Due to its rapid convergence rate and low memory requirements, the conjugate gradient (CG) scheme is a popular technique for solving unconstrained optimization problems. This paper introduces a modified conjugate grad...
详细信息
Due to its rapid convergence rate and low memory requirements, the conjugate gradient (CG) scheme is a popular technique for solving unconstrained optimization problems. This paper introduces a modified conjugate gradient method, GICY. By utilizing the strong Wolfe line search (SWLS), we prove that GICY satisfies the sufficient descent condition at every iteration, guaranteeing significant progress towards the minimum. Additionally, we establish the global convergence of the proposed method. Extensive numerical computations demonstrate the success and promise of this new algorithm, particularly when applied to practical problems involving nonparametric regression functions.
This paper is about nonparametric regression function estimation. Our estimator is a one-step projection estimator obtained by least-squares contrast minimization. The specificity of our work is to consider a new mode...
详细信息
This paper is about nonparametric regression function estimation. Our estimator is a one-step projection estimator obtained by least-squares contrast minimization. The specificity of our work is to consider a new model selection procedure including a cutoff for the underlying matrix inversion, and to provide theoretical risk bounds that apply to non-compactly supported bases, a case which was specifically excluded of most previous results. Upper and lower bounds for resulting rates are provided.
To the greater part, there is a downward tendency for the extraction of building minerals in the Czech Republic, as it is evidenced by the statistics of the State Mining Authority. This also concerns raw materials for...
详细信息
ISBN:
(纸本)9789549181876
To the greater part, there is a downward tendency for the extraction of building minerals in the Czech Republic, as it is evidenced by the statistics of the State Mining Authority. This also concerns raw materials for manufacturing of bricks. The most obvious explanation for the fact is in the drop of the building industries in the country. The objective of this paper is to find such regression function that would successfully describe the extraction trends for brick making minerals in the period 1999-2011, and then by means of the most suitable function to predict extraction of brick making minerals in 2012. The authors have defined a hypothesis that will be accepted or rejected by the paper's conclusion as based on accessible analysis data. The problem will be solved by the application of the SW programme, Microsoft Excel. The programme input data are represented by the statistics of the extraction volumes in the period, 1999-2011. On input of these data, the programme graphs points, which can be interlaid by curve functions offered. We applied three smooth continuous functions (linear, quadratic, and logarithmic), with the aim to establish which of these would agree best with the course of the time sequence. The best tool for this is to apply a determination coefficient for which it is valid that the higher its value the better agreement with the given dependence. In view of the fact that the determination coefficient value grows along with the number of the model parameters, it is necessary to convert it to the so called adjusted determination coefficient, which rectifies the influence of the number of the model parameters.
This paper is concerned with a nonparametric estimator of the regression function based on the local linear estimation method in a twice censoring setting. The proposed method avoid the problem of boundary effect and ...
详细信息
This paper is concerned with a nonparametric estimator of the regression function based on the local linear estimation method in a twice censoring setting. The proposed method avoid the problem of boundary effect and reduces the bias term. Under suitable assumptions, the strong uniform almost sure consistency with rate is established and the finite sample properties of the local linear regression smoother is investigated by means of a simulation study.
By martingale methods, a central limit theorem and laws of large numbers are established for the integrated square error of a general nonparametric estimate in the case of fixed design.
By martingale methods, a central limit theorem and laws of large numbers are established for the integrated square error of a general nonparametric estimate in the case of fixed design.
The bivariate distribution of (X, Y), whereX andY are non-negative integer-valued random variables, is characterized by the conditional distribution ofY givenX=x and a consistent regression function ofX onY. This is a...
详细信息
The bivariate distribution of (X, Y), whereX andY are non-negative integer-valued random variables, is characterized by the conditional distribution ofY givenX=x and a consistent regression function ofX onY. This is achieved when the conditional distribution is one of the distributions: a) binomial, Poisson, Pascal or b) a right translation of these. In a) the conditional distribution ofY is anx-fold convolution of another random variable independent ofX so thatY is a generalized distribution. A main feature of these characterizations is that their proof does not depent on the specific form of the regression function. It is also indicated how these results can be used for good-ness-of-fit purposes.
This paper addresses the semiparametric estimation of the regression function in a situation where the response variable is right-censored and the covariate(s) is completely observed. We present a new copula-based met...
详细信息
This paper addresses the semiparametric estimation of the regression function in a situation where the response variable is right-censored and the covariate(s) is completely observed. We present a new copula-based method to estimate the regression function. The key concept presented in this manuscript is to write the regression function in terms of the copula density and marginal distributions. We suppose a parametric model for the copula density with unknown parameter(s), and we estimate the marginal distributions of the response and the covariate(s) by the Kaplan-Meier estimator and the empirical distribution, respectively. We establish the asymptotic properties of our estimator and extend it to the multivariate case. The proposed method is then applied to analyse a data-set on lifetime with lung-cancer.
The conditional distribution of Y given X=x, where X and Y are non-negative integer-valued random variables, is characterized in terms of the regression function of X on Y and the marginal distribution of X which is a...
详细信息
The conditional distribution of Y given X=x, where X and Y are non-negative integer-valued random variables, is characterized in terms of the regression function of X on Y and the marginal distribution of X which is assumed to be of a power series form. Characterizations are given for a binomial conditional distribution when X follows a Poisson, binomial or negative binomial, for a hypergeometric conditional distribution when X is binomial and for a negative hypergeometric conditional distribution when X follows a negative binomial.
Let × i ( n ) , Y i ( n ) } i = 1 n be a sequence of independent observations from the model Y i ( n ) = g ( x i ( n ) ) + error, where the regression function g is unknown and defined on a compact set in R d . W...
详细信息
Let × i ( n ) , Y i ( n ) } i = 1 n be a sequence of independent observations from the model Y i ( n ) = g ( x i ( n ) ) + error, where the regression function g is unknown and defined on a compact set in R d . We show that a smoothed Nadaraya-Watson estimate of the function g ( x ) is asymptotically weak, mean square, strong, and completely consistent and asymptotically normal. The class of applicable kernels includes those with noncompact support for which ∫ 0 ∞ d−1 sup ‖x‖⩾z K (x) d z < ∞ and K ( x ) ⩾ cI {‖ x ‖ ⩽ r } ( x ), c , r , > 0.
We derive an asymptotic expansion of integrated square error in kernel-type nonparametric regression. A similar result is obtained for a cross-validatory estimate of integrated square error. Together these expansions ...
详细信息
We derive an asymptotic expansion of integrated square error in kernel-type nonparametric regression. A similar result is obtained for a cross-validatory estimate of integrated square error. Together these expansions show that cross-validation is asymptotically optimal in a certain sense.
暂无评论