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This thesis studies the mixed data types kernel estimation framework for the models of discrete dependent variables, which are known as kernel discrete conditional functions. The conventional parametric multinomial logit MNL model is compared with the mixed data types kernel conditional density estimator in Chapter (2). A new kernel estimator for discrete time single state hazard models is developed in Chapter (3), and named as the discrete time “external kernel hazard” estimator. The discrete time (mixed) proportional hazard estimators are then compared with the discrete time external kernel hazard estimator empirically in Chapter (4). The work in Chapter (2) attempts to estimate a labour force participation decision model using a cross-section data from the UK labour force survey in 2007. The work in Chapter (4) estimates a hazard rate for job-vacancies in weeks, using data from Lancashire Careers Service (LCS) between the period from March 1988 to June 1992. The evidences from the vast literature regarding female labour force participation and the job-market random matching theory are used to examine the empirical results of the estimators. The parametric estimator are tighten by the restrictive assumption regarding the link function of the discrete dependent variable and the dummy variables of the discrete covariates. Adding interaction terms improves the performance of the parametric models but encounters other risks like generating multicollinearity problem, increasing the singularity of the data matrix and complicates the computation of the ML function. On the other hand, the mixed data types kernel estimation framework shows an outstanding performance compared with the conventional parametric estimation methods. The kernel functions that are used for the discrete variables, including the dependent variable, in the mixed data types estimation framework, have substantially improved the performance of the kernel estimators. The kernel framework uses very few assumptions about the functional form of the variables in the model, and relay on the right choice of the kernel functions in the estimator. The outcomes of the kernel conditional density shows that female education level and fertility have high impact on females propensity to work and be in the labour force. The kernel conditional density estimator captures more heterogeneity among the females in the sample than the MNL model due to the restrictive parametric assumptions in the later. The (mixed) proportional hazard framework, on the other hand, missed to capture the effect of the job-market tightness in the job-vacancies hazard rate and produce inconsistent results when the assumptions regarding the distribution of the unobserved heterogeneity are changed. The external kernel hazard estimator overcomes those problems and produce results that consistent with the job market random matching theory. The results in this thesis are useful for nonparametric estimation research in econometrics and in labour economics research.