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 ...
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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.
Let ( X , Y ) be a random vector in the plane and denote by m(x) = E ( Y|X = x ) the corresponding regression function. We show that the bootstrap approximation for the distribution of a smoothed nearest neighbor esti...
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Let ( X , Y ) be a random vector in the plane and denote by m(x) = E ( Y|X = x ) the corresponding regression function. We show that the bootstrap approximation for the distribution of a smoothed nearest neighbor estimate of m ( x ) is valid. Also we compare, by Monte Carlo, confidence intervals which are obtained from both the normal and the bootstrap approximation.
Let ( X , Y ) be an R d × R -valued random vector and let ( X 1 , Y 1 ),…,( X N , Y N ) be a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length l 1 , …, l n , fin...
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Let ( X , Y ) be an R d × R -valued random vector and let ( X 1 , Y 1 ),…,( X N , Y N ) be a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length l 1 , …, l n , find the nearest neighbor to X in each block and call the corresponding couple ( X i ∗ , Y i ∗ ). It is shown that the estimate m n (X) = Σ i = 1 n w ni Y i ∗ Σ i = 1 n w ni of m ( X ) = E { Y | X } satisfies E {| m n ( X ) − m ( X )| p } 0 ( p ≥ 1) whenever E {| Y | p } < ∞, l n ∞, and the triangular array of positive weights { w ni } satisfies sup i ≤ n w ni Σ i = 1 n w ni 0. No other restrictions are put on the distribution of ( X , Y ). Also, some distribution-free results for the strong convergence of E {| m n ( X ) − m ( X )| p | X 1 , Y 1 ,…, X N , Y N } to zero are included. Finally, an application to the discrimination problem is considered, and a discrimination rule is exhibited and shown to be strongly Bayes risk consistent for all distributions.
In the paper, for unknown distribution density f(t), t is an element of R-nu, a random vector X is an element of R-nu, and regression function r(t) = E(Y vertical bar X = t) of a random vector (X, Y), X is an element ...
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In the paper, for unknown distribution density f(t), t is an element of R-nu, a random vector X is an element of R-nu, and 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 the distribution of maximal deviation of these estimates from the true distribution density f(t) and regression function r(t) tends to the double exponential law for n -> infinity. With the help of the constructed estimates we found a confidence region for f(t) and r(t), corresponding to the given confidence coefficient alpha (0 < alpha < 1), and we constructed 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, r(0)(t) is a given function.
For a well-known class of nonparametric regression function estimators of nearest neighbor type the uniform measure of deviation from the estimators to the true regression function is studied. Under weak regularity co...
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For a well-known class of nonparametric regression function estimators of nearest neighbor type the uniform measure of deviation from the estimators to the true regression function is studied. Under weak regularity conditions it is shown that the estimators are uniformly consistent with probability one and the corresponding rate of convergence is near-optimal.
This paper deals with an estimator m n of the regression function m ( x ) = E ( Y | X = x ) with X in the real line and Y in a sufficiently regular Banach space. By using infinite dimensional probability inequalities ...
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This paper deals with an estimator m n of the regression function m ( x ) = E ( Y | X = x ) with X in the real line and Y in a sufficiently regular Banach space. By using infinite dimensional probability inequalities for sums, we show that m n is uniformly consistent.
Wavelets are applied to a regression model with an additive stationary noise. By checking the empirical wavelet coefficients with significantly large absolute values across fine scale levels, the jump points are detec...
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Wavelets are applied to a regression model with an additive stationary noise. By checking the empirical wavelet coefficients with significantly large absolute values across fine scale levels, the jump points are detected first. Then the cusp points are identified by checking the wavelet coefficients with significantly large absolute values which are secondly large only to the previous wavelet coefficient across fine scale levels. All estimators are shown to be consistent.
Let (X1, X2, Y1, Y2) be a four dimensional random variable having the joint probability density function f(x1, x2, y1, y2). In this paper we consider the problem of estimating the regression function {Mathematical exp...
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This paper is devoted to the study of large deviation behavior in the setting of the estimation of the regression function on functional data. A large deviation principle is stated for a process Zn, defined below, all...
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This paper is devoted to the study of large deviation behavior in the setting of the estimation of the regression function on functional data. A large deviation principle is stated for a process Zn, defined below, allowing to derive a pointwise large deviation principle for the NadarayaWatson- type l-indexed regression function estimator as a by-product. Moreover, a uniform over VC-classesChernoff type large deviation result is stated for the deviation of the l-indexed regression estimator.
This thesis applies a self-reunion multiple regression (SRMR) model in short-term load forecasting (STLF) and obtains very accurate and steadfast results. This thesis first uses cluster analysis to categorize historic...
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ISBN:
(纸本)9810557027
This thesis applies a self-reunion multiple regression (SRMR) model in short-term load forecasting (STLF) and obtains very accurate and steadfast results. This thesis first uses cluster analysis to categorize historical data. Data with similar features will be put in one category. After that, select one group of multiple regression variables in different categories, which serves as the basis for the load forecasting. Then, determine each selected multiple regression variables' regression function for the predicted load by taking the regression function as the base for the forecasting model and using the least-square error. Finally, with the linear programming, find the reunion coefficient corresponding to each regression function. The SRMR model obtained through the fore-going steps is tested by the actual Taiwan load data. Results prove that the average forecast absolute error sought by the model is about 1%, better than the error by the traditional methods.
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