Empirical Euclidean Likelihood Of Strongly Stationary M Depedent Semiparametric Models

Likelihood is one of the most important tools for statisticians and provides the main approach to inference in parametric models. In many situations,however, we do not exactly know the distribution form,we may have partial information about the distribution. Thus we can not construct and use likelihood functions, we should find the other ways to solve the problem One of these ways is empirical likelihood. It is a nonparametric method of inference and has been discussed by many statisticians and has been applied in many models. But, it is complicated to compute empirical likelihood function, some scholars used Euclidean distance to replace likelihood distance. In 1994 Xu Luo discussed the properties of empirical Euclidean likelihood of semiparametnc models about large sample. But he only discussed independent samples In this paper, we mainly discuss the properties about large samples and estimation of empirical Eucliden likelihood in strongly stationary m dependent semiparametric models.At First, the following are some conditions.ê01(A)Assume E{g(X, 0 0)g1(X, 0 ⁾ } is positive deⁿite, The rank ofE1 cg(X, 0isp ,wliere Cg(X, ⁾ is rXpmatrix, 0 0xsthetme value of 0(B)Cg(X, 0is continuous in a neighborhood of the true value 0 0,And in50'this neighborhood, ('^{X 0 G}1(X), andE{G^?Y) } < ^.cO(C)C 2^c(X. is continuous in a neighborhood of the 0 ^. And in this6)neighborhood II cg(,II^G2(X) and E{G^A7}, Jg(X 0) H C3 (X) andE{Gi (X) } be strongly stationary m dependent random varlablessequenceinRd, EIIg(X 6)112, with probability 1 l( 6 ) attains is maximum value at some point 1 in the interior of the ball ii 6 - 0 o II and satisfy³l(0)⁼ 0Corollary 2.1.1 In addition to the conditions of theorem 2.1 1, we assume that0< 5Then= o(n⁾,e-e0= o(n⁾ as.Theorem 2.2.1 Inaddition to the conditions of theorem 2.1.1, we assume that I5 > a >0, a - 2 5 + -<02ThenniP^O(^.0Y_<sup>AT (0,U)Where V,U will be given in the proof of theorem 2.2.1.Throrem 2.3.1 If the conditions of theorem 2. 1.1 are satisfied, ThenThrorem 2.4.1 In addition to the conditions of theorem 2.1.1, we assume thatrn-iE{g(X, 0 0)g'(X. 6 ⁾ } +2E cov(g(X1, 0 0),g(X1,, 6 ⁾) is positive definite,i=1Then-2/( 0 )_<sup>x2(r) (n-. oo)Theorem 2.4.2 Under the assumptions of theorem 2.1.1, H0 6 0 , when H0 is true.Then...