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Books on the topic 'Asymptotic estimate'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Ioannidis, Evangelos. On the asymptotic behaviour of the Capon estimator. Verlag Shaker, 1993.

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2

Ferguson, Heather. Asymptotic properties of a conditional maximum likelihood estimator. [s.n.], 1989.

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3

Peter, Paule, and SpringerLink (Online service), eds. The Concrete Tetrahedron: Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates. Springer-Verlag/Wien, 2011.

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4

Birman, M., ed. Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations. American Mathematical Society, 1991. http://dx.doi.org/10.1090/advsov/007.

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5

Ruzhansky, Michael. Evolution Equations of Hyperbolic and Schrödinger Type: Asymptotics, Estimates and Nonlinearities. Springer Basel, 2012.

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6

Johansen, Søren. The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model. European University Institute, Department of Economics, 2001.

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7

Baldwin, P. Asymptotic estimates of the eigenvalues of a sixth-order boundary-value problem obtained by using global phase-integralmethods. Royal Society of London, 1987.

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8

Ferraty, Frédéric, and Philippe Vieu. Kernel Regression Estimation for Functional Data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.4.

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This article provides an overview of recent nonparametric and semiparametric advances in kernel regression estimation for functional data. In particular, it considers the various statistical techniques based on kernel smoothing ideas that have recently been developed for functional regression estimation problems. The article first examines nonparametric functional regression modelling before discussing three popular functional regression estimates constructed by means of kernel ideas, namely: the Nadaraya-Watson convolution kernel estimate, the kNN functional estimate, and the local linear fun

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9

Cheng, Russell. Standard Asymptotic Theory. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0003.

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This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter es

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10

Asymptotic Estimates and Entire Functions. Dover Publications, Incorporated, 2020.

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11

Sogge, Christopher D. Improved spectral asymptotics and periodic geodesics. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0005.

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This chapter proves an improved Weyl formula under the assumption that the set of periodic geodesics for (M,g) has measure zero. It then shows trace estimates associated with shrinking spectral bands, details and proves a lemma, and gives a related generalization of the Weyl formula from Chapter 3 that involves pseudodifferential operators. The chapter then proves its main result by using a version of the Duistermaat-Guillemin theorem, which allows the use of the Hadamard parametrix and the arguments from Chapter 3. To conclude, the chapter shows that one can improve the sup-norm estimates fro

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12

Ferguson, Heather Gail. Asymptotic properties of a conditional maximun likelihood estimator. 1989.

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13

Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities. Now Publishers, 2014.

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14

Wang, Junping. Asymptotic expansions and L [infinity symbol]-error estimates for mixed finite element methods for second order elliptic problems. 1988.

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15

Kauers, Manuel, and Peter Paule. The Concrete Tetrahedron: Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates. Springer, 2011.

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16

Ruzhansky, Michael, Jens Wirth, and Mitsuru Sugimoto. Evolution Equations of Hyperbolic and Schrödinger Type: Asymptotics, Estimates and Nonlinearities. Springer, 2012.

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17

Ruzhansky, Michael, Jens Wirth, and Mitsuru Sugimoto. Evolution Equations of Hyperbolic and Schrödinger Type: Asymptotics, Estimates and Nonlinearities. Birkhäuser, 2014.

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18

Edmunds, D. E., та W. D. Evans. Global and Asymptotic Estimates for the Eigenvalues of −Δ‎ + q when q Is Real. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0011.

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This chapter is devoted to the study of the Schrödinger operator −Δ‎ + q with q real, and, in particular, the distribution of its eigenvalues. A general result is established on an open subset Ω‎ of Rn using the Max–Min Principle and covering families of congruent cubes for the Dirichlet problem and a Whitney covering for the Neumann problem. The Cwikel–Lieb–Rosenbljum inequality is proved for q in Ln/2(Rn).

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19

Cheng, Russell. Infinite Likelihood. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0008.

