ESTIMACION PUNTUAL

Cargamos la base de datos Clasificacion Credito:

library(readr)
ClasificacionCredito <- read_csv("ClasificacionCredito.csv") #Cargamos la base de datos

ClasificacionCredito=as.data.frame(unclass(ClasificacionCredito),stringsAsFactors = TRUE)
nrow(ClasificacionCredito)
## [1] 164

Teniendo en cuenta la base de datos “Clasificacion Credito”,sacamos una muestra por conveniencia de nuestra poblacion

Se obtiene una base de datos con N=164

knitr::kable(ClasificacionCredito)
Age Gender Income Education Marital.Status Number.of.Children Home.Ownership Credit.Score
25 Female 50000 Bachelor’s Degree Single 0 Rented High
30 Male 100000 Master’s Degree Married 2 Owned High
35 Female 75000 Doctorate Married 1 Owned High
40 Male 125000 High School Diploma Single 0 Owned High
45 Female 100000 Bachelor’s Degree Married 3 Owned High
50 Male 150000 Master’s Degree Married 0 Owned High
26 Female 40000 Associate’s Degree Single 0 Rented Average
31 Male 60000 Bachelor’s Degree Single 0 Rented Average
36 Female 80000 Master’s Degree Married 2 Owned High
41 Male 105000 Doctorate Single 0 Owned High
46 Female 90000 High School Diploma Married 1 Owned High
51 Male 135000 Bachelor’s Degree Married 0 Owned High
27 Female 35000 High School Diploma Single 0 Rented Low
32 Male 55000 Associate’s Degree Single 0 Rented Average
37 Female 70000 Bachelor’s Degree Married 2 Owned High
42 Male 95000 Master’s Degree Single 0 Owned High
47 Female 85000 Doctorate Married 1 Owned High
52 Male 125000 High School Diploma Married 0 Owned High
28 Female 30000 Associate’s Degree Single 0 Rented Low
33 Male 50000 High School Diploma Single 0 Rented Average
38 Female 65000 Bachelor’s Degree Married 2 Owned High
43 Male 80000 Master’s Degree Single 0 Owned High
48 Female 70000 Doctorate Married 1 Owned High
53 Male 115000 Associate’s Degree Married 0 Owned High
29 Female 25000 High School Diploma Single 0 Rented Low
34 Male 45000 Associate’s Degree Single 0 Rented Average
39 Female 60000 Bachelor’s Degree Married 2 Owned High
44 Male 75000 Master’s Degree Single 0 Owned High
49 Female 65000 Doctorate Married 1 Owned High
25 Female 55000 Bachelor’s Degree Single 0 Rented Average
30 Male 105000 Master’s Degree Married 2 Owned High
35 Female 80000 Doctorate Married 1 Owned High
40 Male 130000 High School Diploma Single 0 Owned High
45 Female 105000 Bachelor’s Degree Married 3 Owned High
50 Male 155000 Master’s Degree Married 0 Owned High
26 Female 45000 Associate’s Degree Single 0 Rented Average
31 Male 65000 Bachelor’s Degree Single 0 Rented Average
36 Female 85000 Master’s Degree Married 2 Owned High
41 Male 110000 Doctorate Single 0 Owned High
46 Female 95000 High School Diploma Married 1 Owned High
51 Male 140000 Bachelor’s Degree Married 0 Owned High
27 Female 37500 High School Diploma Single 0 Rented Low
32 Male 57500 Associate’s Degree Single 0 Rented Average
37 Female 72500 Bachelor’s Degree Married 2 Owned High
42 Male 100000 Master’s Degree Single 0 Owned High
47 Female 90000 Doctorate Married 1 Owned High
52 Male 130000 High School Diploma Married 0 Owned High
28 Female 32500 Associate’s Degree Single 0 Rented Low
33 Male 52500 High School Diploma Single 0 Rented Average
38 Female 67500 Bachelor’s Degree Married 2 Owned High
43 Male 92500 Master’s Degree Single 0 Owned High
48 Female 82500 Doctorate Married 1 Owned High
53 Male 122500 Associate’s Degree Married 0 Owned High
29 Female 27500 High School Diploma Single 0 Rented Low
34 Male 47500 Associate’s Degree Single 0 Rented Average
39 Female 62500 Bachelor’s Degree Married 2 Owned High
44 Male 87500 Master’s Degree Single 0 Owned High
49 Female 77500 Doctorate Married 1 Owned High
