[{"data":1,"prerenderedAt":1677},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/estimador-estadistica:0":3},{"page":4,"book":26,"news":1671,"questionSent":19,"questions":1672,"formData":1673,"attachments":23,"chartData":23,"pending":19,"chartOptions":1674,"afspec":19,"aflink":1676},{"id":5,"book_id":6,"chapter_id":7,"name":8,"slug":9,"html":10,"priority":11,"created_at":12,"updated_at":13,"created_by":14,"updated_by":18,"draft":19,"markdown":20,"revision_count":21,"template":19,"owned_by":22,"editor":20,"trends":23,"raw_html":24,"tags":25},4061,2,0,"Estimador (estadística)","estimador-estadistica","\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-un-e\">\u003Cstrong>En estadística, un estimador\u003C/strong>  es un \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/estadisticos-muestrales\">estadístico\u003C/a>\u003C/strong> o función de los datos muestrales que se utiliza para estimar, cuantificar o extraer conclusiones, sobre un \u003Ca href=\"https://ikusmira.org/p/parametro-poblacional\">parámetro desconocido en una población o modelo aleatorio\u003C/a>. En general, dado un parámetro \\(\\theta\\), un estimador para dicho parámetro se denota \\(\\hat{\\theta}\\). Un ejemplo común de estimador es la media muestral (\\(\\overline{x}\\)) de un grupo de datos, que se suele utilizar como estimador de la media poblaciónal \\(\\mu\\); dicha relación entre media muestral y poblacional la denotamos de esta forma: \\(\\hat{\\mu}=\\overline{x}\\).\u003C/p>\r\n\u003Cp id=\"bkmrk-para-un-par%C3%A1metro-da\">Para un parámetro dado pueden proponerse una infinidad de estimadores posibles; por ejemplo para el caso de la media poblacional. pueden propornerse medias aritméticas simples con diferentes tamaños muestrales y medias aritméticas ponderadas con diferentes ponderaciones para cada dato. La clave consiste en elegir el estimador que mejor estime o más se acerque al valor del parámetro. Para ello, deben examinarse diferentes propiedades del estimador: su insesgadez, precisión, consistencia y suficiencia, principalmente. \u003C/p>",331,"2026-03-03T16:21:58.000000Z","2026-03-04T15:19:50.000000Z",{"id":15,"name":16,"slug":17},1,"Admin","admin",{"id":15,"name":16,"slug":17},false,"",3,{"id":15,"name":16,"slug":17},null,"\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-un-e\">\u003Cstrong>En estadística, un estimador\u003C/strong>  es un \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/estadisticos-muestrales\">estadístico\u003C/a>\u003C/strong> o función de los datos muestrales que se utiliza para estimar, cuantificar o extraer conclusiones, sobre un \u003Ca href=\"https://ikusmira.org/p/parametro-poblacional\">parámetro desconocido en una población o modelo aleatorio\u003C/a>. En general, dado un parámetro \\(\\theta\\), un estimador para dicho parámetro se denota \\(\\hat{\\theta}\\). Un ejemplo común de estimador es la media muestral (\\(\\overline{x}\\)) de un grupo de datos, que se suele utilizar como estimador de la media poblaciónal \\(\\mu\\); dicha relación entre media muestral y poblacional la denotamos de esta forma: \\(\\hat{\\mu}=\\overline{x}\\).\u003C/p>\r\n\u003Cp id=\"bkmrk-para-un-par%C3%A1metro-da\">Para un parámetro dado pueden proponerse una infinidad de estimadores posibles; por ejemplo para el caso de la media poblacional. pueden propornerse medias aritméticas simples con diferentes tamaños muestrales y medias aritméticas ponderadas con diferentes ponderaciones para cada dato. La clave consiste en elegir el estimador que mejor estime o más se acerque al valor del parámetro. Para ello, deben examinarse diferentes propiedades del estimador: su insesgadez, precisión, consistencia y suficiencia, principalmente. \u003C/p>",[],{"id":6,"name":27,"slug":28,"description":20,"created_at":29,"updated_at":30,"created_by":15,"updated_by":15,"owned_by":15,"default_template_id":23,"pages":31,"index":62,"shelves":1664},"Estadística general","estadistica-general","2023-05-06T08:26:42.000000Z","2023-05-16T06:24:05.000000Z",[32,37,42,47,52,57],{"id":33,"name":34,"slug":35,"html":36},3866,"Multicolinealidad","multicolinealidad","\u003Cp id=\"bkmrk-la-multicolinealidad\">\u003Cspan id=\"bkmrk-la-multicolinealidad-1\" class=\"form-control-text textarea\" style=\"display: block;\" role=\"textbox\">\u003Cspan id=\"bkmrk-la-multicolinealidad-2\" class=\"form-control-text textarea\" style=\"display: block;\" role=\"textbox\">La\u003Cstrong> multicolinealidad\u003C/strong> es la situación problemática que suele aparecer en la estimación de los \u003Ca href=\"https://ikusmira.org/p/modelo-de-regresion\">modelos de regresión\u003C/a>, cuando existe correlación entre variables explicativas, lo que implica que proporcionan información repetida. Cuando esta correlación sólo se produce entre dos variables, se puede decir simplemente que hay colinealidad. Existen dos tipos de multicolinealidad: la \u003Cstrong>multicolinealidad exacta\u003C/strong>, cuando la correlación entre las variables explicativas es perfecta, lo que impide totalmente la estimación de los parámetros del modelo, y la multicolinealidad imperfectaq, que impide una estimación precisa de los coeficientes de regresión. En el caso de la colinealidad múltiple total, la solución más clara es eliminar una o varias de las variables que tienen una correlación perfecta entre sí, es decir, una las variables colineales, mientras que en el caso de multicolinealidad imperfecta puede ser una solución aumentar el tamaño de muestra o transforman las variables explicativas (por ejemplo, sus logaritmos).\u003C/span>\u003C/span>\u003C/p>",{"id":38,"name":39,"slug":40,"html":41},2887,"Separabilidad demográfica","separabilidad-demografica","\u003Cp id=\"bkmrk-la-separabilidad-dem\">La \u003Cstrong>separabilidad demográfica\u003C/strong> es la diferencia que se da en una población de referencia respecto de un conjunto de variables. Por ejemplo, si se verifica de forma significativa que hombres y mujeres tienen en promedio diferentes niveles de salario, la separabilidad demográfica es alta, esto es, lo cual implica que los estudios sobre salarios y otras variables asociadas con esta deben tener en cuenta dicha diferencia.\u003C/p>",{"id":43,"name":44,"slug":45,"html":46},1812,"Límite inferior de clase y límite superior de clase","limite-inferior-de-clase-y-limite-superior-de-clase","\u003Cp id=\"bkmrk-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2024-03/iLpfSYI3dVfRe6Ts-ikusmira-amplitud-clase.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg src=\"https://es.gizapedia.org/uploads/images/gallery/2024-03/scaled-1680-/iLpfSYI3dVfRe6Ts-ikusmira-amplitud-clase.png\" alt=\"ikusmira_amplitud_clase.png\">\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-el-l\">En estadística, los \u003Cstrong>límites de clase o fronteras de clase, también llamados límites de intervalo\u003C/strong> son los extremos de los intervalos de clase que agrupan los datos. El \u003Ca href=\"https://ikusmira.org/p/limite-inferior-de-clase-y-limite-superior-de-clase\">\u003Cstrong>límite inferior de clase o intervalo\u003C/strong>\u003C/a> es el valor donde comienza el \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/intervalo-de-clase\">intervalo de clase\u003C/a>\u003C/strong> en el que se agrupar los datos. El \u003Ca href=\"https://ikusmira.org/p/limite-inferior-de-clase-y-limite-superior-de-clase\">\u003Cstrong>límite superior de clase o intervalo\u003C/strong>\u003C/a> es el valor donde finaliza el intervalo de clase para agrupar dichos datos.\u003C/p>\r\n\u003Cp id=\"bkmrk-se-recomienda-genera\">Se recomienda generalmente que los \u003Cstrong>intervalos sean con límites nominales contiguos\u003C/strong>, estro es, que el límite superior del intervalo coincida con el límite inferior del intervalo siguiente (por ejemplo, para alturas, 150-155cm, 155-160cm, 160-165cm, 165-170cm, ...). En estos casos, por convenio, generalmente el límite inferior de clase es cerrado, es decir, los datos cuyos valores coinciden con el límite inferior se incluyen en dicho intervalo, mientras que el límite superior de clase es abierto, es decir, los datos cuyo valor coincide exactamente con dicho límite se incluyen en el intervalo siguiente, a menos que se establezca lo contrario. Por ejemplo, para datos sobre peso de un grupo de personas, el intervalo 55kg-60kg tiene como límite inferior 55kg y como límite superior 60kg. Una persona con 55kg se incluiría dentro de este intervalo, mientras que una persona de 60kg se incluiría en el intervalo siguiente, esto es, 60kg-65kg.