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Mathematics

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Nonparametric Estimation from Incomplete Observations

In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss)....

A new look at the statistical model identification

The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The...

Regression Models and Life-Tables

The analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables...

Principles and procedures of statistics.

R. G. D. Steel, J. H. Torrie

Controlling the False Discovery Rate: a Practical and Powerful Approach to Multiple Testing

SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented....

Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives

This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the...

Matrix analysis

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms...

Statistical Learning Theory

Yuhai Wu, Vladimir Vapnik

A power primer.

One possible reason for the continued neglect of statistical power analysis in research in the behavioral sciences is the inaccessibility of or difficulty with the standard material. A convenient, although not comprehensive, presentation of required sample...

Applied regression analysis

Norman R. Draper, Harry Smith

Co-integration and error correction: representation, estimation, and testing

The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples.If each element of a vector of time series xt first achieves...

Random Forests

Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a...

Alternative Ways of Assessing Model Fit

This article is concerned with measures of fit of a model. Two types of error involved in fitting a model are considered. The first is error of approximation which involves the fit of the model, with optimally chosen but unknown parameter values, to the...

Computer simulation of liquids

M. P. Allen, D. J. Tildesley

Principal component analysis

Principal component analysis

Hierarchical linear models : applications and data analysis methods

Harvey Goldstein, Anthony S. Bryk, Stephen W. Raudenbush

Compressed sensing

Suppose x is an unknown vector in Ropf m (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear...

Distribution of the Estimators for Autoregressive Time Series with a Unit Root

Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2....

Applied linear statistical models

John Neter, Michael H. Kutner, Christopher J. Nachtsheim, William Wasserman

Quantifying heterogeneity in a meta‐analysis

SUMMARY The extent of heterogeneity in a meta-analysis partly determines the diculty in drawing overall con- clusions. This extent may be measured by estimating a between-study variance, but interpretation is then specic to a particular treatment eect...

The central role of the propensity score in observational studies for causal effects

SUMMARY The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove...

Regression Shrinkage and Selection via the Lasso

SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends...

Investigating Causal Relations by Econometric Models and Cross-Spectral Methods

There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple...

A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity

This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By...

On the evaluation of structural equation models

Criteria for evaluating structural equation models with latent variables are defined, critiqued, and illustrated. An overall program for model evaluation is proposed based upon an interpretation of converging and diverging evidence. Model assessment is...

The statistical analysis of failure time data

John D. Kalbfleisch, Ross L. Prentice

A Simple Sequentially Rejective Multiple Test Procedure

This paper presents a simple and widely ap- plicable multiple test procedure of the sequentially rejective type, i.e. hypotheses are rejected one at a tine until no further rejections can be done. It is shown that the test has a prescribed level of significance...

Hierarchical Grouping to Optimize an Objective Function

A procedure for forming hierarchical groups of mutually exclusive subsets, each of which has members that are maximally similar with respect to specified characteristics, is suggested for use in large-scale (n > 100) studies when a precise optimal solution...

The structure and function of complex networks

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems....

Longitudinal data analysis using generalized linear models

SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions...

Multilayer feedforward networks are universal approximators

This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another...

Significance Tests and Goodness of Fit in the Analysis of Covariance Structures

Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models. Large-sample theory provides...

Ordinary differential equations

Ordinary differential equations

Testing for a Unit Root in Time Series Regression

This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly...

Statistical methods in medical research

The explanation and implementation of statistical methods for the medical researcher or statistician remains an integral part of modern medical research. This book explains the use of experimental and analytical biostatistics systems. Its accessible style...

Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces

A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other...

Response surface methodology : process and product optimization using designed experiments

Raymond H. Myers, Douglas C. Montgomery, Christine M. Anderson-Cook

The advanced theory of statistics

The advanced theory of statistics

Initial conditions and moment restrictions in dynamic panel data models

In this paper we consider estimation of the autoregressive error components model. When the autoregressive parameter is moderately large and the number of time series observations is moderately small, the usual Generalised Methods of Moments (GMM) estimator...

Nonlinear Control Systems

Alberto Isidori, M. Thoma, Eduardo D. Sontag, Bradley W. Dickinson, Alfred Fettweis, James L. Massey

Higher transcendental functions

Bateman Manuscript, Harry Bateman, Arthur Erdélyi

The elements of statistical learning: data mining, inference, and prediction

During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has...

A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix

This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general...

Bootstrap Methods: Another Look at the Jackknife

We discuss the following problem given a random sample X = (Xl' X 2 , ••• , Xn) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard...

STATISTICAL ANALYSIS OF COINTEGRATION VECTORS

We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the...

Linear models and empirical bayes methods for assessing differential expression in microarray experiments.

