У меня есть t данные (n=350)
t[,1] = c(4, 16, 4, 2, 10, 28, 6, 15, 8, 11, 11, 8, 18, 5, 3, 6, 5, 10, 10, 10, 2, 2, 3, 9, 2, 7, 4, 4, 5, 17, 11, 7, 9, 10, 3, 6, 5, 8, 2, 9, 5, 9, 15, 8, 4, 4, 4, 4, 4, 5, 2, 11, 12, 6, 4, 4, 8, 4, 9, 23, 8, 8, 5, 13, 9, 8, 5, 15, 9, 7, 13, 22, 6, 4, 2, 5, 6, 15, 6, 7, 10, 8, 16, 3, 35, 39, 3, 8, 20, 22, 18, 13, 17, 11, 3, 38, 4, 3, 47, 72, 72, 9, 5, 48, 8, 3, 11, 3, 55, 48, 96, 54, 18, 48, 48, 72, 6, 5, 5, 16, 3, 8, 7, 4, 8, 6, 4, 3, 6, 7, 6, 2, 9, 10, 2, 5, 9, 10, 5, 7, 5, 2, 6, 5, 6, 4, 11, 7, 19, 11, 2, 5, 3, 5, 11, 2, 3, 8, 7, 2, 11, 11, 2, 10, 9, 3, 16, 6, 2, 4, 4, 19, 40, 12, 5, 6, 6, 5, 13, 8, 7, 7, 3, 3, 5, 2, 5, 3, 9, 9, 7, 2, 3, 13, 5, 6, 10, 2, 8, 4, 3, 8, 5, 3, 6, 3, 3, 6, 12, 5, 3, 3, 11, 5, 2, 2, 7, 7, 8, 4, 8, 5, 18, 2, 8, 7, 9, 4, 7, 2, 3, 6, 8, 8, 4, 18, 12, 3, 4, 5, 14, 8, 7, 5, 4, 3, 7, 13, 4, 2, 3, 9, 4, 7, 1, 2, 10, 2, 4, 12, 9, 15, 7, 6, 7, 9, 6, 6, 7, 4, 20, 19, 9, 6, 5, 4, 9, 7, 6, 6, 3, 3, 4, 4, 3, 3, 11, 2, 3, 5, 5, 8, 11, 2, 14, 14, 3, 2, 6, 6, 4, 3, 4, 3, 3, 6, 6, 17, 9, 7, 12, 7, 31, 8, 7, 26, 63, 315, 12, 5, 2, 7, 3, 3, 10, 3, 2, 4, 6, 7, 6, 13, 9, 8, 4, 8, 7, 4, 3, 6, 6, 2, 4, 2, 17, 13, 11, 3, 8, 4)
t[,2] = c(48.0, 73.6, 52.4, 62.0, 48.5, 99.3, 49.5, 61.0, 56.5, 52.5, 55.5, 89.4, 54.5, 56.5, 67.6, 51.1, 112.0, 51.0, 50.6, 52.0, 77.5, 53.0, 56.0, 51.6, 50.0, 103.9, 50.1, 51.5, 55.1, 64.4, 54.9, 89.5, 50.0, 50.9, 56.5, 54.0, 49.0, 50.0, 51.0, 66.0, 57.9, 57.5, 48.0, 64.0, 52.0, 54.5, 70.5, 51.4, 86.0, 70.5, 61.5, 76.9, 69.6, 47.9, 64.5, 62.5, 72.9, 53.5, 81.4, 53.5, 77.0, 71.5, 87.5, 67.5, 66.0, 139.0, 54.0, 61.5, 59.5, 77.7, 50.5, 48.4, 68.9, 53.5, 49.5, 49.6, 51.1, 67.0, 58.0, 51.0, 64.0, 58.8, 102.9, 61.0, 54.6, 107.1, 49.0, 53.0, 52.1, 65.5, 50.9, 51.7, 77.4, 75.9, 63.5, 120.3, 69.0, 68.5, 63.8, 91.2, 84.0, 57.5, 68.5, 88.8, 54.5, 74.5, 62.2, 65.5, 50.8, 96.0, 62.4, 111.4, 52.0, 79.2, 79.2, 144.0, 54.0, 78.0, 77.0, 51.3, 65.0, 64.5, 