ó áp7]c@ s¯dZddlmZddlmZmZddlZddlm Z ddl m Z m Z m Z mZmZdd d gZde fd „ƒYZd e fd „ƒYZdS( sZ Multivariate Conditional and Unconditional Kernel Density Estimation with Mixed Data Types. References ---------- [1] Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) [2] 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 [3] Racine, J., Li, Q. "Nonparametric Estimation of Distributions with Categorical and Continuous Data." Working Paper. (2000) [4] Racine, J. Li, Q. "Kernel Estimation of Multivariate Conditional Distributions Annals of Economics and Finance 5, 211-235 (2004) [5] Liu, R., Yang, L. "Kernel estimation of multivariate cumulative distribution function." Journal of Nonparametric Statistics (2008) [6] Li, R., Ju, G. "Nonparametric Estimation of Multivariate CDF with Categorical and Continuous Data." Working Paper [7] Li, Q., Racine, J. "Cross-validated local linear nonparametric regression" Statistica Sinica 14(2004), pp. 485-512 [8] Racine, J.: "Consistent Significance Testing for Nonparametric Regression" Journal of Business & Economics Statistics [9] Racine, J., Hart, J., Li, Q., "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models", 2006, Econometric Reviews 25, 523-544 iÿÿÿÿ(tdivision(trangetnextNi(tkernels(t GenericKDEtEstimatorSettingstgpket LeaveOneOutt _adjust_shapetKDEMultivariatetKDEMultivariateConditionalRcB s_eZdZd d d„Zd„Zd„d„Zd d„Zd d„Zd„Z d„Z RS( sª Multivariate kernel density estimator. This density estimator can handle univariate as well as multivariate data, including mixed continuous / ordered discrete / unordered discrete data. It also provides cross-validated bandwidth selection methods (least squares, maximum likelihood). Parameters ---------- data: list of ndarrays or 2-D ndarray The training data for the Kernel Density Estimation, used to determine the bandwidth(s). If a 2-D array, should be of shape (num_observations, num_variables). If a list, each list element is a separate observation. var_type: str The type of the variables: - c : continuous - u : unordered (discrete) - o : ordered (discrete) The string should contain a type specifier for each variable, so for example ``var_type='ccuo'``. bw: array_like or str, optional If an array, it is a fixed user-specified bandwidth. If a string, should be one of: - normal_reference: normal reference rule of thumb (default) - cv_ml: cross validation maximum likelihood - cv_ls: cross validation least squares defaults: EstimatorSettings instance, optional The default values for (efficient) bandwidth estimation. Attributes ---------- bw: array_like The bandwidth parameters. See Also -------- KDEMultivariateConditional Examples -------- >>> import statsmodels.api as sm >>> nobs = 300 >>> np.random.seed(1234) # Seed random generator >>> c1 = np.random.normal(size=(nobs,1)) >>> c2 = np.random.normal(2, 1, size=(nobs,1)) Estimate a bivariate distribution and display the bandwidth found: >>> dens_u = sm.nonparametric.KDEMultivariate(data=[c1,c2], ... var_type='cc', bw='normal_reference') >>> dens_u.bw array([ 0.39967419, 0.38423292]) cC sÔ||_t|jƒ|_t||jƒ|_||_tj|jƒ\|_|_|j|jkrxt dƒ‚n|dkrt ƒn|}|j |ƒ|j s¾|j|ƒ|_n|j|ƒ|_dS(NsGThe number of observations must be larger than the number of variables.