On Adaptive Estimation

Real Data Testing of Model Parameter Estimation Methods for Macroscopic Traffic Flow Model

Multivariate zero-inflated Bell distribution and its inference and applications

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

Journal Article A note on efficient estimation from case-control data Get access DENIEL RABINOWITZ DENIEL RABINOWITZ Department of Statistics, Columbia University, New YorkNew York 10027, U.S.A. e-mail: dan@stat.columbia.edu Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 84, Issue 2, June 1997, Pages 486–488, https://doi.org/10.1093/biomet/84.2.486 Published: 01 June 1997 Article history Received: 01 June 1994 Revision received: 01 September 1996 Published: 01 June 1997

In this article, we introduce adaptive estimators for parameters of the (GPD) Generalized Pareto Distribution under censored data via the KIB-estimator. The KIB-estimator is based on the Maximum Likelihood Estimates (MLE) by the exceedances over the threshold t under random censoring which was developed by [1]. Hence, it was proved that the KIB-estimator is Maximum Likelihood (ML) estimator with the uncensored case. We use the standardized MLE based on the exceedances on the uncensored situation which converge to a centered bivariate normal distribution. Whose found by [2] to standardized our adaptive KIB estimator of the GPD parameters under random censorship. As an application, we establish the asymptotic normality of an estimator of the excess-of- loss reinsurance premium for heavy-tailed distribution, through the adapted KIB estimator of GPD under censored data.

A multi-rate hierarchical fault-tolerant adaptive model predictive control framework: Theory and design for quadrotors

The paper presents a review of methods for adaptive estimation of signals with unknown structures and parameters of models that determine the properties of both the signal itself and the errors of its measurement. The main approaches to solution of adaptive estimation problems are considered. One of them is aimed at designing algorithms with a learning sample, and the other one relies on the Bayesian approach and aims at solving the joint problem of signal estimation and identification of models used to describe the signal and measurement errors in real time. An adaptive estimation algorithm based on the Bayesian approach is described in detail. The problems in which the proposed algorithm is used are discussed. Its effectiveness is illustrated by the example of gravity anomaly estimation on a moving vehicle under model uncertainty of the signal and measurement errors.

This paper investigates the statistical detection of data hidden within DCT coefficients of JPEG images using a Laplacian distribution model. The main contributions is twofold. First, this paper proposes to model the DCT coefficients using a Laplacian distribution but challenges the usual assumption that among a sub-band all the coefficients follow are independent and identically distributed (i.i.d). In this paper it is assumed that the distribution parameters change from DCT coefficient to DCT coefficient. Second this paper applies this model to design a statistical test, based on hypothesis testing theory, which aims at detecting data hidden within DCT coefficient with the JSteg algorithm. The proposed optimal detector carefully takes into account the distribution parameters as nuisance parameters. Numerical results on simulated data as well as on numerical images database show the relevance of the proposed model and the good performance of the ensuing test.

ABSTRACTThis paper describes a method of extracting time-varyingfeatures that is effective for speech signals with high funda-mental frequencies. The proposed method adopts a speechproduction model that consists of a Time-Varying Auto-Regressive (TVAR) process for an articulatory filter and aHidden Markov Model (HMM) for an excitation source.The model represents waveform amplitude variations bytime-varying gain of the excitation source. The proposed algo-rithm is given by extending a Viterbi algorithm so that theproposed algorithm can adaptively estimate TVAR coeffi-cients and time-varying gain with decoding the state tran-sition of the excitation source HMM. We applied the pro-posed method to extracting time-varying features from bothsynthetic and natural speech, and confirmed its feasibility.1. INTRODUCTIONThe conventional Linear Prediction (LP) method is widelyused to analyze speech signals[1]. However, several prob-lems still remain to be solved[2]. One such problem is thatlocal peaks of the LP spectral estimate are strongly biasedtoward the harmonics, especially for high-pitched speech.Several methods have been designed to overcome this prob-lem [3, 4, 5, 6]. The authors have previously indicated thatan analysis method based on a speech production modelconsisting of an Auto-Regressive (AR) process for an artic-ulatoryfilterand a HiddenMarkov Model(HMM)for an ex-citationsource is robustforhighfundamental frequencies[7,8]. However, this method is not suitable for analyzing con-tinuous speech for the following reasons. First, the AR co-efficients and HMM are iteratively estimated within everyanalysis frame, so a large number of operations is needed.Second, the analysis frame size needs to be large in orderto guarantee stable learning of the excitation source HMM.Third, the model parameters are assumed to be constantwithin the analysis frame, so the resulting parameters areaveraged within such a long analysis frame. This makesit difficult to extract the dynamic characteristics of speechwhen features change rapidly, like in a singing voice.In this paper, we extend the speech production model in[7] so that the proposed model can represent time-varyingfeatures of continuous speech. We also describe an anal-ysis method that adaptively estimates Time-Varying Auto-Regressive (TVAR) coefficients and gain based on the newmodel. The proposed method can substantially reduce thenumber of operations by applying the learned HMM andcan also extract dynamic characteristics of continuous speechby estimating those time-varying features adaptively.2. SPEECH PRODUCTION MODEL BASED ONTVAR-HMMThe proposed method adopts a speech production modelthat consists of a TVAR process for an articulatory filterand an HMM for an excitation source. The nodes of theHMM are concatenated in a ring state in order to representperiodicity of voiced sounds. We have previously shownthat LP analysis incorporating the excitation source HMMcan precisely estimate the characteristics of both vocal tractand excitation source from high-pitched speech signal[7, 8].The proposed model represents the time-varying features ofnot only the vocal tract but also the waveform amplitude bymultiplying an excitation source emitted from the HMM bya time-varying gain.