25 Female 57500 Bachelor’s Degree Single 0 Rented Average
30 Male 112500 Master’s Degree Married 2 Owned High
35 Female 85000 Doctorate Married 1 Owned High
25 Female 60000 Bachelor’s Degree Single 0 Rented Average
30 Male 117500 Master’s Degree Married 2 Owned High
35 Female 90000 Doctorate Married 1 Owned High
40 Male 142500 High School Diploma Single 0 Owned High
45 Female 110000 Bachelor’s Degree Married 3 Owned High
50 Male 160000 Master’s Degree Married 0 Owned High
26 Female 47500 Associate’s Degree Single 0 Rented Average
31 Male 67500 Bachelor’s Degree Single 0 Rented Average
36 Female 90000 Master’s Degree Married 2 Owned High
41 Male 115000 Doctorate Single 0 Owned High
46 Female 97500 High School Diploma Married 1 Owned High
51 Male 145000 Bachelor’s Degree Married 0 Owned High
27 Female 37500 High School Diploma Single 0 Rented Low
32 Male 57500 Associate’s Degree Single 0 Rented Average
37 Female 75000 Bachelor’s Degree Married 2 Owned High
42 Male 105000 Master’s Degree Single 0 Owned High
47 Female 95000 Doctorate Married 1 Owned High
52 Male 135000 High School Diploma Married 0 Owned High
28 Female 32500 Associate’s Degree Single 0 Rented Low
33 Male 52500 High School Diploma Single 0 Rented Average
38 Female 67500 Bachelor’s Degree Married 2 Owned High
43 Male 92500 Master’s Degree Single 0 Owned High
48 Female 85000 Doctorate Married 1 Owned High
53 Male 125000 Associate’s Degree Married 0 Owned High
29 Female 27500 High School Diploma Single 0 Rented Low
34 Male 47500 Associate’s Degree Single 0 Rented Average
39 Female 62500 Bachelor’s Degree Married 2 Owned High
44 Male 87500 Master’s Degree Single 0 Owned High
49 Female 77500 Doctorate Married 1 Owned High
25 Female 57500 Bachelor’s Degree Single 0 Rented Average
30 Male 112500 Master’s Degree Married 2 Owned High
35 Female 85000 Doctorate Married 1 Owned High
25 Female 62500 Bachelor’s Degree Single 0 Rented Average
30 Male 117500 Master’s Degree Married 2 Owned High
35 Female 90000 Doctorate Married 1 Owned High
40 Male 142500 High School Diploma Single 0 Owned High
45 Female 115000 Bachelor’s Degree Married 3 Owned High
50 Male 162500 Master’s Degree Married 0 Owned High
26 Female 50000 Associate’s Degree Single 0 Rented Average
31 Male 70000 Bachelor’s Degree Single 0 Rented Average
36 Female 95000 Master’s Degree Married 2 Owned High
41 Male 120000 Doctorate Single 0 Owned High
46 Female 102500 High School Diploma Married 1 Owned High
51 Male 150000 Bachelor’s Degree Married 0 Owned High
27 Female 37500 High School Diploma Single 0 Rented Low
32 Male 57500 Associate’s Degree Single 0 Rented Average
37 Female 77500 Bachelor’s Degree Married 2 Owned High
42 Male 110000 Master’s Degree Single 0 Owned High
47 Female 97500 Doctorate Married 1 Owned High
52 Male 137500 High School Diploma Married 0 Owned High
28 Female 32500 Associate’s Degree Single 0 Rented Low
33 Male 52500 High School Diploma Single 0 Rented Average
38 Female 67500 Bachelor’s Degree Married 2 Owned High
43 Male 95000 Master’s Degree Single 0 Owned High
48 Female 87500 Doctorate Married 1 Owned High
53 Male 127500 Associate’s Degree Married 0 Owned High
29 Female 27500 High School Diploma Single 0 Rented Low
34 Male 47500 Associate’s Degree Single 0 Rented Average
39 Female 62500 Bachelor’s Degree Married 2 Owned High
44 Male 87500 Master’s Degree Single 0 Owned High
49 Female 77500 Doctorate Married 1 Owned High
25 Female 57500 Bachelor’s Degree Single 0 Rented Average
30 Male 112500 Master’s Degree Married 2 Owned High
35 Female 85000 Doctorate Married 1 Owned High
25 Female 60000 Bachelor’s Degree Single 0 Rented Average
30 Male 117500 Master’s Degree Married 2 Owned High
