In statistics, the delta method is a method of deriving the asymptotic distribution of a random variable. It is applicable when the random variable being considered can be defined as a differentiable function of a random variable which is asymptotically Gaussian .

Delta Method在统计里是求渐进分布asymptotic distribution的，是一种转化的方法，用a随机变量转化为b随机变量，可用于求样本均值、样本矩函数等。 如果 且g(Xn)在θ处连续可导，则

The Delta Method gives a technique for doing this and is based on using a Taylor series approxi-mation. Tr(x) = (x a)k: k!

insight: the delta method is just a Taylor expansion, so if 0( ) = 0, we may consider higher-order terms. Consider : d. R ! R for simplicity (in notation) Let rn ! 1 be deterministic and assume rn(Tn be twice continuously di erentiable at . Then. ) d! T, and let. ( )) d! T>r2 ( )T. ). For. d! bn d! W 2.

2021年9月21日 · 本文首先介绍了Delta-Sigma DAC的原理和工作方式，阐述了其设计基础，包括Delta-Sigma调制技术、ADC与DAC的区别，以及理论与实际设计之间的挑战。 接着，本文深入探讨了硬件设计要点、软件优化策略、测试与验证 方法 ，...

Delta Method: Approximating Moments Delta Method: Approximating Distributions Consistency: A Stronger Definition Definition: qˆ n is a uniformly consistent estimator of q(θ), if for every E> 0, lim n→∞ sup[P θ(|q n(X 1,..., X n) − q(θ)| >E)] = 0. θ∈Θ. Example: Consider the sample mean qˆ. n = X. n. for which E [X. n | θ] = θ ...

The Delta Method (DM) states that we can approximate the asymptotic behaviour of functions over a random variable, if the random variable is itself asymptotically normal. In practice, this theorem tells us that even if we do not know the expected value and variance of the function \(g(X)\) we can still approximate it reasonably.

把近似 [T(\hat{F}_n) - T(F)]/ \hat{\text{se}} \approx \mathcal{N}(0,1) 称为 非参数delta方法 。 由正态近似，，一个大样本置信区间为 T(\hat{F}_n) \pm z_{\alpha /2}\hat{\text{se}} ，其中

The Delta method is a theorem that can be used to derive the distribution of a function of an asymptotically normal variable. It is often used to derive standard errors and confidence intervals for functions of parameters whose estimators are asymptotically normal.

2020年8月29日 · Multivariate Delta Method. We have a sequence of random vectors $\mathbf{T}1, \dots, \mathbf{T}_n$, which we can also denote as $(\mathbf{T}_n){n\ge 1}$, and this sequence satisfies \[\sqrt{n}(\mathbf{T}_n-\vec{\theta}) \xrightarrow[n \to \infty]{(\mathbb{d})} \mathbf{T}\] for some $\vec{\theta} \in \mathbb{R}^d$ Then if we have some function