Using a four-month panel of revised Current Population Survey data from September-December 1993, we extend the class of semiparametric hazard models of the type first studied by Prentice and Gloeckler (1978), and brought to the attention of economists by Meyer (1988, 1990), to incorporate inequality restrictions on the shape of the hazard. This extension enables us to test hypotheses regarding the shape of the hazard implied by search theory using duration data alone. These…
Using a four-month panel of revised Current Population Survey data from September-December 1993, we extend the class of semiparametric hazard models of the type first studied by Prentice and Gloeckler (1978), and brought to the attention of economists by Meyer (1988, 1990), to incorporate inequality restrictions on the shape of the hazard. This extension enables us to test hypotheses regarding the shape of the hazard implied by search theory using duration data alone. These…
We study maximum penalized likelihood density estimation using the first roughness penalty functional of Good. We prove a simple pointwise comparison result with a kernel estimator based on the two-sided exponential kernel. This leads to $L^1$ convergence results similar to those for kernel estimators. We also prove Hellinger distance bounds for the roughness penalized estimator.
Given a mixture of binomial distributions, how do we estimate the unknown mixing distribution? We build on earlier work of Lindsay and further elucidate the geometry underlying this question, exploring the approximating role played by cyclic polytopes. Convergence of a resulting maximum likelihood fitting algorithm is proved and numerical examples given; problems over the lack of identifiability of the mixing distribution in part disappear.
Previous time series applications of qualitative response models have ignored features of the data, such as conditional heteroscedasticity, that are routinely addressed in time series econometrics of financial data. This article addresses this issue by adding Markov-switching heteroscedasticity to a dynamic ordered probit model of discrete changes in the bank prime lending rate and estimating via the Gibbs sampler. The dynamic ordered probit model of Eichengreen, Watson, and…
T Banerjee·刊期 1999-09-01 · 卷 86（3）·Biometrika已编入正刊
杂录：用于多项聚类数据的 Morel–Nagaraj 有限混合分布扩展AI 解读
Morel & Nagaraj (1993) proposed a finite mixture distribution for modelling multinomial extra variation when the extra variation is believed to be caused by clumped multinomial sampling with one clumping. We propose an extension of the model to incorporate possible multiple clumping. We show that the extended finite mixture distribution is a multinomial mixing distribution with different mixing coefficients. We derive maximum likelihood estimating equations and an asymptotic…
M Pourahmadi·刊期 1999-09-01 · 卷 86（3）·Biometrika已编入正刊
纵向数据的均值—协方差联合模型：无约束参数化AI 解读
We provide unconstrained parameterisation for and model a covariance using covariates. The Cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix. The entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors. An…
Summary Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. We demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model that is closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the…
Nonparametric maximum likelihood (NPML) is used to estimate regression parameters in a proportional hazards regression model with missing covariates. The NPML estimator is shown to be consistent and asymptotically normally distributed under some conditions. EM type algorithms are applied to solve the maximization problem. Variance estimates of the regression parameters are obtained by a profile likelihood approach that uses EM-aided numerical differentiation. Simulation…
Hormones serve as regulating signals for many biological processes. In recent years, it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern, in addition to the absolute concentration level, is important in regulating biological processes. Consequently, it is necessary to characterize the latent secretion patterns from measurements of concentration levels. The characterization is complicated by the presence of a…
Hormones serve as regulating signals for many biological processes. In recent years, it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern, in addition to the absolute concentration level, is important in regulating biological processes. Consequently, it is necessary to characterize the latent secretion patterns from measurements of concentration levels. The characterization is complicated by the presence of a…
The breakdown point behavior of $M$-estimators in linear models with fixed designs, arising from planned experiments or qualitative factors, is characterized. Particularly, this behavior at fixed designs is quite different from that at designs which can be corrupted by outliers, the situation prevailing in the literature. For fixed designs, the breakdown points of robust $M$-estimators (those with bounded derivative of the score function), depend on the design and the…
Strong consistency for maximum quasi-likelihood estimators of regression parameters in generalized linear regression models is studied. Results parallel to the elegant work of Lai, Robbins and Wei and Lai and Wei on least squares estimation under both fixed and adaptive designs are obtained. Let $y_1,\dots, y_n$ and $x_1,\dots, x_n$ be the observed responses and their corresponding design points ($p \times 1$ vectors), respectively. For fixed designs, it is shown that if the…
This paper deals with a scalar I ( d ) process { y j }, where the integration order d is any real number. Under this setting, we first explore asymptotic properties of various statistics associated with { y j }, assuming that d is known and is greater than or equal to ½. Note that { y j } becomes stationary when d < ½, whose case is not our concern here. It turns out that the case of d = ½ needs a separate treatment from d > ½. We then consider, under the normality…
Summary Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate…
We put forward a state space model where the unobservable state variable can be any Gaussian stochastic process. We discuss both maximum likelihood estimation and Bayesian inference for this generalised model. The methodology developed in this paper is particularly important for the class of long memory plus noise models. Armed with the simulation smoother introduced in this paper, we can estimate a class of non-Gaussian measurement time series models with long memory in the…
The two-sample Student's t-interval can be derived by parametric bootstrap coverage calibration of the naive, plug-in interval that fails to account for the estimation of the common variance parameter. The same technique results in an essentially exact confidence interval for the ratio of two means based on independent samples from gamma distributions. The gamma problem is more difficult computationally because an exact pivot is not available. However, the computational…
We consider hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form $\psi(\alpha + \mathbf{x}^T \mathbf{\beta})$ are mixed. Here $\psi(\cdot)$ is the inverse link function. Suppose the true response $y$ follows an exponential family regression model with mean function belonging to a class of smooth functions of the form $\psi(h(\mathbf{x}))$ where $h(\cdot)\in W_{2; K_0}^{\infty}$ (a Sobolev…
We are concerned here with establishing the consistency and asymptotic normality for the maximum likelihood estimator of a “merit vector” $(u_0,\dots,u_t)$, representing the merits of $t +1$ teams (players, treatments, objects), under the Bradley–Terry model, as $t \to \infty$. This situation contrasts with the well-known Neyman–Scott problem under which the number of parameters grows with $t$ (the amount of sampling), and for which the maximum likelihood estimator fails…
This paper proposes and implements simulated maximum likelihood estimation of bivariate count models with unrestricted correlation pattern of unobserved heterogeneity. The implementation incorporates both antithetic acceleration and adjustment for first-order simulation bias. Both the Monte Carlo simulation evidence and an application to health utilization data confirm that the method is reliable and feasible in data analysis.