\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-a-veces-los-interval\">A veces los intervalos se establecen con\u003Cstrong> límites nominales separados \u003C/strong>para facilitar la comprensión a personas que no tiene conocimientos de estadística de qué observación entra en cada intervalo. En el ejemplo anterior, alternativamente y con el mismo resultado de agrupamiento de datos, podríamos establecer los intervalos nominales 150-154cm, 155-159cm, ... Este tipo de límites nominales separados suelen ser habituales en distribuciones de edades (15-19 años, 20-24 años, ...).\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-l%C3%ADmites-reales-de-cl\">\r\n\u003Cli class=\"null\">\u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/limites-reales-de-clase\">Límites reales de clase\u003C/a>\u003C/strong>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/limites-nominales-de-clase\">\u003Cstrong>Límites nominales de clase\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/limites-aparentes-de-clase\">\u003Cstrong>Límites aparentes de clase\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",{"id":48,"name":49,"slug":50,"html":51},2437,"Prueba ji-cuadrado (chi-cuadrado) de Pearson","prueba-ji-cuadrado-chi-cuadrado-de-pearson","\u003Cp id=\"bkmrk-la-prueba-o-contrast\">La \u003Cstrong>prueba o contraste ji-cuadrado (tambien denominada chi-cuadrado) de Pearson \u003C/strong>es un contraste estadístico con diversas aplicaciones (contraste de bondad de ajuste, contraste de independencia, contraste de homogeneidad) que se basa en el estadístico de prueba ji-cuadrado, que calcula la distancia total relativa entre frecuencias observadas y frecuencias teóricas. Bajo la hipótesis nula en cada caso, este estadístico se distribuye aproximadamente según una distribución ji-cuadrado con región crítica unilateral a la derecha; es decir, la hipótesis nula se rechaza cuando el estadśitico ji-cuadrado de Pearson supera un valor crítico. \u003C/p>\r\n\u003Cp id=\"bkmrk-las-aplicaciones-con\">Las aplicaciones concretas de la prueba ji-cuadrado de Pearson son:\u003C/p>\r\n\u003Cul id=\"bkmrk-prueba-de-ji-cuadrad\">\r\n\u003Cli class=\"null\">prueba de ji-cuadrado de Pearson para la bondad de ajuste;\u003C/li>\r\n\u003Cli class=\"null\">prueba de ji-cuadrado de Pearson para la independencia;\u003C/li>\r\n\u003Cli class=\"null\">prueba de ji-cuadrado de Pearson para la homogeneidad (igualdad de distribuciones multinomiales).\u003C/li>\r\n\u003C/ul>",{"id":53,"name":54,"slug":55,"html":56},2648,"Coeficiente de correlación biserial puntual","coeficiente-de-correlacion-biserial-puntual","\u003Cp id=\"bkmrk-el-coeficiente-de-co\">El \u003Cstrong>coeficiente de correlación biserial puntual o coeficiente de correlación punto-biserial\u003C/strong> es un coeficiente que mide la correlación o relación estadística entre una variable cuantitativa y una variable dicotómica genuina o pura, esto es, que no ha sido el objeto de una dicotomización artificial. Un ejemplo de esta situación es la correlación entre el sexo (variable dicotómica pura) y la calificación obtenida en un examen de matemáticas. Aunque el coeficiente de correlación biserial puntual coincide con el coeficiente de correlación lineal de Pearson cuando en este último la variable dicotómica se ha codificado en términos de 0s y 1s, lo habitual es referise a dicho coeficiente a través de esta fórmula:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24r_%7Bbp%7D%3D%5Ccfrac%7B%5Cove\">$$r_{bp}=\\cfrac{\\overline{x}_p-\\overline{x}_q}{s_x}\\sqrt{pq}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-donde-%5C%28%5Coverline%7Bx%7D\">donde \\(\\overline{x}_p\\) y \\(\\overline{x}_q\\) son las medias artméticas simples de las puntuaciones de la variable cuantitativa para cada grupo de la variable dicotómica (en el ejemplo del párrafo anterior, serían las medias de las calificaciones de los hombres, por un lado; y de las mujeres, por otro), \\(s_x\\) es la desviación típica de la variable cuantitativa, reuniendo los datos de los grupos (en el ejemplo, la desviación típica de todas las calificaciones, sin distinguir si corresponden a un hombre o una mujer), y \\(p\\) y \\(q\\) son las proporciones de elementos en cada grupo sobre el tamaño total de la muestra (en el ejemplo, proporción de hombres y proporción de mujeres).\u003C/p>\r\n\u003Cp id=\"bkmrk-al-igual-que-el-coef\">Al igual que el coeficiente de correlación de Pearson, el coeficiente de correlación biserial puntual toma valores en el intervalo [-1,1] y se interpreta del mismo modo que aquel, siendo la correlación mas intensa según nos acercamos en valor absoluto  al valor 1, mientras que el signo indica que grupo de la variable dicotómica obtiene mayores puntuaciones en la variable cuantitativa.\u003C/p>",{"id":58,"name":59,"slug":60,"html":61},1866,"Población finita","poblacion-finita","\u003Cp id=\"bkmrk-una-poblaci%C3%B3n-finita\">Una \u003Cstrong>población finita\u003C/strong> es una \u003Ca href=\"https://ikusmira.org/p/poblacion-estadistica\">población estadística\u003C/a> en la que todos sus elementos se pueden enumerar hasta formar un número total determinado.  Se contrapone al concepto de población infinita. Por ejemplo, son poblaciones finitas el conjunto de alumnos de un colegio; los habitantes empadronados en una población y los trabajadores de una empresa. Se denomina a la lista o enumeración de todos los elementos de la población \u003Ca href=\"https://ikusmira.org/p/marco-muestral\">marco muestral\u003C/a>. Sin embargo, existen situaciones en las que no existe este marco muestral o registro de todos y cada uno de los elementos o individuos de una población de interés; por ejemplo, los individuos de una especie animal en un área determinada forman una población finita, aunque generalmente no se conoce su tamaño exacto, pudiéndose este estimar a través de métodos de captura-recaptura. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-la-particularidad-de\">La particularidad de las poblaciones finitas es que permiten el desarrollo de métodos de muestreo mejor adaptados que el muestreo aleatorio simple que es el método de muestreo común en poblaciones infinitas, como por ejemplo el muestreo aleatorio sin devolución o reemplazamiento, el muestreo sistemático, el muestreo estratificado o el muestreo por conglomerados. De hecho existe una rama de la estadística denominada muestreo de poblaciones finitas.\u003C/p>",{"":63},[64,68,72,76,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,152,157,162,167,172,177,182,187,192,197,202,207,212,217,222,227,232,236,241,245,250,255,260,265,270,274,278,283,288,293,298,302,307,312,317,322,327,332,337,342,347,352,357,362,367,372,377,382,387,392,397,402,407,412,417,421,426,431,436,441,446,451,456,461,465,470,475,479,484,489,494,499,504,509,514,519,524,528,533,538,543,548,553,558,563,568,573,578,583,588,593,598,603,608,613,618,623,628,633,638,643,648,653,658,663,668,673,678,683,688,693,698,703,708,713,718,723,728,733,738,740,745,750,755,759,763,768,773,777,781,785,790,795,800,805,809,814,819,824,829,834,839,844,848,853,858,863,868,873,878,883,888,893,898,902,907,912,917,922,927,932,937,942,947,951,956,960,965,970,975,980,985,989,994,999,1004,1009,1013,1018,1023,1027,1032,1037,1042,1046,1051,1056,1061,1066,1070,1072,1077,1082,1087,1092,1097,1102,1107,1112,1116,1121,1123,1128,1132,1137,1142,1147,1151,1155,1160,1165,1170,1175,1180,1184,1188,1190,1195,1200,1205,1209,1214,1219,1222,1226,1231,1236,1240,1245,1250,1255,1260,1265,1270,1275,1280,1285,1290,1295,1300,1304,1309,1314,1319,1324,1329,1334,1339,1344,1349,1354,1359,1364,1369,1374,1379,1382,1386,1391,1396,1401,1405,1409,1413,1418,1422,1426,1431,1436,1441,1446,1451,1456,1461,1466,1471,1476,1481,1486,1491,1495,1500,1505,1509,1514,1519,1524,1529,1533,1537,1541,1546,1551,1556,1558,1563,1568,1573,1578,1583,1588,1593,1598,1603,1608,1613,1618,1623,1628,1633,1638,1643,1644,1649,1654,1659],{"id":65,"name":66,"slug":67,"priority":7,"chapter_name":23},3173,"Aleatorización (diseño de experimentos)","aleatorizacion-diseno-de-experimentos",{"id":69,"name":70,"slug":71,"priority":15,"chapter_name":23},631,"Amplitud de clase","amplitud-de-clase",{"id":73,"name":74,"slug":75,"priority":6,"chapter_name":23},387,"Análisis de trayectorias","analisis-de-trayectorias",{"id":77,"name":78,"slug":79,"priority":21,"chapter_name":23},624,"Arranque aleatorio","arranque-aleatorio",{"id":81,"name":82,"slug":83,"priority":84,"chapter_name":23},43,"Asociación estadística","asociacion-estadistica",4,{"id":86,"name":87,"slug":88,"priority":89,"chapter_name":23},2019,"Asociación no estadística","asociacion-no-estadistica",5,{"id":91,"name":92,"slug":93,"priority":94,"chapter_name":23},2948,"Banco de datos","banco-de-datos",6,{"id":96,"name":97,"slug":98,"priority":99,"chapter_name":23},1621,"Base del índice (periodo base)","base-del-indice-periodo-base",7,{"id":101,"name":102,"slug":103,"priority":104,"chapter_name":23},35,"Cálculo de la moda estadística para datos agrupados en intervalos","calculo-de-la-moda-estadistica-para-datos-agrupados-en-intervalos",8,{"id":106,"name":107,"slug":108,"priority":109,"chapter_name":23},3063,"Característica cualitativa","caracteristica-cualitativa",9,{"id":111,"name":112,"slug":113,"priority":114,"chapter_name":23},2708,"Casos particulares","casos-particulares",10,{"id":116,"name":117,"slug":118,"priority":119,"chapter_name":23},2730,"Censo estadístico","censo-estadistico",11,{"id":121,"name":122,"slug":123,"priority":124,"chapter_name":23},2551,"Clase mediana","clase-mediana",12,{"id":126,"name":127,"slug":128,"priority":129,"chapter_name":23},1011,"Clase modal","clase-modal",13,{"id":131,"name":132,"slug":133,"priority":134,"chapter_name":23},2133,"Coeficiente de asimetría de Bowley","coeficiente-de-asimetria-de-bowley",14,{"id":136,"name":137,"slug":138,"priority":139,"chapter_name":23},1714,"Coeficiente de asimetría de Fisher","coeficiente-de-asimetria-de-fisher",15,{"id":141,"name":142,"slug":143,"priority":144,"chapter_name":23},1844,"Coeficiente de asimetría de Pearson","coeficiente-de-asimetria-de-pearson",16,{"id":146,"name":147,"slug":148,"priority":149,"chapter_name":23},2057,"Coeficiente de contingencia de Pearson","coeficiente-de-contingencia-de-pearson",17,{"id":53,"name":54,"slug":55,"priority":151,"chapter_name":23},18,{"id":153,"name":154,"slug":155,"priority":156,"chapter_name":23},1938,"Coeficiente de curtosis de Pearson","coeficiente-de-curtosis-de-pearson",19,{"id":158,"name":159,"slug":160,"priority":161,"chapter_name":23},2032,"Coeficiente de determinación ajustado (coeficiente de determinación corregido)","coeficiente-de-determinacion-ajustado-coeficiente-de-determinacion-corregido",20,{"id":163,"name":164,"slug":165,"priority":166,"chapter_name":23},2649,"Coeficiente de Tschuprow","coeficiente-de-tschuprow",21,{"id":168,"name":169,"slug":170,"priority":171,"chapter_name":23},37,"Coeficiente de variación","coeficiente-de-variacion",22,{"id":173,"name":174,"slug":175,"priority":176,"chapter_name":23},2646,"Coeficiente Q de Yule","coeficiente-q-de-yule",23,{"id":178,"name":179,"slug":180,"priority":181,"chapter_name":23},2218,"Comprobación de Charlier","comprobacion-de-charlier",24,{"id":183,"name":184,"slug":185,"priority":186,"chapter_name":23},2095,"Concepto de estadística","concepto-de-estadistica",25,{"id":188,"name":189,"slug":190,"priority":191,"chapter_name":23},2607,"Constante estadística","constante-estadistica",26,{"id":193,"name":194,"slug":195,"priority":196,"chapter_name":23},2087,"Corrección de Bessel","correccion-de-bessel",27,{"id":198,"name":199,"slug":200,"priority":201,"chapter_name":23},308,"Corrección de Sheppard","correccion-de-sheppard",28,{"id":203,"name":204,"slug":205,"priority":206,"chapter_name":23},1080,"Corrección de 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