Estimating age-specific survival rates from bird-band returns when the reporting rate is constant
报告率恒定时利用鸟环回收估计年龄别存活率AI 解读 ↓
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报告率恒定时利用鸟环回收估计年龄别存活率AI 解读 ↓
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A probability model consisting of a product of multinomial distributions is derived for a bird-banding experiment in which a new batch of nestlings is banded and released at the beginning of each year and the bands from the dead birds are returned by observers in subsequent years. The annual reporting probability is assumed to be the same for all birds and to remain constant from year to year, while the probability of survival is assumed to depend on the age of the bird rather than on the calendar year. By considering the probability distribution of band returns conditional on the total numbers of returns from each release, explicit maximum likelihood estimates of the survival probabilities are obtained together with their asymptotic variance-covariance matrix. A goodness-of-fit test of the model is outlined and the theory is demonstrated by a worked example.
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with every possible prior - and uniformly expand it by a Kullback-Leibler radius to accommodate likelihood misspecification. We show that optimal decisions under this framework are equivalent to minimax decisions with an exponentially tilted loss…
RBF 核高斯过程最大似然估计的精确渐近理论
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…
理性疏忽—加性随机效用模型的估计
This paper develops likelihood-based estimation for parametric rational inattention--additive random utility models. We establish consistency and asymptotic normality of the exact maximum likelihood estimator and provide conditions under which the simulated estimator shares its asymptotic distribution. To implement estimation, we develop Newton--BA, a KKT-guided hybrid of Newton--Raphson and Blahut--Arimoto (BA). The algorithm accommodates both interior and boundary…
面板信息矩阵检验
The Information Matrix (IM) test is a natural specification check for likelihood-based models, yet cross-sectional implementations are often badly sized, confound neglected heterogeneity with distributional misspecification, and require third derivatives. We develop the panel information matrix (PIM) test for models with fixed effects. Explicit fixed effects isolate functional-form misspecification from time-invariant unobserved heterogeneity. Although the profile maximum…
受限因变量模型中可扩展的似然推断
Limited dependent variable models are central to empirical economics, but likelihood-based inference is infeasible when likelihoods involve high-dimensional integration over latent variables. This paper proposes Stochastically Estimated Gradient Ascent (SEGA), a scalable estimation approach for limited dependent variable models. Using Fisher's identity, SEGA replaces the intractable likelihood score with an unbiased augmented data score evaluated at a single conditional draw…
在线实验的设计驱动推断:证据收集、检验与估计的联合最优性
Online multifactorial experiments requires early stopping for practically negligible effects while controlling false stopping under continuous monitoring and retaining precise treatment-effect estimation. We develop a design-driven framework that chooses allocation and the evidence rule jointly, treating allocation as evidence collection and testing and estimation as complementary uses of the same evidence. For multifactor experiments with nuisance block effects and…