choo_siow module

The components of the derivative of the entropy for the Choo and Siow homoskedastic model.

e0_fun_choo_siow(muhat, additional_parameters=None)

Returns the values of \(e_0\) for the Choo and Siow model.

Parameters:

Name	Type	Description	Default
muhat	Matching	a Matching	required

Returns:

Type	Description
np.ndarray	the (X,Y) matrix of the first derivative of the entropy

Source code in cupid_matching/choo_siow.py

def e0_fun_choo_siow(
    muhat: Matching, additional_parameters: list | None = None
) -> np.ndarray:
    """Returns the values of $e_0$ for the Choo and Siow model.

    Args:
        muhat: a Matching

    Returns:
        the (X,Y) matrix of the first derivative of the entropy
    """
    check_additional_parameters(0, additional_parameters)
    entropy_res = cast(tuple[float, np.ndarray], _entropy_choo_siow(muhat, deriv=1))
    return cast(np.ndarray, entropy_res[1])

e0_fun_choo_siow_corrected(muhat, additional_parameters=None)

Returns the values of \(e_0\) for the Choo and Siow model, using the finite-sample correction log(p+(1-p)/(2N))

Parameters:

Name	Type	Description	Default
muhat	Matching	a Matching	required

Returns:

Type	Description
np.ndarray	the (X,Y) matrix of the first derivative of the entropy

Source code in cupid_matching/choo_siow.py

def e0_fun_choo_siow_corrected(
    muhat: Matching, additional_parameters: list | None = None
) -> np.ndarray:
    """Returns the values of $e_0$ for the Choo and Siow model,
    using the finite-sample correction log(p+(1-p)/(2N))

    Args:
        muhat: a Matching

    Returns:
        the (X,Y) matrix of the first derivative of the entropy
    """
    check_additional_parameters(0, additional_parameters)
    e0_val_corrected = _der_entropy_choo_siow_corrected(muhat, hessian=False)
    return e0_val_corrected

hessian_mumu_choo_siow(muhat, additional_parameters=None)

Returns the derivatives of \(e_0\) in \(\mu\) for the Choo and Siow model.

Parameters:

Name	Type	Description	Default
muhat	Matching	a Matching	required

Returns:

Type	Description
ThreeArrays	the three components of the hessian wrt \((\mu,\mu)\) of the entropy

Source code in cupid_matching/choo_siow.py

def hessian_mumu_choo_siow(
    muhat: Matching, additional_parameters: list | None = None
) -> ThreeArrays:
    """Returns the derivatives of $e_0$ in $\\mu$
    for the Choo and Siow model.

    Args:
        muhat: a Matching

    Returns:
        the three components of the hessian wrt $(\\mu,\\mu)$ of the entropy
    """
    check_additional_parameters(0, additional_parameters)
    entropy_res = cast(
        tuple[float, np.ndarray, np.ndarray, np.ndarray],
        _entropy_choo_siow(muhat, deriv=2),
    )
    hessmumu = entropy_res[2]
    muxy, *_ = muhat.unpack()
    X, Y = muxy.shape
    hess_x = np.zeros((X, Y, Y))
    hess_y = np.zeros((X, Y, X))
    hess_xy = np.zeros((X, Y))
    for x in range(X):
        for y in range(Y):
            d2xy = hessmumu[x, y, :, :]
            hess_x[x, y, :] = d2xy[x, :]
            hess_y[x, y, :] = d2xy[:, y]
            hess_xy[x, y] = d2xy[x, y]
    return hess_x, hess_y, hess_xy

hessian_mumu_choo_siow_corrected(muhat, additional_parameters=None)

Returns the derivatives of \(e_0\) in \(\mu\) for the Choo and Siow model, with the small sample correction

Parameters:

Name	Type	Description	Default
muhat	Matching	a Matching	required

Returns:

Type	Description
ThreeArrays	the three components of the hessian wrt \((\mu,\mu)\) of the entropy