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This chapter examines methods that overcome a difficulty with infinite likelihoods. In shifted threshold distributions where the PDF has the form f(y) ∼ k(b,c)(y−a)c−1, if y tends to the threshold parameter a, then the log-likelihood tends to infinity if c < 1 and a also tends to y(1) the smallest observation. The maximum likelihood (ML) method fails in this case, yielding parameter estimates that are not consistent. A method is described overcoming this problem, called the maximum product of spacings method. This yields parameter estimates with the same consistency and asymptotic normality

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20

Birman, M. Sh. Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations (Advances in Soviet Mathematics, Vol 7). American Mathematical Society, 1991.

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21

Mas, André, and Besnik Pumo. Linear Processes for Functional Data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.3.

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This article provides an overview of the basic theory and applications of linear processes for functional data, with particular emphasis on results published from 2000 to 2008. It first considers centered processes with values in a Hilbert space of functions before proposing some statistical models that mimic or adapt the scalar or finite-dimensional approaches for time series. It then discusses general linear processes, focusing on the invertibility and convergence of the estimated moments and a general method for proving asymptotic results for linear processes. It also describes autoregressi

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22

Cheng, Russell. The Skew Normal Distribution. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0012.

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This chapter considers the univariate skew-normal distribution, a generalization of the normal that includes the normal as a special case. The most natural parametrization is non-standard. This is because the Fisher information matrix is then singular at the true parameter value when the true model is the normal special case. The log-likelihood is then particularly flat in a certain coordinate direction. Standard theory cannot then be used to calculate the asymptotic distribution of all the parameter estimates. This problem can be handled using an alternative parametrization. There is another

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23

Cheng, Russell. Bootstrap Analysis. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0004.

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Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit

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24

Cheng, Russell. Embedded Distributions: Two Numerical Examples. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0007.

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This chapter illustrates use of (i) the score statistic and (ii) a goodness-of-fit statistic to test if an embedded model provides an adequate fit, in the latter case with critical values calculated by bootstrapping. Also illustrated is (iii) calculation of parameter confidence intervals and CDF confidence bands using both asymptotic theory and bootstrapping, and (iv) use of profile log-likelihood plots to display the form of the maximized log-likelihood and scatterplots for checking convergence to normality of estimated parameter distributions. Two different data sets are analysed. In the fir

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25

Probasco, John C. Paraneoplastic Neurological Disorders. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780199937837.003.0090.

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Paraneoplastic neurological disorders (PNDs) are estimated to affect approximately 0.01% of all patients with cancer. The majority of PNDs are thought to be the byproduct of immune-mediated processes directed against tumor-related antigens, processes which are sometimes effective against a systemic cancer. The inciting cancer is often asymptomatic or occult, with patients presenting to the neurologist with a variety of neurological symptoms and signs depending on the area(s) of the central, peripheral, and autonomic nervous system involved. The diagnosis of a PND is reserved for patients with

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26

Chakera, Aron, William G. Herrington, and Christopher A. O’Callaghan. Screening for kidney disease. Edited by Patrick Davey and David Sprigings. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199568741.003.0353.

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Renal disease is common and, with routine reporting of estimated glomerular filtration rates, impairment of renal function is increasingly being recognized. As renal impairment is usually asymptomatic until very advanced, chronic kidney disease (CKD) guidelines have been developed to improve the identification and screening of at-risk populations. Target groups include patients with vascular risk factors (e.g. diabetes mellitus and hypertension); patients with certain multisystem diseases which can cause renal impairment; patients with urological conditions; patients on nephrotoxic medication;

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27

Zinn-Justin, Paul, and Jean-Bernard Zuber. Multivariate statistics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.28.

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This article considers some classical and more modern results obtained in random matrix theory (RMT) for applications in statistics. In the classic paradigm of parametric statistics, data are generated randomly according to a probability distribution indexed by parameters. From this data, which is by nature random, the properties of the deterministic (and unknown) parameters may be inferred. The ability to infer properties of the unknown Σ (the population covariance matrix) will depend on the quality of the estimator. The article first provides an overview of two spectral statistical technique

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28

Thomas, David F. M. Urinary tract infection in children. Edited by David F. M. Thomas. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780199659579.003.0114.

