Consider the nonparametric regression model Yi=g(xi) +ei, i=1, 2,...,where g is an unknown function defined on the interval [0, 1], the fixed design points xi(i≥1) are known and ei’s are i.i.d. random variables with...Consider the nonparametric regression model Yi=g(xi) +ei, i=1, 2,...,where g is an unknown function defined on the interval [0, 1], the fixed design points xi(i≥1) are known and ei’s are i.i.d. random variables with median zero. The regressor is assumed to take values in [0, 1]∈ R and the regressand to be real valued. This paper stu-dies the behavior of the nearest neighbor median estimate gnh(x)=m(Yn1(x), Yn2(x),...,Ynh(x)), where h is the number of the nearest neighbor. Under suitable conditions, Bahadur’s representation for the above-mentioned the nonparametric regression function g is obtained. Law of iterated logarithm and asymptotic normality are also established.展开更多
CONSIDER the nonparametric median regression model Y<sub>ni</sub> = g (x<sub>ni</sub>) + ε<sub>ni</sub>, 1≤i≤n （1）where g: [0, 1]|→R is an unknown function of interest; {x<...CONSIDER the nonparametric median regression model Y<sub>ni</sub> = g (x<sub>ni</sub>) + ε<sub>ni</sub>, 1≤i≤n （1）where g: [0, 1]|→R is an unknown function of interest; {x<sub>ni</sub>, 1≤i≤n} is the fixed design pointsin the interval [0, 1]; {ε<sub>ni</sub>, 1≤i≤n} is a triangular array of row iid random variables having medi-an zero, and {Y<sub>ni</sub>, 1≤i≤n} is the observation. For each x∈[0, 1], n≥1, let D<sub>nj</sub>（x） denotethe jth nearest neighber of x, j=1, 2,…, n, i. e. {D<sub>n1</sub>（x）, D<sub>n2</sub>（x）,…, D<sub>nn</sub>（x）} is a trans-position of {x<sub>n1</sub>, x<sub>n2</sub>,…, x<sub>nn</sub>} satisfying |D<sub>n1</sub>（x）-x|≤|D<sub>n2</sub>（x）-x|≤…≤|D<sub>nn</sub>（x）-x|.The tie is broken by the chronological order. The展开更多
文摘Consider the nonparametric regression model Yi=g(xi) +ei, i=1, 2,...,where g is an unknown function defined on the interval [0, 1], the fixed design points xi(i≥1) are known and ei’s are i.i.d. random variables with median zero. The regressor is assumed to take values in [0, 1]∈ R and the regressand to be real valued. This paper stu-dies the behavior of the nearest neighbor median estimate gnh(x)=m(Yn1(x), Yn2(x),...,Ynh(x)), where h is the number of the nearest neighbor. Under suitable conditions, Bahadur’s representation for the above-mentioned the nonparametric regression function g is obtained. Law of iterated logarithm and asymptotic normality are also established.
文摘CONSIDER the nonparametric median regression model Y<sub>ni</sub> = g (x<sub>ni</sub>) + ε<sub>ni</sub>, 1≤i≤n （1）where g: [0, 1]|→R is an unknown function of interest; {x<sub>ni</sub>, 1≤i≤n} is the fixed design pointsin the interval [0, 1]; {ε<sub>ni</sub>, 1≤i≤n} is a triangular array of row iid random variables having medi-an zero, and {Y<sub>ni</sub>, 1≤i≤n} is the observation. For each x∈[0, 1], n≥1, let D<sub>nj</sub>（x） denotethe jth nearest neighber of x, j=1, 2,…, n, i. e. {D<sub>n1</sub>（x）, D<sub>n2</sub>（x）,…, D<sub>nn</sub>（x）} is a trans-position of {x<sub>n1</sub>, x<sub>n2</sub>,…, x<sub>nn</sub>} satisfying |D<sub>n1</sub>（x）-x|≤|D<sub>n2</sub>（x）-x|≤…≤|D<sub>nn</sub>（x）-x|.The tie is broken by the chronological order. The