35 Female 90000 Doctorate Married 1 Owned High
28 Male 75000 Bachelor’s Degree Single 0 Rented Average
33 Female 82000 Master’s Degree Married 1 Owned High
31 Male 95000 Doctorate Single 0 Rented High
26 Female 55000 Bachelor’s Degree Married 1 Owned Average
32 Male 85000 Master’s Degree Single 0 Rented High
29 Female 68000 Doctorate Married 2 Owned Average
34 Male 105000 Bachelor’s Degree Married 1 Rented High
25 Female 55000 Bachelor’s Degree Single 0 Rented Average
30 Male 105000 Master’s Degree Married 2 Owned High
35 Female 80000 Doctorate Married 1 Owned High
40 Male 130000 High School Diploma Single 0 Owned High
45 Female 105000 Bachelor’s Degree Married 3 Owned High
50 Male 155000 Master’s Degree Married 0 Owned High
26 Female 45000 Associate’s Degree Single 0 Rented Average
31 Male 65000 Bachelor’s Degree Single 0 Rented Average
36 Female 85000 Master’s Degree Married 2 Owned High
41 Male 110000 Doctorate Single 0 Owned High
46 Female 95000 High School Diploma Married 1 Owned High
51 Male 140000 Bachelor’s Degree Married 0 Owned High
27 Female 37500 High School Diploma Single 0 Rented Low
32 Male 57500 Associate’s Degree Single 0 Rented Average
37 Female 72500 Bachelor’s Degree Married 2 Owned High
42 Male 100000 Master’s Degree Single 0 Owned High
47 Female 90000 Doctorate Married 1 Owned High
52 Male 130000 High School Diploma Married 0 Owned High
28 Female 32500 Associate’s Degree Single 0 Rented Low
33 Male 52500 High School Diploma Single 0 Rented Average
38 Female 67500 Bachelor’s Degree Married 2 Owned High
43 Male 92500 Master’s Degree Single 0 Owned High
48 Female 82500 Doctorate Married 1 Owned High
53 Male 122500 Associate’s Degree Married 0 Owned High
29 Female 27500 High School Diploma Single 0 Rented Low
34 Male 47500 Associate’s Degree Single 0 Rented Average
39 Female 62500 Bachelor’s Degree Married 2 Owned High
44 Male 87500 Master’s Degree Single 0 Owned High
49 Female 77500 Doctorate Married 1 Owned High 
set.seed(123)
n1=sample(ClasificacionCredito$Age, size = 100, replace = FALSE ) #Muestra de la Edad
n1
##   [1] 53 32 38 29 32 44 34 52 49 25 33 30 30 50 46 34 26 47 47 33 29 41 53 37 35
##  [26] 42 27 51 27 48 53 29 45 31 37 50 30 27 38 40 44 28 29 36 38 52 51 52 38 30
##  [51] 30 42 25 50 32 33 29 37 41 30 41 39 26 40 30 31 49 48 43 44 45 45 34 50 46
##  [76] 25 51 51 38 35 49 41 50 34 34 31 31 43 25 31 28 47 47 25 51 29 25 53 35 46
set.seed(123)
n2=sample(ClasificacionCredito$Income, size = 100, replace = FALSE) #Muetra de los Ingresos
n2
##   [1] 122500  55000  67500  27500  57500  87500  47500 130000  77500  57500
##  [11]  52500 112500 105000 162500  97500  45000  40000  90000  95000  52500
##  [21]  27500 120000 127500  75000  80000 110000  37500 140000  37500  70000
##  [31] 122500  68000 105000  67500  72500 155000 117500  35000  67500 142500
##  [41]  87500  32500  25000  85000  65000 135000 140000 130000  67500 112500
##  [51] 117500  95000  62500 150000  57500  82000  27500  77500 110000 105000
##  [61] 110000  62500  55000 125000 117500  95000  77500  82500  80000  87500
##  [71] 105000 115000  47500 155000  95000  55000 135000 150000  67500  90000
##  [81]  77500 115000 160000 105000  47500  65000  60000  92500  55000  65000
##  [91]  75000  90000  85000  60000 145000  27500  57500 115000  80000 102500
set.seed(123)
n3=sample(ClasificacionCredito$Number.of.Children, size = 100, replace = FALSE)#Muestra de numero de hijos
n3
##   [1] 0 0 2 0 0 0 0 0 1 0 0 2 2 0 1 0 0 1 1 0 0 0 0 2 1 0 0 0 0 1 0 2 3 0 2 0 2
##  [38] 0 2 0 0 0 0 2 2 0 0 0 2 2 2 0 0 0 0 1 0 2 0 2 0 2 1 0 2 0 1 1 0 0 3 3 0 0
##  [75] 1 0 0 0 2 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1

