A SENSITIVE ALGORITHM FOR DETECTING THE INEQUIVALENCE OF HADAMARD MATRICES (2008)
Abstract. A Hadamard matrix of side n is an n × n matrix with every entry either 1 or −1, which satisfies HH T = nI. Two Hadamard matrices are called equivalent if one can be obtained from the...
Transportation Information Systems (2008)
Abstract: Boosting is a machine learning algorithm that is not well known in chemometrics. We apply boosting tree to the classification of mass spectral data. In the experiment, recognition of 15...
AND STOCHASTIC OPTIMIZATION ALGORITHMS FOR UNIFORM DESIGNS WITH THREE OR FOUR LEVELS (2008)
Lower Bounds, Kai-tai Fang, Dietmar Maringer, Yu Tang, Peter Winker
Abstract. New lower bounds for three- and four-level designs under the centered L2-discrepancy are provided. We describe necessary conditions for the existence of a uniform design meeting these lower...
In this paper we propose a new method, based on the conditional distribution method in Monte-Carlo methods, to generate the uniform distribution on the domain Tn (a; b) = f(x 1 ; \Delta \Delta \Delta...
Wrap-Around L_2-discrepancy of Random Sampling, Latin Hypercube and Uniform Designs (2007)
this paper consider their mean and variance under a wrap-around version of the L 2 { discrepancy (WD). The theoretic expectation and variance of this discrepancy are derived for these two designs....
: Considering general prime or prime powered factorials, we give a finite projective geometric formulation for regular fractional factorial splitplot designs. This provides a unified framework for...
Regular Fractions of Mixed Factorials with Maximum Estimation Capacity (2007)
. We use a finite projective geometric approach to investigate the issue of maximum estimation capacity in regular fractions of mixed factorials, recognizing the fact that not all two factor...
Kai-tai Fang, Chang-xing Ma, Peter Winker
. In this paper properties and construction of designs under a centered version of the L2 --discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random...
On Construction Of Orthogonal And Nearly Orthogonal Arrays (2007)
In the past orthogonal arrays were constructed by a number of mathematical tools such as orthogonal Latin squares, Hadamard matrices, group theory and finite fields. Wang and Wu (1992) proposed the...
Testing Multivariate Uniformity and Its Applications (2007)
Jia-Juan Liang, Kai-Tai Fang, Fred J. Hickernell, Run-ze Li
Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0; 1] d (d 2). These statistics are derived from the number-theoretic methods or...
A Coordinate Measuring Machine (CMM) is a computer-controlled device that uses a probe to obtain measurements on a manufactured part's surface. In the process of collecting, analyzing and...
Uniform Design Based on Latin Squares (2007)
Kai-tai Fang, Wai-Chee Shiu, Jian-xin Pan
The uniform design (UD) has been widely used in various fields and is generated by the socalled good lattice point (glp) set. In this paper, we shall propose some new UDs which are based on cyclic...
Optimal U-designs Under Multi-criteria for Fourier Regression Models (2007)
The U-design which is D-optimal under a Fourier model is called an optimal U-design (OUD). Recently, based on the good lattice points Riccomagno, Schwabe and Wynn gave the necessary and sufficient...
Majorization framework for balanced lattice designs (2006)
Zhang, Aijun, Fang, Kai-Tai, Li, Runze, Sudjianto, Agus
This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present...
Critical value determination on similarity of fingerprints (2006)
Fang, Kai-Tai, Liang, Yi-Zeng, Yin, Xiao-lin, Chan, Kelvin C., Lu, Guang-Hua
A high-performance liquid chromatographic (HPLC) fingerprint of Chinese Angelica (CA) was developed basing on the consistent chromatograms of 40 CA samples (Angelica sinensis (Oliv.) Diels). The...
Fang, Kai-Tai, Mukerjee, Rahul
With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest...
Majorization framework for balanced lattice designs (2005)
Zhang, Aijun, Fang, Kai-Tai, Li, Runze, Sudjianto, Agus
This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present...
Critical value determination on similarity of fingerprints (2005)
Fang, Kai-Tai, Liang, Yi-Zeng, Yin, Xiao-lin, Chan, Kelvin, Lu, Guang-Hua
A chemical or DNA fingerprint can be treated as a multi-dimensional vector. Correlation coefficient between two fingerprints which is easy to understand and simple to compute has been widely used to...
Expected lengths of confidence intervals based on empirical discrepancy statistics (2005)
Fang, Kai-tai, Mukerjee, Rahul
We consider a very general class of empirical discrepancy statistics that includes the Cressie–Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order...
Xiao-Ling Peng, Kai-Tai Fang, Qian-Nan Hu, Yi-Zeng Liang
The connectivity index Ç can be regarded as the sum of bond contributions. Inthis article, boiling point (bp)-oriented contributions for each kind of bond are obtainedby decomposing the...
