!gUldZddlZddlmZddZdZdZdZdZ d Z d Z d Z d Z d ZdZdZdZy)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 N)erfc|j|j}|2tjtj|j}tj |j|z|dz z }||k(}|d|z z|||<|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. )reshapesizenpasarrayuniqueones)hXix num_levels kernel_valueidxs ^/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/nonparametric/kernels.pyaitchison_aitkenrsF BGG BZZ " 2 23 77277#a':>:L 'CA,L c|j|j}dd|z z|t||z zz}||k(}|d|z z|||<|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. ?r)rrabs)r r rrrs r wang_ryzinrDs\B BGG B!a%=AR!V$45L 'CA,L rcdtjdtjzz tj||z dz |dzdzz zS)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. ?g@rsqrtpiexpr r rs rgaussianr!lsE" RUU# #rvvQ{ladRi.H'I IIrc||z |z }d|tj|dkD<ddtj|dzz dzzS)a 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. rrg?)rr)r r rus rtricuber%sH" a1 AAbffQi!m RVVAY\)A- --rcdtjdtjzz tj||z dz |dzdzz zS)z, Calculates the Gaussian Convolution Kernel rrg@rr s rgaussian_convolutionr(sC RUU# #rvva! mq!tby.I'J JJrctj|j}tj|D] }|t |||t |||zz }"|SNrzerosrr r)r r Xjorderedrs rwang_ryzin_convolutionr/sUhhrwwG YYr]?:aQ'*QA*>>>? Nrc tj|}tj|j}|j}|D]$}|t ||||t ||||zz }&|SN)r)rr r,rr)r r r-Xi_valsr.rrs raitchison_aitken_convolutionr3soiimGhhrwwGJ E#Ar1D#Ar1DE EE Nrc bd|zdt||z |tjdzz zzS)Nrrr)rrrr s r gaussian_cdfr5s0 7a#q2v!bggaj.9:: ;;rct|}tj|}tj|j}|j}|D]}||ks |t ||||z }|Sr1)intrr r,rr)r r x_ur2r.rrs raitchison_aitken_cdfr9sh c(CiimGhhrwwGJ I 8 '2qZH HGI Nrctj|j}tj|D]}||ks |t |||z }|Sr*r+)r r r8r.rs rwang_ryzin_cdfr;sLhhrwwG YYr], 8 z!R+ +G, Nrc:d||z zt|||z|dzz S)Nr)r!r s r d_gaussianr=s' Q<(1b!, ,q!t 33rchtj|j}||k7}||z}||||<|S)zr A version for the Aitchison-Aitken kernel for nonparametric regression. Suggested by Li and Racine. )rr r)r r rrixinDoms raitchison_aitken_regrAs< 77277#L qB FERyL rc$|t||z zS)zw A version for the Wang-Ryzin kernel for nonparametric regression. Suggested by Li and Racine in [1] ch.4 )rr s rwang_ryzin_regrCs BF rr*)__doc__numpyr scipy.specialrrrr!r%r(r/r3r5r9r;r=rArCrrrHsW *Z%PJ(.,K < 4 r