A recursive kernel estimate ∑ i = 1 n Y i K ⧸( x − X i ) h i )⧸∑ j = 1 n K (( x − X j )⧸ h j ) of a regression m(x) = E{Y|X = x} calculated from independent observations ( X 1 , Y 1 ),…, ( X n , Y n ) of a pair ( X...
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A recursive kernel estimate ∑ i = 1 n Y i K ⧸( x − X i ) h i )⧸∑ j = 1 n K (( x − X j )⧸ h j ) of a regression m(x) = E{Y|X = x} calculated from independent observations ( X 1 , Y 1 ),…, ( X n , Y n ) of a pair ( X, Y ) of random variables is examined. ForE| Y | 1 + δ < ∞, δ > 0, the estimate is weakly pointwise consistent for almost all ( μ ) x ∈ R d , μ is the probability measure of X , if and only if∑ i−1 n h i d I {h i > ɛ } ⧸ ∑ j = 1 n h j d → 0 as n → ∞ , all ɛ > 0, and∑ i = 1 ∞ h i d = ∞, d is the dimension of X . For E|Y| 1 + δ < ∞, δ > 0, the estimate is strongly pointwise consistent for almost all ( μ ) x ∈ R d , if and only if the same conditions hold. ForE|Y| 1 + δ < ∞, δ > 0, weak and strong consistency are equivalent. Similar results are given for complete convergence.
We consider the nonparametric regression model Y i = g ( x i )+ ζ i , where g is a bounded function, over the interval [0,1], to be estimated, x i 's are nonrandom and ζ i 's are independent identically dist...
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We consider the nonparametric regression model Y i = g ( x i )+ ζ i , where g is a bounded function, over the interval [0,1], to be estimated, x i 's are nonrandom and ζ i 's are independent identically distributed random variables with Eζ i =0. This paper studies the behavior of the general family of nonparametric estimates g n ( x )= Σ i =1 n Y i w ni ( x ), where the weight functions { w ni } are of the form w ni ( x )= w ni ( x ; x 1 ,…, x n ), i =1,…, n . The family of estimates includes all known estimates proposed by Priestley and Chao (1972), Clark (1977), Gasser and Müller (1979), Cheng and Lin (1981) as well as Georgiev (1984b, 1985). Sufficient conditions for mean square and complete convergence are derived. New results for the Priestley-Chao and Gasser-Müller-Cheng-Lin estimates are obtained. Also proposed is a class of new nearest neighbor estimates of g . Finally, a simulation experiment demonstrates the remarkable success of the nearest neighbor technique with bandwidth depending on the local density of the design points.
In this paper we propose a new nonparametric regression technique. Our proposal has common ground with existing two-step procedures in that it starts with a parametric model. However, our approach differs from others ...
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In this paper we propose a new nonparametric regression technique. Our proposal has common ground with existing two-step procedures in that it starts with a parametric model. However, our approach differs from others in the choice of parametric start within the parametric family. Our proposal chooses a function that is the projection of the unknown regression function onto the parametric family in a certain metric, while the existing methods select the best approximation in the usual L-2 metric. We find that the difference leads to substantial improvement in the performance of regression estimators in comparison with direct one-step estimation, irrespective of the choice of a parametric model. This is in contrast with the existing two-step methods, which fail if the chosen parametric model is largely misspecified. We demonstrate this with sound theory and numerical experiment.
A discrete multivariate probability distribution for dependent random variables, which contains the Poisson and Geometric conditionals distributions as particular cases, is characterized by means of conditional expect...
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A discrete multivariate probability distribution for dependent random variables, which contains the Poisson and Geometric conditionals distributions as particular cases, is characterized by means of conditional expectations of arbitrary one-to-one functions. Independence of the random variables is also characterized in terms of these conditional expectations. For certain exchangeable and partially exchangeable random variables with a joint distribution of this form it is shown that maximum likelihood estimates coincide with the simple method of moments estimates, suggesting that these models offer a pragmatic way to analyze certain dependent data. (C) 2002 Elsevier Science (USA).
Problems of specification of discrete bivariate: statistical models by a modified power series conditional distribution and a regression function are studied. An identifiability result for a wide class of such mixture...
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Problems of specification of discrete bivariate: statistical models by a modified power series conditional distribution and a regression function are studied. An identifiability result for a wide class of such mixtures with infinite support is obtained. Also the finite support cast: within a more specific model is considered. Applications for Poisson. (truncated) geometric, and binomial mixtures are given. From the viewpoint of Bayesian analysis unique determination of the prior bq a Bayes estimate of the mean for modified power series mixtures is investigated. (C) 2001 Academic Press.
