In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for u...In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.展开更多
This study focuses on the influence of weather and climate on malaria occurrence based on human-biometeorological methods was carried out in Ondo State, Nigeria using meteorological and malaria dataset in the state fo...This study focuses on the influence of weather and climate on malaria occurrence based on human-biometeorological methods was carried out in Ondo State, Nigeria using meteorological and malaria dataset in the state for the period from 1998 to 2008. In addition, sea surface temperatures （SSTs） over equatorial Pacific Ocean were integrated in the analysis. The association between each of the meteorological-biometeorological parameters and clinical-reported malaria cases was examined by using Poisson distribution and log as link function between the two categories of dataset. The next step was the building of a model by using Poisson multiple regression models （GLMs） in order to know the weather variables that lead to statistically changes in clinical-reported malaria cases. The study revealed that an increase of I m.s1 of wind speed can lead to an increase of about 164% and 171% in the monthly occurrence of malaria at 95% confidence interval in derived savanna and humid forest zone respectively. Also, an increase of I ℃ in air temperature and sea surface temperature is associated with 53.4% and 29% increase in monthly malaria occurrence （CI： 95%） in derived savanna while an increase of 1 ℃ in air temperature and sea surface temperature is associated with 56.4% and 15.4% increase in monthly malaria occurrence at 95% confidence interval in humid forest zone of Ondo State展开更多
Home mortgage loan lending firms are exposed to many business risks.This paper focuses on the mortgage loan borrower risks and proposes a prospective loss analysis approach in regard to loan repayment defaults of borr...Home mortgage loan lending firms are exposed to many business risks.This paper focuses on the mortgage loan borrower risks and proposes a prospective loss analysis approach in regard to loan repayment defaults of borrowers.For this purpose,a predictive modeling is presented in three stages.In the first stage,occurrence of borrower defaults in a mortgage loans portfolio is modeled through the generalized linear models(GLMs)type regressions for which we specify a logistic distribution for default events.The second stage of modeling develops a survival analysis in order to estimate survival probability and hazard rate functions for individual loans.Ultimately,an expectable loss amount model is presented in the third stage as a function of conditional survival probabilities and corresponding hazard rates at loan levels.Throughout all modeling stages,a large and real data set is used as an empirical analysis case by which detailed interpretations and practical implications of the obtained results are stated.展开更多
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mix...We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n). Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.展开更多
基金supported by the President Foundation (Grant No. Y1050)the Scientific Research Foundation(Grant No. KYQD200502) of GUCAS
文摘In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.
文摘This study focuses on the influence of weather and climate on malaria occurrence based on human-biometeorological methods was carried out in Ondo State, Nigeria using meteorological and malaria dataset in the state for the period from 1998 to 2008. In addition, sea surface temperatures （SSTs） over equatorial Pacific Ocean were integrated in the analysis. The association between each of the meteorological-biometeorological parameters and clinical-reported malaria cases was examined by using Poisson distribution and log as link function between the two categories of dataset. The next step was the building of a model by using Poisson multiple regression models （GLMs） in order to know the weather variables that lead to statistically changes in clinical-reported malaria cases. The study revealed that an increase of I m.s1 of wind speed can lead to an increase of about 164% and 171% in the monthly occurrence of malaria at 95% confidence interval in derived savanna and humid forest zone respectively. Also, an increase of I ℃ in air temperature and sea surface temperature is associated with 53.4% and 29% increase in monthly malaria occurrence （CI： 95%） in derived savanna while an increase of 1 ℃ in air temperature and sea surface temperature is associated with 56.4% and 15.4% increase in monthly malaria occurrence at 95% confidence interval in humid forest zone of Ondo State
文摘Home mortgage loan lending firms are exposed to many business risks.This paper focuses on the mortgage loan borrower risks and proposes a prospective loss analysis approach in regard to loan repayment defaults of borrowers.For this purpose,a predictive modeling is presented in three stages.In the first stage,occurrence of borrower defaults in a mortgage loans portfolio is modeled through the generalized linear models(GLMs)type regressions for which we specify a logistic distribution for default events.The second stage of modeling develops a survival analysis in order to estimate survival probability and hazard rate functions for individual loans.Ultimately,an expectable loss amount model is presented in the third stage as a function of conditional survival probabilities and corresponding hazard rates at loan levels.Throughout all modeling stages,a large and real data set is used as an empirical analysis case by which detailed interpretations and practical implications of the obtained results are stated.
文摘We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n). Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.