Se extrae una muestra aleatoria por medio de un muestreo por conveniencia de n=100

Media Muestral

Calculamos el promedio muestral de nuestros estimadores.

Promedio_Edad=mean(n1) #Promedio muestral de la Edad
Promedio_Edad
## [1] 38.47
Promedio_Ingresos=mean(n2) #Promedio muestral Ingresos
Promedio_Ingresos
## [1] 87125
Promedio_Hijos=mean(n3)  #Promedio muestral numero de hijos
Promedio_Hijos
## [1] 0.63

Se obtiene que el promedio de nuestro estimador “Edad” ~ 38, el de “Ingresos” ~ 87125 y el de “Numero de hijos” ~ 1

Varianza muestral

Se calcula la varianza muestral de mis estimadores.

Varianza_Edad=var(n1)
Varianza_Edad
## [1] 79.1203
Varianza_Ingresos=var(n2)
Varianza_Ingresos
## [1] 1217198864
Varianza_Hijos=var(n3)
Varianza_Hijos
## [1] 0.7809091

La varianza de mis estimadores:

Edad=79.1203

Ingresos=1217198864

Numero de hijos=0.7809

Desviacion Estandar Muestral

Desviacion_Edad=sd(n1)
Desviacion_Edad
## [1] 8.894959
Desviacion_Ingresos=sd(n2)
Desviacion_Ingresos
## [1] 34888.38
Desviacion_Hijos=sd(n3)
Desviacion_Hijos
## [1] 0.8836906

La desviacion estandar de nuestros estimadores son:

Edad=9.8949

Ingresos=34900

Numero de hijos= 0.8836

Sesgo de la estimacion media

sesgo_edad=Promedio_Edad - mean(ClasificacionCredito$Age) #Valor Sesgado de la Edad
sesgo_edad
## [1] 0.4943902
sesgo_ingresos=Promedio_Ingresos - mean(ClasificacionCredito$Income) #Valor Sesgado de los ingresos
sesgo_ingresos
## [1] 3359.756
sesgo_hijos=Promedio_Hijos - mean(ClasificacionCredito$Number.of.Children) #Valor sesgado de numero de hijos
sesgo_hijos
## [1] -0.02243902

El sesgo de nuestro estimadores son los siguiente:

Edad= Tiene un sesgo de 0.49 a la derecha

Ingresos= Tiene un sesgo de 3359 a la derecha

Numero de hijos= Tiene un sesgo de 0.02 a la izquierda

Eficiencia de los estimadores

Ahora se calcula la eficienta teniendo en cuenta que se extrae otra muestra por conveniencia de 75.

var.edad= Varianza_Edad / 75 #Eficiencia de mi estimador edad
var.edad
## [1] 1.054937
var_ingresos= Varianza_Ingresos / 75  #Eficiencia de mi estimador ingresos
var_ingresos
## [1] 16229318
var_hijos= Varianza_Hijos/75  #Eficiencia del estimador varianza 
var_hijos
## [1] 0.01041212

