Kai Ng - Academia.edu (original) (raw)

Papers by Kai Ng

Research paper thumbnail of The Multivariate Normal Distribution

Biometrics, 1990

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Checking the Adequacy of a Partial Linear Model

A partial linear model is a model where the response variable depends on some covariates linearly... more A partial linear model is a model where the response variable depends on some covariates linearly and on others nonparametrically. In this article, we construct an empirical process-based test for examining the adequacy of partial linearity of model. A re-sampling approach, called random symmetrization (RS), is applied to obtain the approximation to the null distribution of the test. The procedure

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A multivariate threshold GARCH model with time-varying correlations

In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedastici... more In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedasticity model with time-varying correlation (VC-MTGARCH) is proposed. The model extends the idea of Engle (2002) and Tse & Tsui (2002) in a threshold framework. This model retains the interpretation of the univariate threshold GARCH model and allows for dynamic conditional correlations. Extension of Bollerslev, Engle and Wooldridge (1988) in a threshold framework is also proposed as a by-product. Techniques of model identification, estimation and model checking are developed. Some simulation results are reported on the finite sample distribution of the maximum likelihood estimate of the VCMTGARCH model. Real examples demonstrate the asymmetric behaviour of the mean and the variance in financial time series and that the VC-MTGARCH model can capture these phenomena. Email: mawilson@polyu.edu.hk. Department of Applied Mathematics, The Hong Kong Polytechnic University and Department of Statistics and Actuarial Science, The University of Hong Kong. Email: hrntlwk@hku.hk. Department of Statistics and Actuarial Science, The University of Hong Kong Email: kaing@hku.hk Department of Statistics and Actuarial Science, The University of Hong Kong 1

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The nested Dirichlet distribution and incomplete categorical data analysis

Statistica Sinica

The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dime... more The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet dis-tribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for analyzing ICD are proposed and compared with existing likelihood/Bayesian strategies. We show that the new approaches have at least three advantages over existing approaches based on the traditional Dirich-let distribution in both frequentist and conjugate Bayesian inference for ICD. The new methods possess closed-form expressions for both the maximum likelihood and Bayes estimates when the likelihood function is in NDD form; produce computa-tionally efficient EM and data augmentation algorithms when the likelihood is not in NDD form; and provide exact sampling procedures for some special cases. The methodologies are illustrated ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The probabilities of absolute ruin in the renewal risk model with constant force of interest

Journal of Applied Probability, 2010

In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the re... more In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the renewal risk model with constant premium rate and constant force of interest. In the particular case of the compound Poisson model, explicit asymptotic expressions for the finite- and infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression for the infinite-time absolute ruin probability. Conditional distributions of Poisson processes and probabilistic techniques regarding randomly weighted sums are employed in the course of this study.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Symmetric Multivariate and Related Distributions

Journal of the American Statistical Association, 1991

Bookmarks Related papers MentionsView impact

Research paper thumbnail of <i>G</i> and related distributions with applications in reliability growth analysis

Statistics and Its Interface, 2016

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Inversion of Bayes formula: Explicit formulae for unconditional pdf

ABSTRACT

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in me... more In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes. Against this background the relevance of perturbations and subcompositions can be clearly seen. Moreover we can identify a number of hypotheses of interest involving the specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate a...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Second-order properties of tail probabilities of sums and randomly weighted sums

Extremes, 2015

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Higher order approximations with generalized linear models

Institute of Mathematical Statistics Lecture Notes - Monograph Series, 1994

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Exact Distributions for the Variance Ratio Statistics and Small Sample Inferences for Stock Market Returns

The variance ratios (VR) of different periods are commonly used statistics to test the random wal... more The variance ratios (VR) of different periods are commonly used statistics to test the random walk (RW) hypothesis for the returns of stock market – a weak form of efficiency hypothesis. Lo and MacKinlay (1989) have demonstrated that the statistics are more powerful than the unit-root tests of Dicky and Fuller (1979, 1981) and the Q-test of BoxPierce (1970). Faust (1992) has shown that they can be viewed as likelihood ratio statistics for testing a RW hypothesis against the alternative as a first-difference AR model. As for most statistics of time series, asymptotic normality is assumed for the VR statistics in inference. Cecchetti and Lam (1994) has pointed out that the VR tests are unreliable for series of small to moderate length and often can be misleading. Their simulations with small-samples showed a substantial size distortion over many horizons for deciding whether a model should be rejected. This creates a dilemma, since only short series in the most recent horizons are rel...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A remark on contractive mappings

Canadian Mathematical Bulletin, 1970

Much current research is concerned with the fixed points of contractive mappings (mappings which ... more Much current research is concerned with the fixed points of contractive mappings (mappings which shrink distance in some manner) from a metric space into itself. In this remark we shall point out that most mappings treated in the literature are very special in the sense that all these mappings satisfy a condition which is rather severe: every periodic point must necessarily be a fixed point.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Multivariate Threshold Varying Conditional Correlations Model

