Suppose that X C R~d and Y C R are Borel sets and p is a Borel probabilitymeasure defined on the product Z = Z × Y. let ρ(y|x) denotes the conditional probability measureon Y and let ρx be the projection of ρt...
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Suppose that X C R~d and Y C R are Borel sets and p is a Borel probabilitymeasure defined on the product Z = Z × Y. let ρ(y|x) denotes the conditional probability measureon Y and let ρx be the projection of ρto X.
Characterizations of probability distributions by regressional properies have attracted the attentions of many researchers. Suppose that X-r equivalent to X-r,X-n,X-(m) over tilde;,X-k, r = 1, horizontal ellipsis , n ...
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Characterizations of probability distributions by regressional properies have attracted the attentions of many researchers. Suppose that X-r equivalent to X-r,X-n,X-(m) over tilde;,X-k, r = 1, horizontal ellipsis , n are n generalized order statistics (gos). We have studied several basic and regressional propertitis of the gos. Based on these distributional properties some characterizations of continuous distributions are presented. It is also shown that many of the known characterization results are special cases of the results presented in the paper.
SummaryIn the paper we estimate a regressionm(x)=E {Y|X=x} from a sequence of independent observations (X1,Y1),…, (Xn, Yn) of a pair (X, Y) of random variables. We examine an estimate of a type\({{\hat m\left( x \rig...
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SummaryIn the paper we estimate a regressionm(x)=E {Y|X=x} from a sequence of independent observations (X1,Y1),…, (Xn, 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 andϕN 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.
New families of distributions are characterized by regressional properties of order statistics. Among equations for regressions based on order statistics X-1:n,...;X-n:n, n = 1, 2,..., we investigate a relation of the...
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New families of distributions are characterized by regressional properties of order statistics. Among equations for regressions based on order statistics X-1:n,...;X-n:n, n = 1, 2,..., we investigate a relation of the form E(lambdaX(k:2k+1) + (1 - lambda) = Xk+2:2k+1\Xk+1:2k+1 = x) = x, (0 < lambda < 1). As a special case, a characterization of Student's t(2) distribution is obtained.
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.
In this paper, a method for nonparametric regression estimation in a time-varying environment is presented. The orthogonal series-based kernels are used to design learning procedures tracking non-stationary systems ch...
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In this paper, a method for nonparametric regression estimation in a time-varying environment is presented. The orthogonal series-based kernels are used to design learning procedures tracking non-stationary systems changes under non-stationary noise. The presented procedures, constructed in the spirit of generalized regression neural networks, are a very effective tool to deal with stream data. The convergences in probability and with probability one are proved, experimental results are given and discussed. (C) 2017 Elsevier Inc. All rights reserved.
Flexible AC transmission system devices provide the opportunity to improve the usage of the current transmission facilities by controlling network flows and nodal voltages. The optimal steady-state settings of these d...
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Flexible AC transmission system devices provide the opportunity to improve the usage of the current transmission facilities by controlling network flows and nodal voltages. The optimal steady-state settings of these devices can be determined using optimal power flow calculations. However, this requires knowledge of the system parameters, generation settings and loads. A two-stage regression-based control scheme is proposed to determine the optimal settings of thyristor-controlled series compensators (TCSCs) with the objective to optimally utilise the current transmission system in the presence of renewable energy resources. A regression function describing the relationship between a set of key measurements and the optimal device settings is determined in the offline simulation. This function is then used to calculate the optimal device settings by only receiving the information from a limited number of key measurements without solving the OPF problem in the online operation. Studies are carried out with TCSCs in three-test systems, the IEEE 14-bus system, a 28-bus system and the IEEE 118-bus system. The simulation results with one, two and four TCSCs are presented, illustrating the performance of the proposed regression-based control scheme.
The authors prove upper and lower bounds on the VC dimension of sparse univariate polynomials over reals and apply these results to prove uniform learnability of sparse polynomials and rational functions. As an applic...
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The authors prove upper and lower bounds on the VC dimension of sparse univariate polynomials over reals and apply these results to prove uniform learnability of sparse polynomials and rational functions. As an application the solution to the open problem of Vapnik [in Estimation of Dependences Based on Empirical Data, Springer-Verlag, Berlin, 1982] on computational approximation of the regression in a class of polynomials used in the theory of empirical data dependences is given.
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