We consider the semiparametric partially linear regression models with mean function XTβ ＋ g（z）, where X and z are functional data. The new estimators of β and g（z） are presented and some asymptotic results are...We consider the semiparametric partially linear regression models with mean function XTβ ＋ g（z）, where X and z are functional data. The new estimators of β and g（z） are presented and some asymptotic results are given. The strong convergence rates of the proposed estimators are obtained. In our estimation, the observation number of each subject will be completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.展开更多
The objective of prospectivity modeling is prediction of the conditional probability of the presence T = 1 or absence T = 0 of a target T given favorable or prohibitive predictors B, or construction of a two classes {...The objective of prospectivity modeling is prediction of the conditional probability of the presence T = 1 or absence T = 0 of a target T given favorable or prohibitive predictors B, or construction of a two classes {0,1} classification of T. A special case of logistic regression called weights-of-evidence （WofE） is geolo- gists＇ favorite method of prospectivity modeling due to its apparent simplicity. However, the numerical simplicity is deceiving as it is implied by the severe mathematical modeling assumption of joint conditional independence of all predictors given the target. General weights of evidence are explicitly introduced which are as simple to estimate as conventional weights, i.e., by counting, but do not require conditional independence. Complementary to the regres- sion view is the classification view on prospectivity modeling. Boosting is the construction of a strong classifier from a set of weak classifiers. From the regression point of view it is closely related to logistic regression. Boost weights-of-evidence （BoostWofE） was introduced into prospectivity modeling to counterbalance violations of the assumption of conditional independence even though relaxation of modeling assumptions with respect to weak classifiers was not the （initial） purpose of boosting. In the original publication of BoostWofE a fabricated dataset was used to ＂validate＂ this approach. Using the same fabricated dataset it is shown that BoostWofE cannot generally compensate lacking condi- tional independence whatever the consecutively proces- sing order of predictors. Thus the alleged features of BoostWofE are disproved by way of counterexamples, while theoretical findings are confirmed that logistic regression including interaction terms can exactly com- pensate violations of joint conditional independence if the predictors are indicators.展开更多
文摘We consider the semiparametric partially linear regression models with mean function XTβ ＋ g（z）, where X and z are functional data. The new estimators of β and g（z） are presented and some asymptotic results are given. The strong convergence rates of the proposed estimators are obtained. In our estimation, the observation number of each subject will be completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.
文摘The objective of prospectivity modeling is prediction of the conditional probability of the presence T = 1 or absence T = 0 of a target T given favorable or prohibitive predictors B, or construction of a two classes {0,1} classification of T. A special case of logistic regression called weights-of-evidence （WofE） is geolo- gists＇ favorite method of prospectivity modeling due to its apparent simplicity. However, the numerical simplicity is deceiving as it is implied by the severe mathematical modeling assumption of joint conditional independence of all predictors given the target. General weights of evidence are explicitly introduced which are as simple to estimate as conventional weights, i.e., by counting, but do not require conditional independence. Complementary to the regres- sion view is the classification view on prospectivity modeling. Boosting is the construction of a strong classifier from a set of weak classifiers. From the regression point of view it is closely related to logistic regression. Boost weights-of-evidence （BoostWofE） was introduced into prospectivity modeling to counterbalance violations of the assumption of conditional independence even though relaxation of modeling assumptions with respect to weak classifiers was not the （initial） purpose of boosting. In the original publication of BoostWofE a fabricated dataset was used to ＂validate＂ this approach. Using the same fabricated dataset it is shown that BoostWofE cannot generally compensate lacking condi- tional independence whatever the consecutively proces- sing order of predictors. Thus the alleged features of BoostWofE are disproved by way of counterexamples, while theoretical findings are confirmed that logistic regression including interaction terms can exactly com- pensate violations of joint conditional independence if the predictors are indicators.
