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量子层析入门AI 解读

Summary We describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on identical quantum systems. The state can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We present consistency results for pattern function projection estimators and for sieve maximum likelihood…

计数过程的 Cox 回归模型：大样本研究AI 解读

The Cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life-time distribution of an individual. In this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process. This permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring…

删失与随机积分AI 解读

A.2. On constructing a stochastic basis A.3.Proof of Theorem 2.3.4.• A.4. Proof of Lemma 3.2.1 . . . .A.5. Asymptotic normality of an estimator of mean lifetime.A.6.Proof of a theorem of Daniels.P.EFERENCES .

替换试验与乘积极限估计量AI 解读

Let $X_1, X_2, \cdots$ be a sequence of i.i.d. nonnegative rv's with nondegenerate df $F$. Define $\tilde{N}(t) = {\tt\#}\{j: X_1 + \cdots + X_j \leq t\}$. In "testing with replacement" (also known as "renewal testing") $n$ independent copies of $\tilde{N}$ are observed each over the time interval $\lbrack 0, \tau \rbrack$ and we are interested in nonparametric estimation of $F$ based on these observations. We prove consistency of the product limit estimator as $n\rightarrow\infty$…