29
is with probability 1 as n → ∞, Fn(⅛) → F(t) and Gn(t) → G(t) for all t ∈ [o, ∞). ”
Theorem 3. “The copula-graphic estimator is a maximum likelihood estimator. ”
Theorem 4. “For the independence copula C(x,y)=xy, when t ≤ tn, the largest
observed time, the copula-graphic estimates of marginal survival functions are exactly
the Kaplan-Meier estimates. ”
Note: Zheng and Klein (1995) was written before Zheng and Klein (1994), al-
though it was published later than Zheng and Klein (1994).
Zheng and Klein (1994)
Zheng and Klein (1994) apply the copula method to construct an estimator of the
marginal survival function based on dependent competing risk data.
In a competing risks framework, we define X, Y, T and δ same as in Zheng and
Klein (1995). Zheng and Klein (1994) show that the marginal survival function can
be estimated:
⅜)
⅜)
n
* 5√≥ *] +∑(1 -tχ>t∖χ>t^γ = ti∖ *
2=1 ti<t
(2.27)
n
< E/ [f≈ ≥ t∖ + [y > t∖γ
i=l ti<t
> ti,X = ti] .
(2.28)
Here, both S(t) and R(f) are self-consistent estimators. When X and Y are de-
pendent with a known copula C(u, υ), we have:
More intriguing information
1. Individual tradable permit market and traffic congestion: An experimental study2. Review of “The Hesitant Hand: Taming Self-Interest in the History of Economic Ideas”
3. Naïve Bayes vs. Decision Trees vs. Neural Networks in the Classification of Training Web Pages
4. Determinants of U.S. Textile and Apparel Import Trade
5. CURRENT CHALLENGES FOR AGRICULTURAL POLICY
6. The name is absent
7. Asymmetric transfer of the dynamic motion aftereffect between first- and second-order cues and among different second-order cues
8. Gender stereotyping and wage discrimination among Italian graduates
9. Tissue Tracking Imaging for Identifying the Origin of Idiopathic Ventricular Arrhythmias: A New Role of Cardiac Ultrasound in Electrophysiology
10. Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate