (EMTP) IN CHILE. BY USING A PERCEPTION QUESTIONNAIREOF THE PEDAGOGICAL COMPETENCY COMMAND AS WELL AS THESTRUCTURAL MODEL TECHNIQUE, THE COMMAND OF THE DIDACTICPROFESSIONAL COMPETENCIES IS STUDIED IN A STRATIFIED SAMPLE OF151 TEACHERS. THE RESULTS INDICATE THAT MODEL IS SENSITIVE TOTHE CONTEXTS WITH SOCIAL VULNERABILITY AND TO THE COMPETENCYBASEDACTION OF TEACHERS WITH NO FORMATION, WHICH BECOMES ACONTRIBUTION TO DETERMINE THE FOCUSED CONTINUING COURSES.

USING THEORETICAL ARGUMENTS, WE PRESENT TWO NOVEL SPECTRUM MODELS OF THE STREAMWISE VELOCITY COMPONENT WITH ROBUST CORRELATION STRUCTURES, WHICH ACCOUNT FOR AND DECOUPLE THE FRACTAL DIMENSION AND HURST EFFECT. THE FORMULATIONS THAT USE ISOTROPIC CONCEPTS ARE ADAPTED FROM THE MODERN PROBABILITY THEORY USING THE SO-CALLED GENERALIZED CAUCHY AND DAGUM MODELS, WHICH BELONG TO WIDE-SENSE-STATIONARY RANDOM FIELDS. A COMPLEMENTARY INSPECTION OF THESE TWO MODELS WITH FIELD DATA FROM A MET-TOWER-MOUNTED SONIC ANEMOMETER LOCATED WITHIN THE ATMOSPHERIC SURFACE LAYER REVEALS GOOD AGREEMENT AND BETTER PERFORMANCE THAN OTHER CONVENTIONALLY USED ISOTROPIC-BASED MODELS OF STREAMWISE VELOCITY SPECTRA. THE FRACTAL DIMENSION, D, OF BOTH MODELS IS CONSISTENT WITH THE WELL-KNOWN KOLMOGOROV ?5/3 POWER LAW IN THE INERTIAL SUB-RANGE. FOR COMPLETENESS, THE STUDY INCLUDES A DERIVATION OF THE EXPLICIT FORMS OF THE ENERGY SPECTRAL DENSITIES OF THE CAUCHY AND DAGUM COVARIANCES.

WE STUDY THE ESTIMATION AND PREDICTION OF GAUSSIAN PROCESSES WITH SPACE-TIME COVARIANCE MODELS BELONGING TO THE DYNAMICAL GENERALIZED WENDLAND (???) FAMILY, UNDER FIXED-DOMAIN ASYMPTOTICS. SUCH A CLASS IS NONSEPARABLE, HAS DYNAMICAL COMPACT SUPPORTS, AND PARAMETERIZES DIFFERENTIABILITY AT THE ORIGIN SIMILARLY TO THE SPACE-TIME MATÉRN CLASS. OUR RESULTS ARE PRESENTED IN TWO PARTS. FIRST, WE ESTABLISH THE STRONG CONSISTENCY AND ASYMPTOTIC NORMALITY FOR THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE MICROERGODIC PARAMETER ASSOCIATED WITH THE ??? COVARIANCE MODEL, UNDER FIXED-DOMAIN ASYMPTOTICS. THE SECOND PART FOCUSES ON OPTIMAL KRIGING PREDICTION UNDER THE ??? MODEL AND AN ASYMPTOTICALLY CORRECT ESTIMATION OF THE MEAN SQUARED ERROR USING A MISSPECIFIED MODEL. OUR THEORETICAL RESULTS ARE, IN TURN, BASED ON THE EQUIVALENCE OF GAUSSIAN MEASURES UNDER SOME GIVEN FAMILIES OF SPACE-TIME COVARIANCE FUNCTIONS, WHERE BOTH SPACE OR TIME ARE COMPACT. THE TECHNICAL RESULTS ARE PROVIDED IN THE ONLINE SUPPLEMENTARY MATERIAL.

