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"Estimation theory"
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Greater estimations
Examples and colorful illustrations introduce beginning readers to the skill of making good estimations with regard to quantity, length, and volume.
Book
Dynamics of the Box-Ball System with Random Initial Conditions via Pitman’s Transformation
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In
this article, we study the BBS when started from a random two-sided infinite particle configuration. For such a model, Ferrari et al.
recently showed the invariance in distribution of Bernoulli product measures with density strictly less than
eBook
Great estimations
Uses a giant jar of jellybeans to introduce the concept of estimation to young readers and challenges them to use the lessons provided to make good estimations of their very own.
Book
Introduction to empirical processes and semiparametric inference
The goal of this book is to introduce statisticians, and other researchers with a background in mathematical statistics, to empirical processes and semiparametric inference.These powerful research techniques are surpr- ingly useful for studying large sample properties of statistical estimates from realistically complex models as well as for.
eBook
SPARSE MODELS AND METHODS FOR OPTIMAL INSTRUMENTS WITH AN APPLICATION TO EMINENT DOMAIN
We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic \"beta-min\" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso-based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 𝓁₁-penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.
Journal Article
Electrochemical Impedance Spectroscopy: A New Chapter in the Fast and Accurate Estimation of the State of Health for Lithium-Ion Batteries
Lithium-ion batteries stand out from other clean energy sources because of their high energy density and small size. With the increasing application scope and scale of lithium-ion batteries, real-time and accurate monitoring of its state of health plays an important role in ensuring the healthy and stable operation of an energy storage system. Due to the interaction of various aging reactions in the aging process of lithium-ion batteries, the capacity attenuation shows no regularity. However, the traditional monitoring method is mainly based on voltage and current, which cannot reflect the internal mechanism, so the accuracy is greatly reduced. Recently, with the development of electrochemical impedance spectroscopy, it has been possible to estimate the state of health quickly and accurately online. Electrochemical impedance spectroscopy can measure battery impedance in a wide frequency range, so it can reflect the internal aging state of lithium-ion batteries. In this paper, the latest impedance spectroscopy measurement technology and electrochemical impedance spectroscopy based on lithium-ion battery health state estimation technology are summarized, along with the advantages and disadvantages of the summary and prospects. This fills the gap in this aspect and is conducive to the further development of this technology.
Journal Article
A Constrained ℓ1 Minimization Approach to Sparse Precision Matrix Estimation
This article proposes a constrained ℓ
1
minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p-variate random variables. The resulting estimator is shown to have a number of desirable properties. In particular, the rate of convergence between the estimator and the true s-sparse precision matrix under the spectral norm is
when the population distribution has either exponential-type tails or polynomial-type tails. We present convergence rates under the elementwise ℓ
∞
norm and Frobenius norm. In addition, we consider graphical model selection. The procedure is easily implemented by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods.
Journal Article