AUTOMATIC SELECTION OF PARAMETERS IN SPLINE REGRESSION VIA KULLBACK－LEIBLER INFORMATION

ＡＵＴＯＭＡＴＩＣＳＥＬＥＣＴＩＯＮＯＦＰＡＲＡＭＥＴＥＲＳＩＮＳＰＬＩＮＥＲＥＧＲＥＳＳＩＯＮＶＩＡＫＵＬＬＢＡＣＫ－ＬＥＩＢＬＥＲＩＮＦＯＲＭＡＴＩＯＮＡＵＴＯＭＡＴＩＣＳＥＬＥＣＴＩＯＮＯＦＰＡＲＡＭＥＴＥＲＳＩＮＳＰＬＩＮＥＲＥＧＲＥＳＳＩＯ...     

CONSISTENCY FOR KERNEL ESTIMATE OF CONDITIONAL FUNCTION

ＣＯＮＳＩＳＴＥＮＣＹＦＯＲＫＥＲＮＥＬＥＳＴＩＭＡＴＥＯＦＣＯＮＤＩＴＩＯＮＡＬＦＵＮＣＴＩＯＮ￥ＨＵＳｈｕｈｅ（ＤｅｐａｒｔｍｅｎｔＯｆＭａｔｈｅｍｏｔｉｃｓ，ＡｎｈｕｉＵｎｉｖｅｒｓｉｔｙ，Ｈｅｆｅｉ２３００３９，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：...     

A LAW OF THE ITERATED LOGARITHM FOR RANDOM WINDOW-WIDTH KERNEL ESTIMATOR OF A NONPARAMETRIC REGRESSION FUNCTION

In this paper we study the estimation of the regression function.We establish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an application,fora nearest neighbor estimator.These results give sharp pointwise rates of strong consistency ofthese estimators.     

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS IN THE CLASS OF ALL ESTIMATORS UNDER THE MATRIX LOSS FUNCTION

For the general fixed effects linear model:Y=Xτ+ε,ε～N(0,V)(or N(0,σ~2V)),V≥0,we obtain the necessary and sufficient condition for LY+α to be admissible for Sτ in the class of allestimators under matrix loss function(d-Sτ)(d-Sτ)′;for the general random effects linear model:Y=Xβ+ε,(?)where (?)=XV_(11)X′+XV_(12)+V_(21)X′+V_(22)≥0,we also obtain the necessary and sufficient condition for LY+α to be admissible for Sα+Qβin the class of all estimators under matrix loss function(d-Sα-Qβ)(d-Sα-Qβ)′.     

SEVERAL RESULTS ON ESTIMATION OF PARAMETERS UNDER MATRIX LOSS FUNCTION

In this paper,the definitions of Bayes estimator,minimax estimator,minimumrisk equivariant estimator and admissible estimator under the general matrix loss functionare given.Several results on estimation of parameters with the ordinary loss function areextended to the case of the matrix loss function.     

STRONG CONSISTENCY OF THE PERIODIC SMOOTHING SPLINES

Consider the regression model Y_i=u(x_i)+ε_i,i=1,2,…,n,where u(x)∈W_(2,per)~2[0,1],x_i=(i-1)/n,{ε_i}(?)are i.i.d,random variables.We use the periodic smoothing spline u_(λp)(x)toestimate u(x).Under certain conditions,strong consistency results of u_(λp)(x)are obtained,i.e.,forall 0相似文献   

MUCLTIVARIATE RESISTANT REGRESSION SPLINES FOR ESTIMATING MULTIVARIATE FUNCTIONS FROM NOISY DATA

1.IntroductionMultivariatesurfaceestimationisanimportantproblemforwhichseveralmethodologieshavebeendevelopedwiththeaimofconstructinganestimatorg,,(x)ofaJ--dimensionalsurfacego(x)basedonnoisyobservations{(Xi,K),15i5n}.Existingestimatorsofgoareobtainedonthe…     

ALL ADMISSIBLE LINEAR ESTIMATES OF REGRESSION COEFFICIENTS UNDER MATRIX LOSS

The necessary and sufficient conditions for a linear estimator of a linear estimable functionof regression coefficients in a general fixed effects linear model with the assumptions of normality to beadmissible in the class of all estimators under matrix liss function are given.For a general randomeffects or mixted effects linear model the necessary and sufficient conditions are obtained too.     

ON B-SPLINE M-ESTIMATORS IN A SEMIPARAMETRIC REGRESSION MODEL

ＯＮＢ－ＳＰＬＩＮＥＭ－ＥＳＴＩＭＡＴＯＲＳＩＮＡＳＥＭＩＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＭＯＤＥＬ￥ＳＨＩＰｅｉｄｅ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｎｇ１...     