WE STUDY THE ESTIMATION AND PREDICTION OF GAUSSIAN PROCESSES WITH SPACE-TIME COVARIANCE MODELS BELONGING TO THE DYNAMICAL GENERALIZED WENDLAND (???) FAMILY, UNDER FIXED-DOMAIN ASYMPTOTICS. SUCH A CLASS IS NONSEPARABLE, HAS DYNAMICAL COMPACT SUPPORTS, AND PARAMETERIZES DIFFERENTIABILITY AT THE ORIGIN SIMILARLY TO THE SPACE-TIME MATÉRN CLASS. OUR RESULTS ARE PRESENTED IN TWO PARTS. FIRST, WE ESTABLISH THE STRONG CONSISTENCY AND ASYMPTOTIC NORMALITY FOR THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE MICROERGODIC PARAMETER ASSOCIATED WITH THE ??? COVARIANCE MODEL, UNDER FIXED-DOMAIN ASYMPTOTICS. THE SECOND PART FOCUSES ON OPTIMAL KRIGING PREDICTION UNDER THE ??? MODEL AND AN ASYMPTOTICALLY CORRECT ESTIMATION OF THE MEAN SQUARED ERROR USING A MISSPECIFIED MODEL. OUR THEORETICAL RESULTS ARE, IN TURN, BASED ON THE EQUIVALENCE OF GAUSSIAN MEASURES UNDER SOME GIVEN FAMILIES OF SPACE-TIME COVARIANCE FUNCTIONS, WHERE BOTH SPACE OR TIME ARE COMPACT. THE TECHNICAL RESULTS ARE PROVIDED IN THE ONLINE SUPPLEMENTARY MATERIAL.

WE INTRODUCE A NEW APPROACH TO CLUSTERING CATEGORICAL DATA: CONDORCET CLUSTERING WITH A FIXED NUMBER OF GROUPS, DENOTED ?-CONDORCET. AS K-MODES, THIS APPROACH IS ESSENTIALLY BASED ON SIMILARITY AND DISSIMILARITY MEASURES. THE PAPER IS DIVIDED INTO THREE PARTS: FIRST, WE PROPOSE A NEW CONDORCET CRITERION, WITH A FIXED NUMBER OF GROUPS (TO SELECT CASES INTO CLUSTERS). IN THE SECOND PART, WE PROPOSE A HEURISTIC ALGORITHM TO CARRY OUT THE TASK. IN THE THIRD PART, WE COMPARE ?-CONDORCET CLUSTERING WITH K-MODES CLUSTERING. THE COMPARISON IS MADE WITH A QUALITY?S INDEX, ACCURACY OF A MEASUREMENT, AND A WITHIN-CLUSTER SUM-OF-SQUARES INDEX. OUR FINDINGS ARE ILLUSTRATED USING REAL DATASETS: THE FELINE DATASET AND THE US CENSUS 1990 DATASET.

WE INTRODUCE A NEW APPROACH TO CLUSTERING CATEGORICAL DATA: CONDORCET CLUSTERING WITH A FIXED NUMBER OF GROUPS, DENOTED A-CONDORCET. AS K-MODES, THIS APPROACH IS ESSENTIALLY BASED ON SIMILARITY AND DISSIMILARITY MEASURES. THE PAPER IS DIVIDED INTO THREE PARTS: FIRST, WE PROPOSE A NEW CONDORCET CRITERION, WITH A FIXED NUMBER OF GROUPS (TO SELECT CASES INTO CLUSTERS). IN THE SECOND PART, WE PROPOSE A HEURISTIC ALGORITHM TO CARRY OUT THE TASK. IN THE THIRD PART, WE COMPARE ?-CONDORCET CLUSTERING WITH K-MODES CLUSTERING. THE COMPARISON IS MADE WITH A QUALITY?S INDEX, ACCURACY OF A MEASUREMENT, AND A WITHIN-CLUSTER SUM-OF-SQUARES INDEX. OUR FINDINGS ARE ILLUSTRATED USING REAL DATASETS: THE FELINE DATASET AND THE US CENSUS 1990 DATASET.