(tvar_typetlentk_varsRtdatat data_typetnptshapetnobst ValueErrortNoneRt _set_defaultst efficientt _compute_bwtbwt_compute_efficient(tselfRR Rtdefaults((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyt__init__hs    cC sjd}|dt|jƒd7}|dt|jƒd7}|d|jd7}|d|jd7}|S(s Provide something sane to print.s KDE instance sNumber of variables: k_vars = s sNumber of samples: nobs = sVariable types: sBW selection method: (tstrR RR t _bw_method(Rtrpr((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyt__repr__xs cC s|S(N((tx((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyttc C s}t|jƒ}d}x`t|ƒD]R\}}t|d| d|j|dd…f d|jƒ}|||ƒ7}q"W| S(sV Returns the leave-one-out likelihood function. The leave-one-out likelihood function for the unconditional KDE. Parameters ---------- bw: array_like The value for the bandwidth parameter(s). func: callable, optional Function to transform the likelihood values (before summing); for the log likelihood, use ``func=np.log``. Default is ``f(x) = x``. Notes ----- The leave-one-out kernel estimator of :math:`f_{-i}` is: .. math:: f_{-i}(X_{i})=\frac{1}{(n-1)h} \sum_{j=1,j\neq i}K_{h}(X_{i},X_{j}) where :math:`K_{h}` represents the generalized product kernel estimator: .. math:: K_{h}(X_{i},X_{j}) = \prod_{s=1}^{q}h_{s}^{-1}k\left(\frac{X_{is}-X_{js}}{h_{s}}\right) iRt data_predictNR (RRt enumerateRR (RRtfunctLOOtLtitX_not_itf_i((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pytloo_likelihoods* c C s¬|dkr|j}nt||jƒ}g}xfttj|ƒdƒD]K}|jt|j d|jd||dd…fd|j ƒ|j ƒqJWtj |ƒ}|S(sR Evaluate the probability density function. Parameters ---------- data_predict: array_like, optional Points to evaluate at. If unspecified, the training data is used. Returns ------- pdf_est: array_like Probability density function evaluated at `data_predict`. Notes ----- The probability density is given by the generalized product kernel estimator: .. math:: K_{h}(X_{i},X_{j}) = \prod_{s=1}^{q}h_{s}^{-1}k\left(\frac{X_{is}-X_{js}}{h_{s}}\right) iRR$NR ( RRRR RRRtappendRRR Rtsqueeze(RR$tpdf_estR)((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pytpdf¥s   cC s¾|dkr|j}nt||jƒ}g}xxttj|ƒdƒD]]}|jt|j d|jd||dd…fd|j dddd d d ƒ|j ƒqJWtj |ƒ}|S( s¡ Evaluate the cumulative distribution function. Parameters ---------- data_predict: array_like, optional Points to evaluate at. If unspecified, the training data is used. Returns ------- cdf_est: array_like The estimate of the cdf. Notes ----- See http://en.wikipedia.org/wiki/Cumulative_distribution_function For more details on the estimation see Ref. [5] in module docstring. The multivariate CDF for mixed data (continuous and ordered/unordered discrete) is estimated by: .. math:: F(x^{c},x^{d})=n^{-1}\sum_{i=1}^{n}\left[G(\frac{x^{c}-X_{i}}{h})\sum_{u\leq x^{d}}L(X_{i}^{d},x_{i}^{d}, \lambda)\right] where G() is the product kernel CDF estimator for the continuous and L() for the discrete variables. Used bandwidth is ``self.bw``. iRR$NR tckertypet gaussian_cdftukertypetaitchisonaitken_cdftokertypet wangryzin_cdf( RRRR RRRR-RRR RR.