STRONG CONSISTENCY OF M-ESTIMATES OF MULTIPLE REGRESSION COEFFICIENTS

ＳＴＲＯＮＧＣＯＮＳＩＳＴＥＮＣＹＯＦＭ－ＥＳＴＩＭＡＴＥＳＯＦＭＵＬＴＩＰＬＥＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＣＨＥＮＸｉｒｕ（ＧｒａｄｕａｔｅＳｃｈｏｏｌｏｆｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１００...     

BEHAVIOR OF STOCHASTIC APPROXIMATION ALGORITHM IN ROOT SET OF REGRESSION FUNCTION

1.IntroductionStochasticapproximation(SA)iswidelyappliedinoptimization,systemindelltification,adaptivecontrolandsignalprocessing.ThebasicproblemofSAistoseektherootsoreXtremaofafunctionf(.)calledregressionfunctionwhichcanbeestimateattimekandletthe(k 1)thobservationi,e,Yk 1~f(Xk) ek 1,(1)whereek 1istheobservationnoise.RobbinsandMonroll]in1951proposedthefollowingalgorithmxk l=xk akyk 1,(2)toestimatetherootsofj(.),whereahisthestepsize.ThisalgorithmisnowcalledRobbinsMonro(RM)algorithm.Denoteb…     

PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION

Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the thresh-old parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.     

A FAST PROCEDURE OF VARIABLE SELECTION IN LINEAR REGRESSION MODEL

In many situations,we are interested in selection of important variables whichare adequate for prediction under a linear regression model.In this paper,a fast selectionprocedure is proposed and is proved to be strongly consistent.Also,the convergence rate ofmisjudgement probability is given.     

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M－ESTIMATES FOR NONPARAMETRIC REGRESSION

ＯＰＴＩＭＡＬＧＬＯＢＡＬＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＭ－ＥＳＴＩＭＡＴＥＳＦＯＲＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＳＨＩＰｅｉｄｅ；ＬＩＧｕｏｙｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉ...     

GOAL PROGRAMMING ALGORITHM FOR A TYPE OF LEAST ABSOLUTE VALUE REGRESSION PROBLEM

This paper develops goal programming algorithm to solve a type of least absolute value (LAV) problem. Firstly, we simplify the simplex algorithm by proving the existence of solutions of the problem. Then, we present a goal programming algorithm on the basis of the original techniques. Theoretical analysis and numerical results indicate that the new method contains a lower number of deviation variables and consumes less computational time as compared to current LAV methods.     

EXISTENCE OF CONSISTENT ESTIMATES OF LINEAR REGRESSION COEFFICIENTS WHEN THE ERROR VARIANCES ARE UNEQUAL

Consider the linear regression model Y_i=x_i′β+σ_ie_i,i=1,…,n,…,where E(e_i)=0,E(e_ie_j)=δ_(ij),0<σ_1~2(?)σ_2~2(?)…and {x_i} satisfies A_1(?)sum from i=1 to n x_ix_i′/n(?)A_2,for n large,A_1>0,A_2>0.This paper shows that (i) ifσ_i~2,i=1,2…,are known,then the necessary and sufficient condition for theconsistency of the best unbiased linear estimate of β is sum from i=1 to ∞σ_i~(-2)=∞;(ii)if{σ_i~2}is only known to belong to the set {(h_1,h_2,…)∶0相似文献   

ROBUST NONPARAMETRIC REGRESSION BASED ON L_1-NORM AND B-SPLINES

ＲＯＢＵＳＴＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＢＡＳＥＤＯＮＬ＿１－ＮＯＲＭＡＮＤＢ－ＳＰＬＩＮＥＳＳＨＩＰｅｉｄｅ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎ...     

ADMISSIBILITY OF SIMULTANEOUS ESTIMATION OF SEVERAL LOSSES

In this paper,admissibility and inadmissibility results of simultaneous estimation oflosses of multivariate normal mean estimators are given.Admissible estimators for losses ofusual estimators of multivariate gamma parameters,multivariate binomial parameters andPoisson parameters are obtained respectively.     

ASSESSMENT OF LOCAL INFLUENCE FOR F-TEST IN LINEAR REGRESSION MODEL

1.IntroductionTheaimofthediagnosticsandinfluenceanalysisistoidentifytheoutliersorinfluelltialobservationsthatsubstantiallyaffecttheparameterestimatesandstatisticalinference.Therelatedworkthathasreceivedconsiderableattentioninlinearregressionmodelistheinfluenceontheregressioncoefficients(see[l--4]).Theinfluencefortheotheraspectsoflinearregressionmodelsuchasconfidenceregionshasalsobeenconsideredby[5].However,theinfluenceonFiestreceivedlessattentionasweknowtheF-testisverysensitivetotheinfluentia…     

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.