Let ( X , Y ), ( X 1 , Y 1 ), …, ( X n , Y n ) be i.d.d. R r × R -valued random vectors with E | Y | < ∞, and let Q n ( x ) be a kernel estimate of the regression function Q ( x ) = E ( Y | X = x ). In this ...
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Let ( X , Y ), ( X 1 , Y 1 ), …, ( X n , Y n ) be i.d.d. R r × R -valued random vectors with E | Y | < ∞, and let Q n ( x ) be a kernel estimate of the regression function Q ( x ) = E ( Y | X = x ). In this paper, we establish an exponential bound of the mean deviation between Q n ( x ) and Q ( x ) given the training sample Z n = ( X 1 , Y 1 , …, X n , Y n ), under conditions as weak as possible.
Suppose one has a random sample from a distributionFY,X,the goal being to estimate μ, the unconditional mean ofY. If the regression function ofYonXis of a known parametric form, one might consider estimating μ by th...
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Suppose one has a random sample from a distributionFY,X,the goal being to estimate μ, the unconditional mean ofY. If the regression function ofYonXis of a known parametric form, one might consider estimating μ by the average of the estimated regression function values at the sample points. It is shown here that such an estimator can offer substantial improvement over the sample mean ofY, and that in no case does the former estimator have larger asymptotic variance than the latter estimator. Applications of this asymptotic distribution theory to the double-sampling setting are also given.
In this paper we propose a smooth nonparametric estimation for the conditional probability density function based on a Bernstein polynomial representation. Our estimator can be written as a finite mixture of beta dens...
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In this paper we propose a smooth nonparametric estimation for the conditional probability density function based on a Bernstein polynomial representation. Our estimator can be written as a finite mixture of beta densities with data-driven weights. Using the Bernstein estimator of the conditional density function, we derive new estimators for the distribution function and conditional mean. We establish the asymptotic properties of the proposed estimators, by proving their asymptotic normality and by providing their asymptotic bias and variance. Simulation results suggest that the proposed estimators can outperform the Nadaraya-Watson estimator and, in some specific setups, the local linear kernel estimators. Finally, we use our estimators for modeling the income in Italy, conditional on year from 1951 to 1998, and have another look at the well known Old Faithful Geyser data. (C) 2019 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
Let ( X , Y ), ( X 1 , Y 1 ),…, ( X n , Y n ) be i.i.d. ( R r × R )-valued random vectors with E | Y | < ∞, and let m n ( x ) be a nearest neighbor estimate of the regression function m ( x ) = E ( YsβX = x...
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Let ( X , Y ), ( X 1 , Y 1 ),…, ( X n , Y n ) be i.i.d. ( R r × R )-valued random vectors with E | Y | < ∞, and let m n ( x ) be a nearest neighbor estimate of the regression function m ( x ) = E ( YsβX = x ). We establish an exponential bound of the mean deviation between m n ( x ) and m ( x ) given the training sample Z n = ( X 1 , Y 1 ,…, X n , Y n ), under the conditions as weak as possible. This is a substantial improvement on Beck's result.
In the paper we estimate a regressionm(x)=E {Y|X=x} from a sequence of independent observations (X 1,Y 1),…, (X n, Yn) of a pair (X, Y) of random variables. We examine an estimate of a type $${{\hat m\left( x \right)...
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In the paper we estimate a regressionm(x)=E {Y|X=x} from a sequence of independent observations (X 1,Y 1),…, (X n, Yn) of a pair (X, Y) of random variables. We examine an estimate of a type $${{\hat m\left( x \right) = \sum\limits_{j = 1}^n {Y_{j\varphi N} } \left( {x,X_j } \right)} \mathord{\left/ {\vphantom {{\hat m\left( x \right) = \sum\limits_{j = 1}^n {Y_{j\varphi N} } \left( {x,X_j } \right)} {\sum\limits_{j = 1}^n {\varphi _N } \left( {x,X_j } \right)}}} \right. \kern-\nulldelimiterspace} {\sum\limits_{j = 1}^n {\varphi _N } \left( {x,X_j } \right)}}$$ , whereN depends onn andϕ N is Dirichlet kernel and the kernel associated with the hermite series. Assuming, that E|Y|<∞ and |Y|≦γ≦∞, we give condition for $$\hat m\left( x \right)$$ to converge tom(x) at almost allx, provided thatX has a density. if the regression hass derivatives, then $$\hat m\left( x \right)$$ converges tom(x) as rapidly asO(nC−(2s−1)/4s) in probability andO(n −(2s−1)/4s logn) almost completely.
Estimation of regression function from independent and identically distributed data is considered. In this paper, we investigate partitioning and modified partitioning estimation for regression functions. The asymptot...
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Estimation of regression function from independent and identically distributed data is considered. In this paper, we investigate partitioning and modified partitioning estimation for regression functions. The asymptotic normality of partitioning and modified partitioning function estimation is shown.
The authors propose a family of robust nonparametric estimators for regression or autoregression functions based on kernel methods. They show the strong uniform consistency of these estimators under a general ergodici...
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The authors propose a family of robust nonparametric estimators for regression or autoregression functions based on kernel methods. They show the strong uniform consistency of these estimators under a general ergodicity condition when the data are unbounded and range over suitably increasing sequences of compact sets. They give some implications of these results for stating the prediction in Markovian processes with finite order and show, through simulation, the efficiency of the predictors they propose.
We consider the regression model H = h(x) + E, where h is an unknown smooth regression function and E is the random error with unknown distribution F. In this context we present and examine the asymptotic behavior of ...
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Modular Steel Buildings (MSBs) are fast evolving as an effective alternative to conventional on-site steel construction. An explanation of the concept of modular steel design, including its unique detailing requiremen...
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Modular Steel Buildings (MSBs) are fast evolving as an effective alternative to conventional on-site steel construction. An explanation of the concept of modular steel design, including its unique detailing requirements is given in this paper. The paper also focuses on a typical MSB floor system which is achieved by welding the webs of the stringers directly to the floor beams. A typical modular floor grid structure is designed using conventional methods. The floor is then modelled using the finite element method and analyzed under the effect of dead and live service loads. This allows an assessment of the effect of direct welding between stringers and floor beams on the analysis and design of floor beams, stringers, and welded connections. The results reveal that consideration of the true behaviour of direct welding leads to a distribution of forces and moments which is different from those found in conventional steel buildings. A simplified analytical model is proposed to capture such behaviour. regression functions have been developed to describe the model. In practice, the proposed model can predict the actual forces and moments, leading to a reliable design of modular steel floors.
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