Econometric Reviews, 2009

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Asymptotics of sliced inverse regression

Statistica Sinica

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims

Recently, Tang (2005, Scand. Actuar. J., no. 1, 1–5) obtained a simple asymp-totic formula for th... more Recently, Tang (2005, Scand. Actuar. J., no. 1, 1–5) obtained a simple asymp-totic formula for the ruin probability of the renewal risk model with constant interest force and regularly varying tailed claims. In this paper, we use a completely differ-ent approach to extend Tang’s result to the case in which the claims are pairwise negatively dependent and extended regularly varying tailed.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Uniqueness and Decay Properties of Markov Branching Processes with Disasters

Journal of Applied Probability, 2014

Bookmarks Related papers MentionsView impact

Research paper thumbnail of 2004), “A Multivariate Threshold GARCH Model with Timevarying Correlations”, unpublished paper

In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedastici... more In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedasticity model with time-varying correlation (VC-MTGARCH) is proposed. The model extends the idea of Engle (2002) and Tse & Tsui (2002) to a threshold framework. This model retains the interpretation of the univariate threshold GARCH model and allows for dynamic conditional correlations. Techniques of model identification, estimation and model checking are developed. Some simulation results are reported on the finite sample distribution of the maximum likelihood estimate of the VC-MTGARCH model. A time-varying covariance multivariate GARCH model with a threshold structure is also proposed as a by-product. Real examples demonstrate the asymmetric behaviour of the mean and the variance in financial time series and the ability of the VC-MTGARCH model to capture these phenomena. Keywords: Multivariate GARCH model; Threshold nonlinearity; Varying correlation;

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Checking the adequacy of a partial linear model

A partial linear model is a model where the response variable depends on some covariates linearly... more A partial linear model is a model where the response variable depends on some covariates linearly and on others nonparametrically. In this article, we construct an empirical process-based test for examining the adequacy of partial linearity of model. A re-sampling approach, called random symmetrization (RS), is applied to obtain the approximation to the null distribution of the test. The procedure is easy to implement. A simulation study is carried out and application to an example is made.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Fast Em Algorithm for Quadratic Optimization Subject to Convex Constraints

Convex constraints (CCs) such as box constraints and linear inequal- ity constraints appear frequ... more Convex constraints (CCs) such as box constraints and linear inequal- ity constraints appear frequently in statistical inference and in applications. The problems of quadratic optimization (QO) subject to CCs occur in isotonic regres- sion, shape-restricted non-parametric regression, variable selection (via the lasso algorithm and bridge regression), limited dependent variables models, image recon- struction, and so on. Existing packages for QO are not generally applicable to CCs. Although EM-type algorithms may be applied to such problems (Tian, Ng and Tan (2005)), the convergence rate/speed of these algorithms is painfully slow, especially for high-dimensional data. This paper develops a fast EM algorithm for QO with CCs. We construct a class of data augmentation schemes indexed by a 'work- ing parameter' r (r 2 R), and then optimize r over R under several convergence criteria. In addition, we use Cholesky decomposition to reduce both the number of latent variables and the ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Multivariate Normal Distribution

Biometrics, 1990

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Checking the Adequacy of a Partial Linear Model

A partial linear model is a model where the response variable depends on some covariates linearly... more A partial linear model is a model where the response variable depends on some covariates linearly and on others nonparametrically. In this article, we construct an empirical process-based test for examining the adequacy of partial linearity of model. A re-sampling approach, called random symmetrization (RS), is applied to obtain the approximation to the null distribution of the test. The procedure

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A multivariate threshold GARCH model with time-varying correlations

In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedastici... more In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedasticity model with time-varying correlation (VC-MTGARCH) is proposed. The model extends the idea of Engle (2002) and Tse & Tsui (2002) in a threshold framework. This model retains the interpretation of the univariate threshold GARCH model and allows for dynamic conditional correlations. Extension of Bollerslev, Engle and Wooldridge (1988) in a threshold framework is also proposed as a by-product. Techniques of model identification, estimation and model checking are developed. Some simulation results are reported on the finite sample distribution of the maximum likelihood estimate of the VCMTGARCH model. Real examples demonstrate the asymmetric behaviour of the mean and the variance in financial time series and that the VC-MTGARCH model can capture these phenomena. Email: mawilson@polyu.edu.hk. Department of Applied Mathematics, The Hong Kong Polytechnic University and Department of Statistics and Actuarial Science, The University of Hong Kong. Email: hrntlwk@hku.hk. Department of Statistics and Actuarial Science, The University of Hong Kong Email: kaing@hku.hk Department of Statistics and Actuarial Science, The University of Hong Kong 1

