67 research outputs found
ASYMPTOTIC-BEHAVIOR OF NONPARAMETRIC CONDITIONAL QUANTILE ESTIMATES FOR TIME-SERIES
No full textNonparametric regression quantiles provide informative and powerful alternatives and generalizations to the more traditional mean and median. The use of B-spline approximation in the conditional quantile estimation has been studied recently by He and Shi (1994). The regression quantile splines are given by minimizing Sigma(i=1)(n) rho alpha(Y-i -g(X(i))), where rho alpha(t) = \t\ - (2 alpha - 1)t is the Czech function and g is taken from the space spanned by normalized B-splines basis functions. This paper relaxes the independence assumption on the stationary sequence {X(i), Y-i}. If the true conditional quantile function is smooth up to order r and the observed sequence is beta-mixing (or absolutely regular), it is shown, under suitable mixing conditions, that the optimal global convergence rates can be achieved by the B-spline based estimators and their derivatives.Statistics & ProbabilitySCI(E)1ARTICLE2161-1692
A joint regression variable and autoregressive order selection criterion
No full textIn linear regression models with autocorrelated errors, we apply the residual likelihood approach to obtain a residual information criterion (RIC), which can jointly select regression variables and autoregressive orders. We show that RIC is a consistent criterion. In addition, our simulation studies indicate that it outperforms heuristic selection criteria - the Akaike information criterion and the Bayesian information criterion - when the signal-to-noise ratio is not weak.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000224433600006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Mathematics, Interdisciplinary ApplicationsStatistics & ProbabilitySCI(E)11ARTICLE6923-9412
A NOTE ON THE CONVERGENT RATES OF M-ESTIMATES FOR A PARTLY LINEAR-MODEL
No full textThis paper concerns with M-estimators for the partly linear model Y-i = X(i)(tau) beta(o) + g(o)(T-i) + u(i), where (T-1,X(1)(tau), Y-1),...,(T-n,X(n)(tau),Y-n) are i.i.d. random (d + 2)-vectors such that Y-i is real-valued, X(i) epsilon R(d), and T-i ranges over a nondegenerate compact interval; u(i) is a random error; beta(o) is a d-vector of parameters; and g(o)(.) is an unknown function. A piecewise polynomial is used to approximate g(o)(.). The estimators of beta(o) and g(o)(t) considered are <(beta)over cap> and (g) over cap(n)(t) = phi(t)(tau)<(alpha)over cap> respectively, where <(alpha)over cap> and <(beta)over cap> are the solutions of the minimization problem [GRAPHICS] and phi(.) is a vector of the basis functions of a piecewise polynomial space and rho(.) is a function chosen suitably. Under some regular conditions, it is shown that (g) over cap(n) achieves the convergence rate which is Stone's optimal global rate of convergence of least square estimators for nonparametric regression and <(beta)over cap> achieves the convergence rate n(-1/2).Statistics & ProbabilitySCI(E)19ARTICLE127-472
Automatic Selection of Parameters in Spline Regression via Kullback-Leibler Information
No full textBased on Kullback-Leibler information we propose a data-driven selector, called GAIC (c) , for choosing parameters of regression splines in nonparametric regression via a stepwise forward/backward knot placement and deletion strategy [1] . This criterion unifies the commonly used information criteria and includes the Akaike information criterion (AIC) [2] and the corrected Akaike information criterion (AICC) [3] as special cases. To show the performance of GAIC (c) for c = 1=2, 3=4, 7=8, and 15=16, we compare it with cross-validation (CV), the generalized cross-validation (GCV), AIC, and AICC by an extensive simulation. Applications to the selection of the penalty parameters of smoothing splines are also discussed. Our simulation results indicate that the information criteria work well and are superior to cross-validation-based criteria in most of the cases considered, particularly in small sample cases. Under certain mild conditions, GAIC (c) is shown to be asymptotically..
M-Type Regression Splines Involving Time Series
No full textConsider a strictly stationary time series Zb=f(X i ; Y i ) : i = 1; 2; \Delta \Delta \Deltag with X i being R d - valued and Y i real-valued. The nonparametric M-type regression function g 0 (\Delta) is defined by E(\Psi(Y 1 \Gamma g 0 (X 1 )) j X 1 = x) = 0. Tensor products of B-splines are adopted to approximate g 0 and a class of M-type regression spline estimators of this function are obtained based on a segment, (X 1 ; Y 1 ); \Delta \Delta \Delta ; (X n ; Y n ), of Z. Suppose that g 0 (\Delta) is smooth up to order r (? d=2). Under certain regularity conditions, the M-type regression spline estimators can achieve the optimal rates of convergence n \Gammar=(2r+d) in L 2 -norms restricted to a compact domain when the spline knots are deterministically given. The M-estimators considered here include Huber's estimator, L 1 -norm estimator, regression quantile estimator and L P -norm estimator as special cases. Key words: Nonparametric regression, regression spline, optimal rate..
Global Convergence Rates of B-Spline M-Estimators in Nonparametric Regression
No full text. To compensate for lack of robustness in using regression splines via the least squares principle, a robust data smoothing procedure is proposed for obtaining a robust regression spline estimator of an unknown regression function, g 0 , of a one-dimensional measurement variable. This robust regression spline estimator is computed by using the usual M-type iteration procedures proposed for linear models. A simulation study is carried out and numerical examples are given to illustrate the utility of the proposed method. Assume that g 0 is smoothed up to order r ? 1=2 and denote the derivative of g 0 of order l by g (l) 0 . Let b g (l) n denote an M-type regression spline estimator of g (l) 0 based on a training sample of size n. Under appropriate regularity conditions, it is shown that the proposed estimator, b g (l) n , achieves the optimal rate, n \Gamma(r\Gammal)=(2r+1) (0 l ! r), of convergence of estimators for nonparametric regression when the spline knots are determinist..
Monotone B-spline Smoothing
No full textEstimation of growth curves or item response curves often involves monotone data smoothing. Methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated. Built upon the ideas of Ramsay (1988) and Koenker, Ng and Portnoy (1994), we propose monotone B-spline smoothing based on L 1 optimization. It inherits the desirable properties of spline approximations and the computational efficiency of linear programs. The constrained fit is similar to the unconstrained estimate in terms of computational complexity and asymptotic rate of convergence. Through applications to some real and simulated data we show that the method is useful in a variety of applications. The basic ideas utilized in monotone smoothing can be useful in some other constrained function estimation problems. KEY WORDS: B-spline, constraints, information criterion, least absolute deviation, linear programming, median, monotone..
Some Neutrosophic Uncertain Linguistic Number Heronian Mean Operators and Their Application to Multi-Attribute Group Decision Making
No full textHeronian mean (HM) is a useful aggregation operator which is marked by catching the interrelations of the
aggregated arguments and the neutrosophic uncertain linguistic set can be better to express the incomplete, indeterminate and inconsistent information. In this paper, we combine the Heronian mean and the neutrosophic uncertain linguistic set and proposed some Heronian mean operators based on neutrosophic uncertain linguistic numbers. Firstly, we introduce some definition and properties of uncertain linguistic numbers, the single valued neutrosophic set, and some heronian mean (HM) operators including the generalized weighted Heronian mean (GWHM) operator, the improved generalized weighted Heronian mean (IGWHM) operator, the improved generalized geometric weighted Heronian mean (IGGWHM)
operator
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