(RR$tcdf_estR)((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pytcdfÉs    cC sed}tdtjdtjdtjƒ}|j}|j }|j}tj g|D]}|dk^qSƒ}||j ƒ} tj |j ƒ} x§t |ƒD]™} x^t|ƒD]P\} } || || |dd…| f|| | fƒ| dd…| f>> import statsmodels.api as sm >>> nobs = 300 >>> c1 = np.random.normal(size=(nobs,1)) >>> c2 = np.random.normal(2,1,size=(nobs,1)) >>> dens_c = sm.nonparametric.KDEMultivariateConditional(endog=[c1], ... exog=[c2], dep_type='c', indep_type='c', bw='normal_reference') >>> dens_c.bw # show computed bandwidth array([ 0.41223484, 0.40976931]) cC s||_||_|||_t|jƒ|_t|jƒ|_t||jƒ|_t||jƒ|_t j |jƒ\|_ |_t j |j|jfƒ|_ t j |j ƒd|_|dkr×tƒn|}|j|ƒ|js|j|ƒ|_n|j|ƒ|_dS(Ni(tdep_typet indep_typeRR tk_deptk_indepRtendogtexogRRRt column_stackRR RRRRRRR(RR\R]RXRYRR((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyRšs     cC sšd}|dt|jƒd7}|dt|jƒd7}|dt|jƒd7}|d|jd7}|d|jd7}|d|jd7}|S( s Provide something sane to print.s$KDEMultivariateConditional instance s+Number of independent variables: k_indep = s s'Number of dependent variables: k_dep = sNumber of observations: nobs = s!Independent variable types: sDependent variable types: sBW selection method: (RR[RZRRYRXR(RR((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyR ­scC s|S(N((R!((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyR"ºR#c C sìt|jƒ}t|jƒjƒ}d}xºt|ƒD]¬\}}t|ƒ}t|d| d|j|dd…f d|j|jƒ} t||j d| d|j|dd…f d|jƒ} | | } ||| ƒ7}q7W| S(sï Returns the leave-one-out conditional likelihood of the data. If `func` is not equal to the default, what's calculated is a function of the leave-one-out conditional likelihood. Parameters ---------- bw: array_like The bandwidth parameter(s). func: callable, optional Function to transform the likelihood values (before summing); for the log likelihood, use ``func=np.log``. Default is ``f(x) = x``. Returns ------- L: float The value of the leave-one-out function for the data. Notes ----- Similar to ``KDE.loo_likelihood`, but substitute ``f(y|x)=f(x,y)/f(x)`` for ``f(x)``. iRR$NR ( RRR]t__iter__R%RRRXRYRZ( RRR&tyLOOtxLOOR(R)tY_jR*tf_yxtf_xR+((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyR,ºs *  c C s-|dkr|j}nt||jƒ}|dkrB|j}nt||jƒ}g}tj||fƒ}x®ttj |ƒdƒD]“}t |j d|j d||dd…fd|j |jƒ}t |j |jd|jd||dd…fd|jƒ}|j||ƒq‰Wtj|ƒS(sN Evaluate the probability density function. Parameters ---------- endog_predict: array_like, optional Evaluation data for the dependent variables. If unspecified, the training data is used. exog_predict: array_like, optional Evaluation data for the independent variables. Returns ------- pdf: array_like The value of the probability density at `endog_predict` and `exog_predict`. Notes ----- The formula for the conditional probability density is: .. math:: f(y|x)=\frac{f(x,y)}{f(x)} with .. math:: f(x)=\prod_{s=1}^{q}h_{s}^{-1}k \left(\frac{x_{is}-x_{js}}{h_{s}}\right) where :math:`k` is the appropriate kernel for each variable. iRR$NR (RR\RRZR]R[RR^RRRRRRXRYR-R.(Rt endog_predictt exog_predictR/R$R)RcRd((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyR0âs"      c C s­|dkr|j}nt||jƒ}|dkrB|j}nt||jƒ}tj|ƒd}tj|ƒ}x0t |ƒD]"}t |j |jd|jd||dd…fd|j ƒ|j }tj|ƒ}t |j d|j!d|jd||dd…fd|jdddd d d d tƒ}t |j |jd|jd||dd…fd|j d tƒ}||jd dƒ} | |j |||/ *"cC s(d}|j|j|jf}||fS(s@Helper method to be able to pass needed vars to _compute_subset.R (RZRXRY(RRRRS((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyRT®sN( RURVRWRRR R,R0R8RQRT(((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyR Xs@  (4H P(RWt __future__Rtstatsmodels.compat.pythonRRtnumpyRR#Rt _kernel_baseRRRRRt__all__R R (((sGlib/python2.7/site-packages/statsmodels/nonparametric/kernel_density.pyts (ÿ-