We consider the problems of image segmentation and classification, and image restoration when the true image is made up of a small number of (unordered) colors. Our emphasis is on both performance and speed; speed has become increasingly important for analyzing large images and multispectral images with many bands, processing large image databases, real-time or near realtime image analysis, and the online analysis of video. Bayesian image analysis provides an elegant…
1 Introduction.- 2 Models, Data Generating Processes, and Estimators.- 3 Basic Structure of the Classical Consistency Proof.- 4 Further Comments on Consistency Proofs.- 5 Uniform Laws of Large Numbers.- 6 Approximation Concepts and Limit Theorems.- 7 Consistency: Catalogues of Assumptions.- 8 Basic Structure of the Asymptotic Normality Proof.- 9 Asymptotic Normality under Nonstandard Conditions.- 10 Central Limit Theorems.- 11 Asymptotic Normality: Catalogues of…
We consider the problems of image segmentation and classification, and image restoration when the true image is made up of a small number of (unordered) colors. Our emphasis is on both performance and speed; speed has become increasingly important for analyzing large images and multispectral images with many bands, processing large image databases, real-time or near realtime image analysis, and the online analysis of video. Bayesian image analysis provides an elegant…
Some sufficient conditions to establish the rate of convergence of certain $M$-estimators in a Gaussian white noise model are presented. They are applied to some concrete problems, including jump point estimation and nonparametric maximum likelihood estimation, for the regression function. The results are shown by means of a maximal inequality for continuous martingales and some techniques developed recently in the context of empirical processes.
We study maximum penalized likelihood density estimation using the first roughness penalty functional of Good. We prove a simple pointwise comparison result with a kernel estimator based on the two-sided exponential kernel. This leads to L1 convergence results similar to those for kernel estimators. We also prove Hellinger distance bounds for the roughness penalized estimator.
Breakdown points and variation exponents of robust M-estimators in linear models
The breakdown point behavior of M-estimators in linear models with fixed designs, arising from planned experiments or qualitative factors, is characterized. Particularly, this behavior at fixed designs is quite different from that at designs which can be corrupted by outliers, the situation prevailing in the literature. For fixed designs, the breakdown points of robust M-estimators (those with bounded derivative of the score function), depend on the design and the…
Strong consistency for maximum quasi-likelihood estimators of regression parameters in generalized linear regression models is studied. Results parallel to the elegant work of Lai, Robbins and Wei and Lai and Wei on least squares estimation under both fixed and adaptive designs are obtained. Let y1,…,yn and x1,…,xn be the observed responses and their corresponding design points (p×1 vectors), respectively. For fixed designs, it is shown that if the…
We consider hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form ψ(α+xTβ) are mixed. Here ψ(⋅) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form ψ(h(x)) where h(⋅)∈W2;K0∞ (a Sobolev…
We are concerned here with establishing the consistency and asymptotic normality for the maximum likelihood estimator of a “merit vector” (u0,…,ut), representing the merits of t+1 teams (players, treatments, objects), under the Bradley–Terry model, as t→∞. This situation contrasts with the well-known Neyman–Scott problem under which the number of parameters grows with t (the amount of sampling), and for which the maximum likelihood estimator fails…
A maximal inequality for continuous martingales and M-estimation in a Gaussian white noise model
Some sufficient conditions to establish the rate of convergence of certain M-estimators in a Gaussian white noise model are presented. They are applied to some concrete problems, including jump point estimation and nonparametric maximum likelihood estimation, for the regression function. The results are shown by means of a maximal inequality for continuous martingales and some techniques developed recently in the context of empirical processes.