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Urinary tract infection (UTI) is one of the commonest conditions of childhood, affecting an estimated 10% of girls and 3% of boys in the first 16 years of life. Whereas asymptomatic bacteriuria and low-grade lower tract infection pose little or no risk of renal damage, pyelonephritis can cause severe systemic illness and poses a significant threat of long-term renal morbidity. The principal aim of investigation is to identify underlying abnormalities of the urinary tract, notably vesicoureteric reflux. Guidelines on investigation and management published by the National Institute of Clinical E

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29

Rafii, Michael S. Alzheimer’s Disease. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780199937837.003.0016.

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Alzheimer’s disease (AD) is the most common cause of dementia worldwide, and is characterized by a protracted asymptomatic phase estimated to begin approximately 15 to 20 years. Clinically, AD initially manifests itself by progressive memory impairment, specifically, a loss of episodic memory function characterized by impaired free recall that does not improve with cueing. This is followed by a gradual decline in other cognitive domains leading to functional dependency, which essentially defines the dementia phase of the illness and has been the cornerstone of diagnostic criteria. About 50% of

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30

Herrington, William G., Aron Chakera, and Christopher A. O’Callaghan. Diabetic renal disease. Edited by Patrick Davey and David Sprigings. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199568741.003.0164.

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Diabetic nephropathy is kidney damage occurring as a result of diabetes mellitus. Overt diabetic nephropathy is defined as proteinuria greater than 0.5 g/day. Diabetic nephropathy has a complicated pathogenesis including glomerular hypertension with hyperfiltration and advanced glycation end products. Poor glycaemic control is associated with progression to microalbuminuria and overt diabetic nephropathy. The lifetime risk is fairly equivalent for type 1 and type 2 diabetes mellitus. Early disease is usually asymptomatic. Hyperglycaemia causes an osmotic diuresis and, thus, diabetes can presen

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31

Rours, G. Ingrid J. G., and Margaret R. Hammerschlag. Chlamydia trachomatis. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780190604813.003.0018.

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The estimated incidence of Chlamydia trachomatis infection is over 100 million cases globally and almost 1 million in the United States. Infection with C. trachomatis tends to be asymptomatic and of long duration. If a pregnant woman has active infection during delivery, the infant may acquire the infection, which can result in conjunctivitis or pneumonia. The most effective method of controlling perinatal C. trachomatis infection is the screening and treatment of pregnant women. Identification of infected mothers offers the opportunity to provide treatment for their sexual partners to help pr

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32

Honegger, Jonathan R. Hepatitis C Virus. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780190604813.003.0005.

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An estimated 185 million individuals have been infected with hepatitis C virus (HCV) worldwide. Although often clinically silent for decades, chronic HCV infection predisposes to late-onset complications, including liver cirrhosis and hepatocellular carcinoma. Mother-to-child transmission (MTCT) of HCV affects approximately 5% of children born to viremic mothers and is the primary route of HCV infection in young children. While some vertically acquired HCV infections are resolved during the first years of life, many persist indefinitely. Chronically infected children tend to be asymptomatic an

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33

Izzedine, Hassan, and Victor Gueutin. Drug-induced chronic tubulointerstitial nephritis. Edited by Adrian Covic. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199592548.003.0087.

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The chronic form of drug-induced tubulointerstitial nephritis (CTIN) is an insidious disease and most probably represents the common final response pattern of the kidney to a variety of agents (including analgesics, lithium, antineoplastic chemotherapeutic agents, like cisplatin and nitrosoureas, and immunosuppressive drugs, such as ciclosporin and tacrolimus). Drug-induced CTIN is usually asymptomatic, presenting with slowly progressive renal impairment. Because of its insidious nature, CTIN is often diagnosed incidentally on routine laboratory screening or evaluation of CKD. The diagnosis of

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