Minimax Linear Predictor Under Lipschitz Type Conditions for the Regression Fun
Minimax Linear Predictor Under Lipschitz Type Conditions for the Regression Fun
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Minimax predictor under higher order conditions .
Next we shall consider a more complicated situation, that is we shall consider a higher order Lipschitz condition. On the other hand, we assume simply that x. Are placed at equal distances, i. E. We shall assume that x. - i, i = l, ... , n, and that x„ = 0.
We define a difference operator A by A f(x) = f(x+l) - f(x) and power A^ of A by AJ(f(x)) = A(AJ-^f(x+l) -AJ-^f(x)), j=2, 3, ... .
We assume that Assumption 2. JA '^f(x)|^ca, and we shall obt...ain a minimax linear predictor under this assumption. For simplicity we put a = 1 as before.
Let f(0) = > ai, Yj^ be a linear predictor. Then E(f(o) - f(o))'^ = ( y- a^, f(k)- f(o))" +y and f(k) can be expressed as -11- f(k) = f(0) + j^c^d^ + ^c^d^ + ... + j^c^^d^ ^-^-1 h+1 (2. 1) \' where d. = A f(0), ,c. Is the binomial coefficient with the definition that, c. =Oifl
What to read after Minimax Linear Predictor Under Lipschitz Type Conditions for the Regression Fun?
You can find similar books in the "Read Also" column, or choose other free books by Kei Takeuchi to read online
To quickly assess the difficulty of the text, read a short excerpt:
Minimax predictor under higher order conditions .
Next we shall consider a more complicated situation, that is we shall consider a higher order Lipschitz condition. On the other hand, we assume simply that x. Are placed at equal distances, i. E. We shall assume that x. - i, i = l, ... , n, and that x„ = 0.
We define a difference operator A by A f(x) = f(x+l) - f(x) and power A^ of A by AJ(f(x)) = A(AJ-^f(x+l) -AJ-^f(x)), j=2, 3, ... .
We assume that Assumption 2. JA '^f(x)|^ca, and we shall obt...ain a minimax linear predictor under this assumption. For simplicity we put a = 1 as before.
Let f(0) = > ai, Yj^ be a linear predictor. Then E(f(o) - f(o))'^ = ( y- a^, f(k)- f(o))" +y and f(k) can be expressed as -11- f(k) = f(0) + j^c^d^ + ^c^d^ + ... + j^c^^d^ ^-^-1 h+1 (2. 1) \' where d. = A f(0), ,c. Is the binomial coefficient with the definition that, c. =Oifl
What to read after Minimax Linear Predictor Under Lipschitz Type Conditions for the Regression Fun?
You can find similar books in the "Read Also" column, or choose other free books by Kei Takeuchi to read online
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