Xiao-ling Peng, Kai-tai Fang, Qian-nan Hu, Yi-zeng Liang
Abstract: The connectivity index χ can be regarded as the sum of bond contributions. In this article, boiling point (bp)-oriented contributions for each kind of bond are obtained by decomposing the...
Growth Curve Models and Statistical Diagnostics (2002)
Growth-curve models are generalized multivariate analysis-of-variance models. The basic idea of the models is to use different polynomials to fit different treatment groups involved in the...
In a known normal population, one desires to select a given number of representative points that retain as much information about the population as possible. To obtain these points, the solution of...
In this paper we generalize the theory of maximum likelihood estimation and likelihood ratio criteria from normal distributions to multivariate elliptically contoured distributions for which the...
Testing multivariate uniformity and its applications (2001)
Jia-juan Liang, Kai-tai Fang, Fred J. Hickernell, Runze Li
Abstract. Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1] d (d ≥ 2). These statistics are derived from number-theoretic or...
A note on generalized aberration in factorial designs (2001)
Abstract. In this paper we extend the wordlength pattern and minimum aberration for non-regular factorials. The new concepts, the generalized wordlength pattern and minimum generalized aberration,...
Qing-Song Xu, Yi-zeng Liang, Kai-Tai Fang
Using the experimental design methods, instead of deterministic ones commonly used by chemists, to estimate the kinetic constants is a very important subject in chemical researches, since...
Uniformity In Fractional Factorials (1999)
Kai-tai Fang, Chang-xing Ma, Rahul Mukerjee
. The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For...
On Isomorphism of Fractional Factorial Designs (1999)
Two fractional factorial designs are called isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs and switching the levels of factors. To identify the...
In this paper we create the connection of wrap-around-discrepancy and aberration of regular fractional factorial designs with two and three levels. For any level we give the connection of uniformity...
Connection Between Uniformity and Aberration in Regular Fractions of Two-level Factorials (1999)
We show a link between two apparently unrelated areas, namely uniformity and minimum aberration, both of which have been of substantial recent interest. Specifically, with reference to regular...
On the Theory of Multivariate Elliptically Contoured Distributions and Their Applications. (1998)
In this paper, the multivariate elliptically contoured distributions which generalize the elliptically contoured distribution to the case of a matrix are defined and a special class of multivariate...
This paper extends the theory of the distributions of quadratic forms and Cochran's theorem from normal populations to elliptically contoured distributions. Some interesting applications are...
Theory and Applications of Elliptically Contoured and Related Distributions. (1998)
Anderson, T. W., Fang, Kai-Tai
A random vector X is said to have elliptically contoured distribution if it has the distribution of micron + AY, where micron is a constant matrix, and the random vector Y has a spherical...
Application Of Threshold-Accepting To The Evaluation Of The Discrepancy Of A Set Of Points (1997)
. E#cient routines for multidimensional numerical integration are provided by quasi-- Monte Carlo methods. These methods are based on evaluating the integrand at a set of representative points of the...
Asymptotics for kernel estimate of sliced inverse regression (1996)
To explore nonlinear structures hidden in high-dimensional data and to estimate the effective dimension reduction directions in multivariate nonparametric regression, Li and Duan proposed the sliced...
Influential Observation In The Growth Curve Model With Unstructured Covariance Matrix (1996)
. Under a normal assumption, Liski (1991) gave some measurements for assessing influential observations in the growth curve model (GCM) with a known covariance. For the GCM with an unstructured...
A Note on the Mixed Geographically Weighted Regression Model
Chang-Lin Mei, Shu-Yuan He, Kai-Tai Fang
A mixed, geographically weighted regression (GWR) model is useful in the situation where certain explanatory variables influencing the response are global while others are local. Undoubtedly, how to...
Some necessary uniform tests for spherical symmetry
Jiajuan Liang, Kai-Tai Fang, Fred Hickernell
Goodness-of-fit, Monte Carlo study, Spherical symmetry, Uniformity,
Expected lengths of confidence intervals based on empirical discrepancy statistics
We consider a very general class of empirical discrepancy statistics that includes the Cressie--Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order...
With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest...
Discrete discrepancy in factorial designs
Discrepancy measure can be utilized as a uniformity measure for comparing factorial designs. A so-called discrete discrepancy has been used to evaluate the uniformity of factorials. In this paper we...
A Lower Bound for the Centered L 2-Discrepancy on Asymmetric Factorials and its Application
Kashinath Chatterjee, Kai-Tai Fang, Hong Qin
Asymmetric factorial, Centered L 2-discrepancy, Uniformity, Uniform design, 62K15, 62K10,
Multiple outlier detection in growth curve model with unstructured covariance matrix
Elliptically contoured distribution, growth curve model, influential observation, multiple outlier detection criterion, statistical diagnostic,
Bayesian Statistical Inference on Elliptical Matrix Distributions
In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parameters[mu]and[Sigma]. Under a noninformative prior distribution, we obtain the...