79.6, 48.9, 76.6, 50.5, 52.6, 81.1, 65.5, 61.0, 54.9, 57.5, 60.0, 54.0, 50.0, 57.5, 65.0, 50.6, 63.5, 62.6, 100.0, 49.5, 72.0, 81.5, 48.3, 49.0, 69.0, 49.0, 49.1, 75.5, 63.0, 74.5, 58.6, 49.4, 52.0, 50.0, 101.0, 72.5, 48.1, 51.0, 60.5, 50.1, 62.0, 51.6, 49.6, 56.1, 80.1, 81.4, 48.0, 52.5, 49.9, 63.1, 81.9, 105.5, 85.0, 56.4, 49.6, 64.1, 48.6, 54.5, 75.0, 64.5, 64.9, 54.6, 86.5, 51.0, 52.4, 55.0, 50.5, 96.0, 50.5, 49.5, 55.9, 65.0, 60.9, 49.0, 49.6, 60.5, 55.4, 107.5, 60.1, 64.5, 51.6, 54.0, 76.0, 64.5, 63.0, 73.0, 90.0, 62.0, 70.5, 95.0, 77.5, 61.1, 60.0, 48.0, 94.5, 68.0, 79.5, 60.4, 75.0, 55.0, 55.0, 67.0, 158.0, 91.5, 61.5, 73.0, 79.0, 67.5, 58.0, 102.5, 87.0, 74.5, 55.5, 112.5, 75.5, 57.5, 48.5, 55.0, 61.0, 85.4, 79.5, 59.5, 48.0, 72.0, 61.0, 50.0, 55.5, 48.0, 88.0, 55.5, 108.0, 52.6, 99.5, 60.0, 100.0, 53.5, 83.5, 83.0, 56.8, 68.1, 126.6, 54.5, 59.4, 59.1, 50.0, 52.5, 67.0, 129.0, 81.5, 57.5, 54.5, 55.5, 65.0, 53.0, 77.1, 81.5, 72.6, 61.4, 58.0, 59.5, 56.5, 126.1, 77.5, 84.5, 56.0, 62.0, 74.5, 82.0, 52.5, 52.5, 78.0, 57.5, 55.0, 59.5, 51.0, 52.5, 60.0, 88.5, 52.0, 56.0, 59.0, 87.0, 65.5, 108.5, 57.0, 52.0, 62.0, 56.0, 64.0, 54.0, 92.5, 73.0, 55.0, 73.5, 76.5, 117.5, 73.5, 54.0, 58.5, 83.0, 53.0, 48.0, 78.5, 72.5, 52.0, 57.0, 55.5, 57.0, 53.0, 52.5, 59.5, 79.0, 67.0, 73.0, 62.5, 80.5, 54.0, 58.0, 98.0, 49.0, 52.5, 55.0, 58.0, 80.0, 60.0, 83.5, 75.5, 67.0)
с использованием непараметрических параметров c Оценка плотности ядра, я хочу поместить данные в связку:
k1 <- density(t[,1])$y
k2 <- density(t[,2])$y
k <- cbind(k1,k2)
kn1 <- fitCopula(claytonCopula(), data = k, method = "ml")
но я получаю предупреждение:
Warning message:
In fitCopula.ml(copula, u = data, method = method, start = start, :
Hessian matrix not invertible: Lapack routine dgesv: system is exactly singular: U[1,1] = 0
(1) Что это значит и как я могу решить эту проблему? (2) и как выбрать лучшее start начальное значение для ml метода?