ó áp7]c@ s¥dZddlmZddlZddlmZdd„Zd„Z d„Z d„Z d „Z d „Z d „Zd „Zd „Zd„Zd„Zd„ZdS(s° 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 iÿÿÿÿ(tdivisionN(terfcC s€|j|jƒ}|dkr<tjtj|ƒjƒ}ntj|jƒ||d}||k}|d||||<|S(s 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. iN(treshapetsizetNonetnptasarraytuniquetones(thtXitxt num_levelst kernel_valuetidx((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytaitchison_aitkens#  cC sX|j|jƒ}dd||t||ƒ}||k}|d||||<|S(s• 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. gà?i(RRtabs(R R R R R((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pyt wang_ryzinFs !  cC s:dtjdtjƒtj||d |ddƒS(sø 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. gð?ig@(Rtsqrttpitexp(R R R ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytgaussiannscC s:dtjdtjƒtj||d |ddƒS(s, Calculates the Gaussian Convolution Kernel gð?iig@(RRRR(R R R ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytgaussian_convolutionƒscC sVtj|jƒ}x=tj|ƒD],}|t|||ƒt|||ƒ7}q"W|S(N(RtzerosRRR(R R tXjtorderedR ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytwang_ryzin_convolutionˆs*c C sqtj|ƒ}tj|jƒ}|j}x@|D]8}|t|||d|ƒt|||d|ƒ7}q1W|S(NR (RRRRR(R R RtXi_valsRR R ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytaitchison_aitken_convolution“s  cC s+d|dt|||tjdƒƒS(Ngà?ii(RRR(R R R ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pyt gaussian_cdfžscC svt|ƒ}tj|ƒ}tj|jƒ}|j}x9|D]1}||kr=|t|||d|ƒ7}q=q=W|S(NR (tintRRRRR(R R tx_uRRR R ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytaitchison_aitken_cdf¢s    #cC sUtj|jƒ}x<tj|ƒD]+}||kr"|t|||ƒ7}q"q"W|S(N(RRRRR(R R RRR ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytwang_ryzin_cdf®s  cC s$d||t|||ƒ|dS(Ni(R(R R R ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pyt d_gaussian·scC s:tj|jƒ}||k}||}||||<|S(sr A version for the Aitchison-Aitken kernel for nonparametric regression. Suggested by Li and Racine. (RRR(R R R R tixtinDom((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytaitchison_aitken_reg¼s   cC s|t||ƒS(sw A version for the Wang-Ryzin kernel for nonparametric regression. Suggested by Li and Racine in [1] ch.4 (R(R R R ((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pytwang_ryzin_regÉs(t__doc__t __future__RtnumpyRt scipy.specialRRRRRRRRRR R!R"R%R&(((s@lib/python2.7/site-packages/statsmodels/nonparametric/kernels.pyt s  - (