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...
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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...
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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...
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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.
Uniqueness of specification of a bivariate distribution by a Pareto conditional and a consistent regression function is investigated. New characterizations of the Mardia bivariate Pareto distribution and the bivariate...
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Uniqueness of specification of a bivariate distribution by a Pareto conditional and a consistent regression function is investigated. New characterizations of the Mardia bivariate Pareto distribution and the bivariate Pareto conditionals distribution are obtained.
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.
We consider an infinite sequence X-1,X-2,... of independent random variables having a common continuous distribution function F(x). For 1 less than or equal to i less than or equal to n, let {X-i:n} denote the ith ord...
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We consider an infinite sequence X-1,X-2,... of independent random variables having a common continuous distribution function F(x). For 1 less than or equal to i less than or equal to n, let {X-i:n} denote the ith order statistic among X-1,...,X-n. In this paper, we characterize the distributions for which the regression E((X-1:n + + X-n:n)/n\X-k:n = x) is a linear function of x. (C) 2003 Elsevier Science B.V. All rights reserved.
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...
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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.
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...
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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.
Letm n (x) be the recursive kernel estimator of the multiple regression functionm(x)=E[Y|X=x]. For given α (00 we define a certain class of stopping timesN=N(α,d, x) and takeI ...
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Letm
n
(x) be the recursive kernel estimator of the multiple regression functionm(x)=E[Y|X=x]. For given α (0<α<1) andd>0 we define a certain class of stopping timesN=N(α,d, x) and takeI
N,d
(x)=[m
N
(x)−d, m
N
(x)+d] as a 2d-width confidence interval form(x) at a given pointx. In this paper it is shown that the probability P{m(x)∈I
N,d
(x)} converges to α asd tends to zero.
In this paper, for an unknown distribution function f(t), t is an element of R-nu, a random vector X is an element of R-nu, and a regression function r(t) = E(Y vertical bar X = t) of a random vector (X, Y), X is an e...
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In this paper, for an unknown distribution function f(t), t is an element of R-nu, a random vector X is an element of R-nu, and a regression function r(t) = E(Y vertical bar X = t) of a random vector (X, Y), X is an element of R-nu, Y is an element of R-1, nonparametric kernel estimates f(n)(t) and r(n)(t) are constructed. It is proved that distribution of the maximal deviation of these estimators from the true distribution density f(t) and the regression function r(t) tend to the double exponential law as n -> infinity. With the aid of the constructed estimators we find a confidence region for f(t) and r(t), corresponding to the given confidence coefficient alpha (0 < alpha < 1), and construct a criterion for testing the hypothesis H-0 : f(t) = f(0)(t) (respectively, H'(0) : r(t) = r(0)(t)), where f(0)(t) is a given a priori distribution density, and r(0)(t) is a given function.
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