The aim of this paper is to study the behavior of a covariate function in a multivariate risks scenario. The first part of this paper deals with the problem of estimating the \(c\)-upper level sets \({L(c)= \{F(x) \ge...
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The aim of this paper is to study the behavior of a covariate function in a multivariate risks scenario. The first part of this paper deals with the problem of estimating the \(c\)-upper level sets \({L(c)= \{F(x) \ge c \}}\), with \(c \in (0,1)\), of an unknown distribution function \(F\) on \(\mathbb {R}^d_+\). A plug-in approach is followed. We state consistency results with respect to the volume of the symmetric difference. In the second part, we obtain the \(L_p\)-consistency, with a convergence rate, for the regression function estimate on these level sets \(L(c)\). We also consider a new multivariate risk measure: the Covariate-Conditional-Tail-Expectation. We provide a consistent estimator for this measure with a convergence rate. We propose a consistent estimate when the regression cannot be estimated on the whole data set. Then, we investigate the effects of scaling data on our consistency results. All these results are proven in a non-compact setting. A complete simulation study is detailed and a comparison with parametric and semi-parametric approaches is provided. Finally, a real environmental application of our risk measure is provided.
Realistic assessments of the reliability of networked systems, series and parallel systems being special cases, require that we account for interdependence between the component life-lengths. The key to doing this is ...
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Realistic assessments of the reliability of networked systems, series and parallel systems being special cases, require that we account for interdependence between the component life-lengths. The key to doing this is the specification and use of a suitable probability model in two or more dimensions. Consequently, several multivariate probabilistic models have been proposed in the literature. Many of these models have marginal distributions that are exponential;the ones by Gumbel, and by Marshall and Olkin being some of the earliest and the best known. The purpose of this paper is two fold: The first purpose is to articulate the nature of dependence encapsulated by such models, using a perspective which is best appreciated by a user. Specifically, we anchor on the bivariate case, and focus attention on the conditional mean as a measure of dependence. The second purpose, motivated by the first, is to introduce a new family of multivariate distributions with exponential marginals, whose conditional mean fills a void in the general forms of the conditional means of the available models. The method of "copulas" is used to generate this new family of distributions. Attention is focused on the case of exponential marginals, because the notion of "hazard potentials" enables us to use multivariate distributions with exponential marginals as a seed for generating multivariate distributions with marginals other than the exponential.
This paper presents the results of experimental research and mathematical modelling on the influence of dynamic instabilities on the condensation phase change of R507 refrigerant in tubular mini-channels. This agent i...
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This paper presents the results of experimental research and mathematical modelling on the influence of dynamic instabilities on the condensation phase change of R507 refrigerant in tubular mini-channels. This agent is currently being utilised as a temporary substitute for R404A, with R448A intended as the target substitute. In addition to the results, this paper contains a dimensional analysis procedure based on the Pi-Buckingham theorem that has allowed for the development of a regressive model for the velocities of the dynamic instabilities. The experimental part of this paper was conducted using tubular mini-channels with internal diameters of 1.44, 2.3, and 3.3 mm. (C) 2019 Elsevier Ltd. All rights reserved.
The PIN ABRASION TEST is an international well-known experimental arrangement in order to measure abrasive wear under laboratory conditions. It will be shown how by means of this test a prognosis can be given of abras...
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The PIN ABRASION TEST is an international well-known experimental arrangement in order to measure abrasive wear under laboratory conditions. It will be shown how by means of this test a prognosis can be given of abrasive wear expectet of heavy plate components used in industrial practice. For this purpose a specific statistical method is applied to design and carry out the experiments proposed for the first time by R. A. Fisher. By that so-called full factorial 2(n)-plans can be performed which regard n=5 factors of influence: normal load, sliding velocity, size, hardness of abrasive particles and hardness of heavy plate materials. The experimental results are evaluated by means of regression analysis in order to define a mathematical function of multilinear type. By means of this function the prognosis can be realized regarding all significant effects and interactions of the factors. Thus the experimental results of the laboratory test can be transfered in industrial practice successfully.
The main purpose of the present work is to introduce and investigate a simple kernel procedure based on marginal integration that estimates the regression function for stationary and ergodic continuous time processes ...
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The main purpose of the present work is to introduce and investigate a simple kernel procedure based on marginal integration that estimates the regression function for stationary and ergodic continuous time processes in the setting of the additive model introduced by Stone (1985). We obtain the uniform almost sure consistency with exact rate and the asymptotic normality of the kernel-type estimators of the components of the additive model. Asymptotic properties of these estimators are obtained, under mild conditions, by means of martingale approaches. Finally, a general notion of the bootstrapped additive components, constructed by exchangeably weighting sample, is presented.
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