U Kv fUã@s†dZddlZddlmZddd„Zdd„Zdd „Zd d „Zd d „Z dd„Z dd„Z dd„Z dd„Z dd„Zdd„Zdd„Zdd„ZdS)a° Module of kernels that are able to handle continuous as well as categorical variables (both ordered and unordered). This is a slight deviation from the current approach in statsmodels.nonparametric.kernels where each kernel is a class object. Having kernel functions rather than classes makes extension to a multivariate kernel density estimation much easier. NOTE: As it is, this module does not interact with the existing API éN)ÚerfcCs^| |j¡}|dkr&t t |¡j¡}t |j¡||d}||k}|d||||<|S)a! The Aitchison-Aitken kernel, used for unordered discrete random variables. Parameters ---------- h : 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : 2-D ndarray of ints, shape (nobs, K) The value of the training set. x : 1-D ndarray, shape (K,) The value at which the kernel density is being estimated. num_levels : bool, optional Gives the user the option to specify the number of levels for the random variable. If False, the number of levels is calculated from the data. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. Notes ----- See p.18 of [2]_ for details. The value of the kernel L if :math:`X_{i}=x` is :math:`1-\lambda`, otherwise it is :math:`\frac{\lambda}{c-1}`. Here :math:`c` is the number of levels plus one of the RV. References ---------- .. [*] J. Aitchison and C.G.G. Aitken, "Multivariate binary discrimination by the kernel method", Biometrika, vol. 63, pp. 413-420, 1976. .. [*] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88., 2008. Né)ÚreshapeÚsizeÚnpZasarrayÚuniqueÚones)ÚhÚXiÚxÚ num_levelsÚ kernel_valueÚidx©rúE/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/nonparametric/kernels.pyÚaitchison_aitkens# rcCsH| |j¡}dd||t||ƒ}||k}|d||||<|S)a• The Wang-Ryzin kernel, used for ordered discrete random variables. Parameters ---------- h : scalar or 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : ndarray of ints, shape (nobs, K) The value of the training set. x : scalar or 1-D ndarray of shape (K,) The value at which the kernel density is being estimated. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. Notes ----- See p. 19 in [1]_ for details. The value of the kernel L if :math:`X_{i}=x` is :math:`1-\lambda`, otherwise it is :math:`\frac{1-\lambda}{2}\lambda^{|X_{i}-x|}`, where :math:`\lambda` is the bandwidth. References ---------- .. [*] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88., 2008. http://dx.doi.org/10.1561/0800000009 .. [*] M.-C. Wang and J. van Ryzin, "A class of smooth estimators for discrete distributions", Biometrika, vol. 68, pp. 301-309, 1981. çà?r)rrÚabs)r r r r rrrrÚ wang_ryzinDs ! rcCs4dt dtj¡t ||d |dd¡S)a÷ Gaussian Kernel for continuous variables Parameters ---------- h : 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : 1-D ndarray, shape (K,) The value of the training set. x : 1-D ndarray, shape (K,) The value at which the kernel density is being estimated. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. çð?ég@©rÚsqrtÚpiÚexp©r r r rrrÚgaussianlsrcCs8|||}d|t |¡dk<ddt |¡ddS)aö Tricube Kernel for continuous variables Parameters ---------- h : 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : 1-D ndarray, shape (K,) The value of the training set. x : 1-D ndarray, shape (K,) The value at which the kernel density is being estimated. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. rrgÍ‹”§ë?é)rr)r r r ÚurrrÚtricube€s rcCs4dt dtj¡t ||d |dd¡S)z, Calculates the Gaussian Convolution Kernel rérg@rrrrrÚgaussian_convolution–sr!cCs<t |j¡}t |¡D] }|t|||ƒt|||ƒ7}q|S©N©rÚzerosrrr)r r ÚXjÚorderedr rrrÚwang_ryzin_convolution›s r'c CsNt |¡}t |j¡}|j}|D](}|t||||dt||||d7}q |S©N)r )rrr$rr)r r r%ÚXi_valsr&r r rrrÚaitchison_aitken_convolution¦s  ÿr*cCs&d|dt|||t d¡ƒS)Nrrr)rrrrrrrÚ gaussian_cdf±sr+cCsNt|ƒ}t |¡}t |j¡}|j}|D] }||kr(|t||||d7}q(|Sr()Úintrrr$rr)r r Úx_ur)r&r r rrrÚaitchison_aitken_cdfµs  r.cCs8t |j¡}t |¡D]}||kr|t|||ƒ7}q|Sr"r#)r r r-r&r rrrÚwang_ryzin_cdfÁs  r/cCs d||t|||ƒ|dS)Nr)rrrrrÚ d_gaussianÊsr0cCs,t |j¡}||k}||}||||<|S)zr A version for the Aitchison-Aitken kernel for nonparametric regression. Suggested by Li and Racine. )rrr)r r r r ÚixZinDomrrrÚaitchison_aitken_regÏs   r2cCs|t||ƒS)zw A version for the Wang-Ryzin kernel for nonparametric regression. Suggested by Li and Racine in [1] ch.4 )rrrrrÚwang_ryzin_regÜsr3)N)Ú__doc__ZnumpyrZ scipy.specialrrrrrr!r'r*r+r.r/r0r2r3rrrrÚs   -(