On Estimated Projection Pursuit-Type Crámer-von Mises Statistics, ,
Zhu, Li-Xing, Fang, Kai-Tai, Bhatti, M Ishaq
This paper addresses the problem of testing for a multivariate distribution, which belongs to a known parametric distribution family. The estimated Crámer-Von Mises-type test statistics are...
Bayesian Local Influence for the Growth Curve Model with Rao's Simple Covariance Structure,
Pan, Jian-Xin, Fang, Kai-Tai, Liski, Erkki P.
In this paper, the Bayesian local influence approach is employed to diagnose the adequacy of the growth curve model with Rao's simple covariance structure, based on the Kullback-Leibler divergence....
Some families of mutivariate symmetric distributions related to exponential distribution
This paper introduces a family of multivariate symmetric distributions, which includes the one with i.i.d. exponential components as its special member. This family, denoted by Fn, is defined as...
Orthogonality and D-optimality of the U-type design under general Fourier regression models
Xie, Min-Yu, Ning, Jian-Hui, Fang, Kai-Tai
Riccomagno et al. [1997. Lattice-based D-optimum design for Fourier regression. Ann. Statist. 25, 2313-2317] gave a comprehensive study on D-optimality under a symmetric Fourier regression model and...
A note on optimal foldover design
Fang, Kai-Tai, Lin, Dennis K. J., Qin, Hong
This note provides a theoretical justification for the optimal foldover plans for two-level designs, including the regular 2s-p, non-regular, saturated and supersaturated designs.
A note on construction of nearly uniform designs with large number of runs
Uniform designs have been used in computer experiments (Fang et al., Technometrics 42 (2000) 237). A uniform design seeks its design points to be uniformly scattered on the experimental domain. When...
A characterization for orthogonal arrays of strength two via a regression model
Chan, Ling-Yau, Fang, Kai-Tai, Mukerjee, Rahul
We give a characterization for orthogonal arrays of strength two in terms of D-optimality under a multiple regression model with continuous factor levels.
A stratified sampling model in spherical feature inspection using coordinate measuring machines
Fang, Kai-Tai, Wang, Song-Gui, Wei, Gang
A coordinate measuring machine (CMM) is a computer-controlled device that uses a probe to obtain measurements on a manufactured part's surface. In the process of collecting, analyzing and...
In this paper we propose a new method, based on the conditional distribution method in Monte-Carlo methods, to generate the uniform distribution on the domain Tn(a,b)={(x1,...,xn):...
On the posterior distribution of the covariance matrix of the growth curve model
Pan, Jian-Xin, Fang, Kai-Tai, Von Rosen, Dietrich
For the growth curve model with an unstructured covariance matrix, the posterior distributions of the dispersion matrix is derived under a non-informative prior distribution. The results are...
A characterization of multivariate normal distribution and its application
Yang, Zhen-Hai, Fang, Kai-Tai, Liang, Jia-Juan
Let X1, X2, ..., Xn be i.i.d. d-dimensional random vectors with a continuous density. Let and . In this paper we find that the distribution of Zk (or Yk) can be used for characterizing multivariate...
Estimation of scale matrix of elliptically contoured matrix distributions
In this paper, the problem of estimation of scale matrix is considered under entropy loss, quadratic loss and squared error loss. With respect to entropy and quadratic loss, we obtain the best...
A largest characterization of spherical and related distributions
It is well known that the family of spherical distributions has many nice properties. Is it possible to extend those properties to some bigger family [triple bond; length as m-dash] (y) which...
A characterization of multivariate l1-norm symmetric distributions
Let z be an n x 1 interchangeable random vector and z(1) [less-than-or-equals, slant] ... [less-than-or-equals, slant] z(n) be its order statistics. Let ui = (n - i + 1) x (z(i) - z(i - 1))i = 1, ......
On the Student's t-distribution and the t-statistic
Yang, Zhenhai, Fang, Kai-Tai, Kotz, Samuel
In this paper we provide rather weak conditions on a distribution which would guarantee that the t-statistic of a random vector of order n follows the t-distribution with n-1 degrees of freedom. The...
Restricted expected multivariate least squares
Fang, Kai-Tai, Wang, Song-Gui, Von Rosen, Dietrich
A new approach of estimating parameters in multivariate models is introduced. A fitting function will be used. The idea is to estimate parameters so that the fitting function equals or will be close...
The Meta-elliptical Distributions with Given Marginals
Fang, Hong-Bin, Fang, Kai-Tai, Kotz, Samuel
Based on an analysis of copulas of elliptically contoured distributions, joint densities of continuous variables with given strictly increasing marginal distributions are constructed. A method...
Monte Carlo Methoden haben sich auf vielen Gebieten der Statistik und Ökonometrie als wertvolles Instrument erwiesen. Die übliche Verwendung von Pseudozufallszahlen führt dazu, daß der...