Moses方差检验代码

以下是使用Python实现的Moses方差检验代码：

import numpy as np
from scipy.stats import f

def moses_variance_test(X, y, alpha=0.05):
    """
    Perform Moses variance test on input data X and output variable y,
    with significance level alpha.
    
    Parameters:
    X: numpy array of shape (n_samples, n_features)
        Input data
    y: numpy array of shape (n_samples,)
        Output variable
    alpha: float, optional (default=0.05)
        Significance level of the test
        
    Returns:
    result: bool
        True if the null hypothesis of equal variances is rejected,
        False otherwise.
    """
    n = X.shape[0]
    p = X.shape[1]
    
    # Compute the residuals
    beta = np.linalg.inv(X.T @ X) @ X.T @ y
    y_hat = X @ beta
    residuals = y - y_hat
    
    # Compute the sum of squared residuals
    sse = np.sum(residuals ** 2)
    
    # Compute the sum of squared errors for each feature
    sse_j = np.zeros(p)
    for j in range(p):
        x_j = X[:, j]
        beta_j = np.linalg.inv(x_j.T @ x_j) @ x_j.T @ residuals
        y_j_hat = x_j @ beta_j
        residuals_j = residuals - y_j_hat
        sse_j[j] = np.sum(residuals_j ** 2)
    
    # Compute the F-statistic
    f_stat = (sse / (n - p)) / (np.sum(sse_j) / (n - 2 * p))
    
    # Compute the p-value
    p_value = 1 - f.cdf(f_stat, p, n - 2 * p)
    
    # Compare p-value to significance level
    result = p_value < alpha
    
    return result

此代码实现了Moses方差检验，该检验用于确定多元回归模型中输入变量的方差是否相等。函数接受输入数据矩阵X和输出变量向量y，并返回一个布尔值，表示是否拒绝了等方差的零假设。如果返回True，则意味着输入变量之间的方差不同，反之则是相同的。