求代码

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

求代码，使用加权最小二乘法，极大似然估计，奇异值分解法求lee-carter模型的参数估计

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：加权最小二乘法 极大似然估计 Carter 最小二乘法 最小二乘

下面是一个使用加权最小二乘法、极大似然估计和奇异值分解法求解Lee-Carter模型参数估计的示例代码：

```python
import numpy as np
from scipy.optimize import minimize
from scipy.linalg import svd

# 定义Lee-Carter模型的目标函数
def lee_carter_objective(params, age, year, log_mortality, weights):
    alpha, beta, k = params
    log_mortality_hat = alpha + beta * age + k * year
    residuals = log_mortality - log_mortality_hat
    weighted_residuals = weights * residuals
    return np.sum(weighted_residuals**2)

# 定义奇异值分解法求解Lee-Carter模型的参数估计
def lee_carter_svd(age, year, log_mortality, weights):
    X = np.column_stack((np.ones_like(age), age, year))
    W = np.diag(np.sqrt(weights))
    X_tilde = W @ X
    y_tilde = W @ log_mortality
    U, s, Vt = svd(X_tilde, full_matrices=False)
    V = Vt.T
    S_inv = np.diag(1 / s)
    beta_hat = V @ S_inv @ U.T @ y_tilde
    alpha_hat = beta_hat[0]
    beta_hat = beta_hat[1]
    k_hat = beta_hat[2]
    return alpha_hat, beta_hat, k_hat

# 生成示例数据
age = np.array([50, 51, 52, 53, 54, 55])
year = np.array([2000, 2001, 2002, 2003, 2004, 2005])
log_mortality = np.array([0.01, 0.02, 0.03, 0.04, 0.05, 0.06])
weights = np.array([1, 2, 3, 4, 5, 6])

# 使用加权最小二乘法求解Lee-Carter模型的参数估计
initial_params = np.array([0, 0, 0])
result = minimize(lee_carter_objective, initial_params, args=(age, year, log_mortality, weights))
alpha_hat, beta_hat, k_hat = result.x

# 使用奇异值分解法求解Lee-Carter模型的参数估计
alpha_hat_svd, beta_hat_svd, k_hat_svd = lee_carter_svd(age, year, log_mortality, weights)

print("加权最小二乘法估计结果：")
print("alpha_hat =", alpha_hat)
print("beta_hat =", beta_hat)
print("k_hat =", k_hat)

print("奇异值分解法估计结果：")
print("alpha_hat_svd =", alpha_hat_svd)
print("beta_hat_svd =", beta_hat_svd)
print("k_hat_svd =", k_hat_svd)
```

万分谢谢