>h7nSrSSKrSSKJr SSjrSrSrSrSr S r S r S r S r S rSrSrSrg)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)erfcURUR5nUc4[R"[R"U5R5n[R "UR5U-US- - nX:HnUSU- -UXE'U$)a The Aitchison-Aitken kernel, used for unordered discrete random variables. Parameters ---------- h : 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : 2-D ndarray of ints, shape (nobs, K) The value of the training set. x : 1-D ndarray, shape (K,) The value at which the kernel density is being estimated. num_levels : bool, optional Gives the user the option to specify the number of levels for the random variable. If False, the number of levels is calculated from the data. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. Notes ----- See p.18 of [2]_ for details. The value of the kernel L if :math:`X_{i}=x` is :math:`1-\lambda`, otherwise it is :math:`\frac{\lambda}{c-1}`. Here :math:`c` is the number of levels plus one of the RV. References ---------- .. [*] J. Aitchison and C.G.G. Aitken, "Multivariate binary discrimination by the kernel method", Biometrika, vol. 63, pp. 413-420, 1976. .. [*] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88., 2008. )reshapesizenpasarrayuniqueones)hXix num_levels kernel_valueidxs tC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/nonparametric/kernels.pyaitchison_aitkenrs{F BGG BZZ " 2 23 77277#a':>:L 'CA,L cURUR5nSSU- -U[X- 5--nX:HnUSU- -UX4'U$)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_ryzinrDsVB BGG B!a%=ARV$45L 'CA,L rcS[R"S[R-5- [R"X- S-*US-S-- 5-$)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!lsC" RUU# #rvv{ladRi.H'I IIrcX- U- nSU[R"U5S:'SS[R"U5S-- S--$)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%sF" 1 AAbffQi!m RVVAY\)A- --rcS[R"S[R-5- [R"X- S-*US-S-- 5-$)z+Calculates the Gaussian Convolution Kernel rrg@rr s rgaussian_convolutionr(sA RUU# #rvv! mq!tby.I'J JJrc[R"UR5n[R"U5HnU[ XU5[ XU5-- nM! U$Nrzerosrr r)r r Xjorderedrs rwang_ryzin_convolutionr/sLhhrwwG YYr]:aQ'*QA*>>> Nrc [R"U5n[R"UR5nURnUHnU[ XXeS9[ XXeS9-- nM U$N)r)rr r,rr)r r r-Xi_valsr.rrs raitchison_aitken_convolutionr3s`iimGhhrwwGJ #A1D#A1DE E Nrc bSU-S[X!- U[R"S5-- 5--$)Nrrr)rrrr s r gaussian_cdfr5s. 7a#qv!bggaj.9:: ;;rc [U5n[R"U5n[R"UR5nURnUHnXb::dM U[ XXeS9- nM U$r1)intrr r,rr)r r x_ur2r.rrs raitchison_aitken_cdfr9s[ c(CiimGhhrwwGJ  8 'qH HG Nrc[R"UR5n[R"U5HnXB::dM U[ XU5- nM U$r*r+)r r r8r.rs rwang_ryzin_cdfr;sChhrwwG YYr] 8 z!+ +G Nrc6SX- -[XU5-US-- $)Nr)r!r s r d_gaussianr=s# <(1!, ,q!t 33rcb[R"UR5nX:gnX@-nXTX4'U$)zf A version for the Aitchison-Aitken kernel for nonparametric regression. Suggested by Li and Racine. )rr r)r r rrixinDoms raitchison_aitken_regrAs4 77277#L B FEyL rc"U[X- 5-$)zk 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