ESTE ARTÍCULO DA CUENTA DE LAS ETAPAS DE VALIDACIÓN DE UN MODELO ESTRUCTURAL PARA ABORDAR LAS COMPETENCIAS PEDAGÓGICAS EN PROFESORAS Y PROFESORES DE EDUCACIÓN MEDIA TÉCNICO PROFESIONAL (EMPT). PARA LA VALIDEZ DEL CONSTRUCTO Y LOS CRITERIOS, SE FORMULÓ UN CUESTIONARIO QUE INTEGRÓ SENTENCIAS ASOCIADAS CON LAS VARIABLES LATENTES: ACCIÓN PROFESIONAL, COMPETENCIA SOCIAL Y VOCACIÓN PROFESIONAL DOCENTE, QUE SE EVALUARON CON JUECES EXPERTOS NACIONALES E INTERNACIONALES. POSTERIORMENTE, SE DETERMINÓ EL ÍNDICE DE VALIDEZ DE CONTENIDOS; SE EVALUÓ EL COMPORTAMIENTO DE LA ESCALA DE VALORACIÓN CONCEPTUAL Y DEL EL INSTRUMENTO, EN UNA MUESTRA ALEATORIA, USANDO ANÁLISIS FACTORIAL CONFIRMATORIO. EL ARTÍCULO FINALIZA CON LA PRESENTACIÓN DE LA CONVERGENCIA TEÓRICA DE LOS NUEVOS MODELOS ESTRUCTURALES QUE SE DEVELAN CON BASE EN LA OPCIÓN INICIAL DE CONSTRUCTOS AJUSTADOS A LA REALIDAD CHILENA, DE LAS Y LOS PROFESORES DE EMTP QUE REALIZAN DOCENCIA EN CONTEXTOS CON ALTOS ÍNDICES DE VULNERABILIDAD SOCIAL.

THIS ARTICLE EXAMINES THE VALIDATION STAGES OF A RATING SCALE TO ASSESS THE IMPACT OF EDUCATIONAL RESEARCH ON TEACHING PRACTICE, PAYING PARTICULAR ATTENTION TO THE PROCEDURES TO VALIDATE THE UNDERLYING CONSTRUCT. TO ACHIEVE THIS AIM, WE CONSIDERED THE RESEARCH PROBLEM, SAMPLE AVAILABILITY, AND CRITERIA OF SCIENTIFIC RIGOR FOR DEVELOPING SURVEY INSTRUMENTS, SPECIFICALLY A RATING SCALE. DATA DRAWN FROM A RATING SCALE ARE APPLIED TO A SAMPLE OF 62 TEACHERS AT THE UNIVERSITY OF GRANADA (SPAIN) AND 117 NON-UNIVERSITY TEACHERS. THROUGH A SECONDARY ANALYSIS OF THE DATA, THE DIFFERENT STAGES TO VALIDATE THE CONSTRUCT WERE DEVELOPED, OBTAINING THREE CONSTRUCTS COMPRISING 16 ITEMS OF THE 43 ITEMS AVAILABLE. THE STUDY SHOWS THAT CONFIRMATORY FACTOR ANALYSIS IS MORE POWERFUL THAN EXPLORATORY FACTOR ANALYSIS IN VALIDATING THE UNDERLYING CONSTRUCT OF A MEASUREMENT INSTRUMENT (RATING SCALE) AND IN REDUCING THE SCALE ITEMS.

WE CONSIDER A NEW OPERATOR ACTING ON RESCALED WEIGHTED DIFFERENCES BETWEEN TWO MEMBERS OF THE CLASS OF POSITIVE DEFINITE RADIAL FUNCTIONS. IN PARTICULAR, WE STUDY THE POSITIVE DEFINITENESS OF THE OPERATOR FOR THE MATÉRN, GENERALIZED CAUCHY AND WENDLAND FAMILIES.