Consistencia de nuestros estimadores

Para realizar nuestra consistencia debemos calcular una segunda muestra aleatoria de nuestros estimadores y calcular el promedio

set.seed(123)
muestra2_edad=sample(ClasificacionCredito$Age, size = 80, replace = FALSE ) #Muestra 2 de la Edad
muestra2_edad
##  [1] 53 32 38 29 32 44 34 52 49 25 33 30 30 50 46 34 26 47 47 33 29 41 53 37 35
## [26] 42 27 51 27 48 53 29 45 31 37 50 30 27 38 40 44 28 29 36 38 52 51 52 38 30
## [51] 30 42 25 50 32 33 29 37 41 30 41 39 26 40 30 31 49 48 43 44 45 45 34 50 46
## [76] 25 51 51 38 35
set.seed(123)
muestra2_ingresos=sample(ClasificacionCredito$Income, size = 80, replace = FALSE) #Muestra 2 de los Ingresos
muestra2_ingresos
##  [1] 122500  55000  67500  27500  57500  87500  47500 130000  77500  57500
## [11]  52500 112500 105000 162500  97500  45000  40000  90000  95000  52500
## [21]  27500 120000 127500  75000  80000 110000  37500 140000  37500  70000
## [31] 122500  68000 105000  67500  72500 155000 117500  35000  67500 142500
## [41]  87500  32500  25000  85000  65000 135000 140000 130000  67500 112500
## [51] 117500  95000  62500 150000  57500  82000  27500  77500 110000 105000
## [61] 110000  62500  55000 125000 117500  95000  77500  82500  80000  87500
## [71] 105000 115000  47500 155000  95000  55000 135000 150000  67500  90000
set.seed(123)
muestra2_hijos=sample(ClasificacionCredito$Number.of.Children, size = 80, replace = FALSE)#Muestra 2 de numero de hijos
muestra2_hijos
##  [1] 0 0 2 0 0 0 0 0 1 0 0 2 2 0 1 0 0 1 1 0 0 0 0 2 1 0 0 0 0 1 0 2 3 0 2 0 2 0
## [39] 2 0 0 0 0 2 2 0 0 0 2 2 2 0 0 0 0 1 0 2 0 2 0 2 1 0 2 0 1 1 0 0 3 3 0 0 1 0
## [77] 0 0 2 1

Se calcula el promedio de las muestras

Promedio.muestra2edad=mean(muestra2_edad) #Promedio muestra 2 edad
Promedio.muestra2edad
## [1] 38.65
Promedio.muestra2ingresos=mean(muestra2_ingresos) #Promedio muestra 2 ingresos
Promedio.muestra2ingresos
## [1] 87906.25
Promedio.muestra2hijos=mean(muestra2_hijos) #Promedio muestra 2 hijos
Promedio.muestra2hijos
## [1] 0.7125
Consistencia.edad=Promedio_Edad/ Promedio.muestra2edad #Consistencia de la Edad
Consistencia.edad
## [1] 0.9953428
Consistencia.ingresos=Promedio_Ingresos / Promedio.muestra2ingresos #Consistencia del estimador ingresos
Consistencia.ingresos
## [1] 0.9911127
Consistencia.hijos=Promedio_Hijos / Promedio.muestra2hijos #Consistencia del estimador hijos
Consistencia.hijos
## [1] 0.8842105

##INTERVALOS DE CONFIANZA

Se realizara por intervalos de confianza nuestro estimador EDAD

nivel.confianza=0.95 #Nivel de confianza
Promedio_Edad  #Media muestral de la edad
## [1] 38.47
Desviacion_Edad #Desviacion estandar muestral de Edad
## [1] 8.894959
n1=100    #Tamaño muestral
Error.estandar= Desviacion_Edad/ sqrt(n1)
Error.estandar
## [1] 0.8894959
Valor.Critico= qnorm((1+nivel.confianza)/2)
Valor.Critico
## [1] 1.959964
Margen.error= Valor.Critico*Error.estandar
Margen.error
## [1] 1.74338