Source code in cupid_matching/choo_siow.py

def hessian_mumu_choo_siow_corrected(
    muhat: Matching, additional_parameters: list | None = None
) -> ThreeArrays:
    """Returns the derivatives of $e_0$ in $\\mu$
    for the Choo and Siow model, with the small sample correction

    Args:
        muhat: a Matching

    Returns:
        the three components of the hessian wrt $(\\mu,\\mu)$ of the entropy
    """
    check_additional_parameters(0, additional_parameters)
    _, hessmumu, _ = _der_entropy_choo_siow_corrected(muhat, hessian=True)
    muxy, *_ = muhat.unpack()
    X, Y = muxy.shape
    hess_x = np.zeros((X, Y, Y))
    hess_y = np.zeros((X, Y, X))
    hess_xy = np.zeros((X, Y))
    for x in range(X):
        for y in range(Y):
            d2xy = hessmumu[x, y, :, :]
            hess_x[x, y, :] = d2xy[x, :]
            hess_y[x, y, :] = d2xy[:, y]
            hess_xy[x, y] = d2xy[x, y]
    return hess_x, hess_y, hess_xy

hessian_mur_choo_siow(muhat, additional_parameters=None)

Returns the derivatives of \(e_0\) in \(r\) for the Choo and Siow model.

Parameters:

Name	Type	Description	Default
muhat	Matching	a Matching	required

Returns:

Type	Description
TwoArrays	the two components of the hessian wrt \((\mu,r)\) of the entropy

Source code in cupid_matching/choo_siow.py

def hessian_mur_choo_siow(
    muhat: Matching, additional_parameters: list | None = None
) -> TwoArrays:
    """Returns the derivatives of $e_0$ in $r$
    for the Choo and Siow model.

    Args:
        muhat: a Matching

    Returns:
        the two components of the hessian wrt $(\\mu,r)$ of the entropy
    """
    check_additional_parameters(0, additional_parameters)
    entropy_res = cast(
        tuple[float, np.ndarray, np.ndarray, np.ndarray],
        _entropy_choo_siow(muhat, deriv=2),
    )
    hessmur = entropy_res[3]
    muxy, *_ = muhat.unpack()
    X, Y = muxy.shape
    hess_nx = np.zeros((X, Y))
    hess_my = np.zeros((X, Y))
    for x in range(X):
        for y in range(Y):
            d2r = hessmur[x, y, :]
            hess_nx[x, y] = d2r[x]
            hess_my[x, y] = d2r[X + y]
    return hess_nx, hess_my

hessian_mur_choo_siow_corrected(muhat, additional_parameters=None)

Returns the derivatives of \(e_0\) in \(r\) for the Choo and Siow model, with the small sample correction

Parameters:

Name	Type	Description	Default
muhat	Matching	a Matching	required

Returns:

Type	Description
TwoArrays	the two components of the hessian wrt \((\mu,r)\) of the entropy

Source code in cupid_matching/choo_siow.py

def hessian_mur_choo_siow_corrected(
    muhat: Matching, additional_parameters: list | None = None
) -> TwoArrays:
    """Returns the derivatives of $e_0$ in $r$
    for the Choo and Siow model, with the small sample correction

    Args:
        muhat: a Matching

    Returns:
        the two components of the hessian wrt $(\\mu,r)$ of the entropy
    """
    check_additional_parameters(0, additional_parameters)
    _, _, hessmur = _der_entropy_choo_siow_corrected(muhat, hessian=True)
    muxy, *_ = muhat.unpack()
    X, Y = muxy.shape
    hess_nx = np.zeros((X, Y))
    hess_my = np.zeros((X, Y))
    for x in range(X):
        for y in range(Y):
            d2r = hessmur[x, y, :]
            hess_nx[x, y] = d2r[x]
            hess_my[x, y] = d2r[X + y]
    return hess_nx, hess_my