We consider the problem of inference on one of the two parameters of a probability distribution when we have some prior information on a nuisance parameter. When a prior probability distribution on this nuisance parameter is given, the marginal distribution is the classical tool to account for it. If the prior distribution is not given, but we have partial knowledge such as a fixed number of moments, we can use the maximum entropy principle to assign a prior law and thus go back to the previous case. In this work, we consider the case where we only know the median of the prior and propose a new tool for this case. This new inference tool looks like a marginal distribution. It is obtained by first remarking that the marginal distribution can be considered as the mean value of the original distribution with respect to the prior probability law of the nuisance parameter, and then, by using the median in place of the mean.

Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Generalized Residuals

This article addresses the problem of estimating a covariance matrix in a multivariate skew-normal distribution relative to two different losses. The estimation problem can be reduced to that of a scale matrix of a noncentral Wishart distribution. The noncentrality parameter matrix, which is a nuisance parameter, brings about non optimality of the best triangular invariant estimators which are minimax under normality. Some improving techniques under normality are proven to remain robust under the multivariate skew-normal distribution.

In Bayesian decision theory, stochastic simulation techniques have been widely used by decision makers. The Markov chain Monte Carlo method (MCMC) plays a key role in stochastic simulation within the framework of Bayesian statistics. The notion of "slice sampling", or employing auxiliary variables in sampling, has been recently suggested in the literature for improving the efficiency of the traditional MCMC methods. In the existing literature, the one dimensional slice sampler has been extensively studied, yet the literature on the multidimensional case is sparse. In this study, we utilize multiple auxiliary variables in our sampling algorithms for multivariate normal distributions, which adapt better to the local properties of the target probability distributions. We show that these methods are flexible enough to allow for truncation to rectangular regions and/or the exclusion of any n dimensional hyper-quadrant. We compare these algorithms for both efficiency and accuracy via simulation experiments. Our results show that our new sampling techniques are accurate and more effective than the traditional single auxiliary variable slice sampler, especially for truncated multivariate distributions. Further, we extend our methods to general multivariate distributions including multivariate student t distributions, multivariate elliptical distributions, multivariate skew normal distributions, multivariate skew t distributions and a general class of multivariate skew elliptical distributions. We also discuss and outline some applications of our algorithms in the real business world, especially in the production and operations management and the finance areas. With regard to production and operations management, we find that the proposed multivariate normal slice sampler can be implemented in a stochastic optimization process for finding the optimal fulfillment rate of an assembly system. This system consists of n components, from which m products are assembled via a periodic review control policy. In finance area, we show that multivariate slice samplers can be used to update model parameters and predict future asset returns in a higher moments Bayesian portfolio optimization model, which is based on a general class of multivariate skew t distributions. The application of a multivariate slice sampler improves the model's ability of handling large data sets and saves computation time for deriving complicated posterior probability distributions.

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. The structure of these problems allows efficient optimization strategies—a well-known example is variable projection, where nonlinear least-squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood and maximum a posteriori likelihood problems with nuisance parameters, such as variance or degrees of freedom (d.o.f.). As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, d.o.f. parameter estimation in the context of robust inverse problems, and automatic calibration. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large-scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.

We consider causal inference in randomized survival studies with right censored outcomes and all-or-nothing compliance, using semiparametric transformation models to estimate the distribution of survival times in treatment and control groups, conditional on covariates and latent compliance type. Estimands depending on these distributions, for example, the complier average causal effect (CACE), the complier effect on survival beyond time t, and the complier quantile effect are then considered. Maximum likelihood is used to estimate the parameters of the transformation models, using a specially designed expectation-maximization (EM) algorithm to overcome the computational difficulties created by the mixture structure of the problem and the infinite dimensional parameter in the transformation models. The estimators are shown to be consistent, asymptotically normal, and semiparametrically efficient. Inferential procedures for the causal parameters are developed. A simulation study is conducted to evaluate the finite sample performance of the estimated causal parameters. We also apply our methodology to a randomized study conducted by the Health Insurance Plan of Greater New York to assess the reduction in breast cancer mortality due to screening.