The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a...

A note on two problems in connexion with graphs

A note on two problems in connexion with graphs

Independent component analysis

Independent component models have gained increasing interest in various fields of applications in recent years. The basic independent component model is a semiparametric model assuming that a p-variate observed random vector is a linear transformation...

Introduction to numerical analysis

Introduction to numerical analysis

Linear statistical inference and its applications

Linear statistical inference and its applications

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial...

Low-density parity-check codes

A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance...

Mean shift: a robust approach toward feature space analysis

A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean...

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an /2-orthogonal basis...

Nonlinear total variation based noise removal algorithms

A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lanrange...

The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems

It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material...

Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?

The standard conclusion that is drawn from this empirical evidence is that many or most aggregate economic time series contain a unit root. However, it is important to note that in this empirical work the unit root is set up as the null hypothesis testing...

A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting

In the first part of the paper we consider the problem of dynamically apportioning resources among a set of options in a worst-case on-line framework. The model we study can be interpreted as a broad, abstract extension of the well-studied on-line prediction...

Nonlinear Programming: Theory and Algorithms

COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED"Nonlinear Programming: Theory and Algorithms"--now in an extensively updated Third Edition--addresses the problem of optimizing an objective function...

Another look at the instrumental variable estimation of error-components models

This article develops a framework for efficient IV estimators of random effects models with information in levels which can accommodate predetermined variables. Our formulation clarifies the relationship between the existing estimators and the role of...

A Practical Guide to Wavelet Analysis

A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis...

A LOGICAL CALCULUS OF THE IDEAS IMMANENT IN NERVOUS ACTIVITY

Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of...

Rank correlation methods

Rank correlation methods

Atomic Decomposition by Basis Pursuit

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries---stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete...

Robust Locally Weighted Regression and Smoothing Scatterplots

The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which...

VERY HIGH RESOLUTION INTERPOLATED CLIMATE SURFACES FOR GLOBAL LAND AREAS

We developed interpolated climate surfaces for global land areas (excluding Antarctica) at a spatial resolution of 30 arc s (often referred to as 1-km spatial resolution). The climate elements considered were monthly precipitation and mean, minimum, and...

Modeling by shortest data description

The number of digits it takes to write down an observed sequence x1, …, xN of a time series depends on the model with its parameters that one assumes to have generated the observed data. Accordingly, by finding the model which minimizes the description...

De-noising by soft-thresholding

Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data di=f(ti )+σzi, i=0, …, n-1,ti=i/n, where the zi are independent and identically distributed standard Gaussian...

Active contours without edges

We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined...

Atomic Decomposition by Basis Pursuit

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries --- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete...

Testing for unit roots in heterogeneous panels

This paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics. In particular it proposes a standardized t -bar test statistic based on the (augmented) Dickey–Fuller statistics averaged across...

Introduction to statistical analysis

W. J. Dixon, Frank J. Massey

Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models

This paper contains the likelihood analysis of vector autoregressive models allowing for cointegration. The author derives the likelihood ratio test for cointegrating rank and finds it asymptotic distribution. He shows that the maximum likelihood estimator...

Nonlinear and Adaptive Control Design

From the Publisher:Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced...

Dispersion on a Sphere

Any topological framework requires the development of a theory of errors of characteristic and appropriate mathematical form. The paper develops a form of theory which appears to be appropriate to measurements of position on a sphere. The primary problems...

Nearest neighbor pattern classification

The nearest neighbor decision rule assigns to an unclassified sample point the classification of the nearest of a set of previously classified points. This rule is independent of the underlying joint distribution on the sample points and their classifications,...

Decision Making in a Fuzzy Environment

By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of...

Bayesian measures of model complexity and fit

We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure "p" "D" for the effective number of parameters in a model as the difference...

An algorithm for the machine calculation of complex Fourier series

An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al. (1). Good (2) generalized these methods and gave elegant...

Introduction to statistical time series

Introduction to statistical time series

Generalized Additive Models

Trevor Hastie, Robert Tibshirani

Analysis of longitudinal data

Peter J. Diggle, Patrick J. Heagerty, Kung-Yee Liang

Optimization by Vector Space Methods

From the Publisher:Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book...

Computational complexity

Once we have developed an algorithm (q.v.) for solving a computational problem and analyzed its worst-case time requirements as a function of the size of its input (most usefully, in terms of the O-notation; see ALGORITHMS, ANALYSIS OF), it is inevitable...

Fuzzy sets and fuzzy logic: theory and applications

Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets, Uncertainty,and Information—an earlier work of Professor Klir and Tina Folger—Fuzzy Sets and Fuzzy Logicaddresses practically every significant topic in the broad expanse...

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