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The nested Dirichlet distribution and incomplete categorical data analysis

Statistica Sinica

The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dime... more The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet dis-tribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for analyzing ICD are proposed and compared with existing likelihood/Bayesian strategies. We show that the new approaches have at least three advantages over existing approaches based on the traditional Dirich-let distribution in both frequentist and conjugate Bayesian inference for ICD. The new methods possess closed-form expressions for both the maximum likelihood and Bayes estimates when the likelihood function is in NDD form; produce computa-tionally efficient EM and data augmentation algorithms when the likelihood is not in NDD form; and provide exact sampling procedures for some special cases. The methodologies are illustrated ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The probabilities of absolute ruin in the renewal risk model with constant force of interest

Journal of Applied Probability, 2010

In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the re... more In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the renewal risk model with constant premium rate and constant force of interest. In the particular case of the compound Poisson model, explicit asymptotic expressions for the finite- and infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression for the infinite-time absolute ruin probability. Conditional distributions of Poisson processes and probabilistic techniques regarding randomly weighted sums are employed in the course of this study.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Symmetric Multivariate and Related Distributions

Journal of the American Statistical Association, 1991

Bookmarks Related papers MentionsView impact

Research paper thumbnail of <i>G</i> and related distributions with applications in reliability growth analysis

Statistics and Its Interface, 2016

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Inversion of Bayes formula: Explicit formulae for unconditional pdf

ABSTRACT

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in me... more In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes. Against this background the relevance of perturbations and subcompositions can be clearly seen. Moreover we can identify a number of hypotheses of interest involving the specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate a...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Second-order properties of tail probabilities of sums and randomly weighted sums

Extremes, 2015

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Higher order approximations with generalized linear models

Institute of Mathematical Statistics Lecture Notes - Monograph Series, 1994

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Exact Distributions for the Variance Ratio Statistics and Small Sample Inferences for Stock Market Returns

The variance ratios (VR) of different periods are commonly used statistics to test the random wal... more The variance ratios (VR) of different periods are commonly used statistics to test the random walk (RW) hypothesis for the returns of stock market – a weak form of efficiency hypothesis. Lo and MacKinlay (1989) have demonstrated that the statistics are more powerful than the unit-root tests of Dicky and Fuller (1979, 1981) and the Q-test of BoxPierce (1970). Faust (1992) has shown that they can be viewed as likelihood ratio statistics for testing a RW hypothesis against the alternative as a first-difference AR model. As for most statistics of time series, asymptotic normality is assumed for the VR statistics in inference. Cecchetti and Lam (1994) has pointed out that the VR tests are unreliable for series of small to moderate length and often can be misleading. Their simulations with small-samples showed a substantial size distortion over many horizons for deciding whether a model should be rejected. This creates a dilemma, since only short series in the most recent horizons are rel...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A remark on contractive mappings

Canadian Mathematical Bulletin, 1970

Much current research is concerned with the fixed points of contractive mappings (mappings which ... more Much current research is concerned with the fixed points of contractive mappings (mappings which shrink distance in some manner) from a metric space into itself. In this remark we shall point out that most mappings treated in the literature are very special in the sense that all these mappings satisfy a condition which is rather severe: every periodic point must necessarily be a fixed point.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Multivariate Threshold Varying Conditional Correlations Model

Econometric Reviews, 2009

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Asymptotics of sliced inverse regression

Statistica Sinica

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims

Recently, Tang (2005, Scand. Actuar. J., no. 1, 1–5) obtained a simple asymp-totic formula for th... more Recently, Tang (2005, Scand. Actuar. J., no. 1, 1–5) obtained a simple asymp-totic formula for the ruin probability of the renewal risk model with constant interest force and regularly varying tailed claims. In this paper, we use a completely differ-ent approach to extend Tang’s result to the case in which the claims are pairwise negatively dependent and extended regularly varying tailed.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Uniqueness and Decay Properties of Markov Branching Processes with Disasters

Journal of Applied Probability, 2014

Bookmarks Related papers MentionsView impact

Research paper thumbnail of 2004), “A Multivariate Threshold GARCH Model with Timevarying Correlations”, unpublished paper

In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedastici... more In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedasticity model with time-varying correlation (VC-MTGARCH) is proposed. The model extends the idea of Engle (2002) and Tse & Tsui (2002) to a threshold framework. This model retains the interpretation of the univariate threshold GARCH model and allows for dynamic conditional correlations. Techniques of model identification, estimation and model checking are developed. Some simulation results are reported on the finite sample distribution of the maximum likelihood estimate of the VC-MTGARCH model. A time-varying covariance multivariate GARCH model with a threshold structure is also proposed as a by-product. Real examples demonstrate the asymmetric behaviour of the mean and the variance in financial time series and the ability of the VC-MTGARCH model to capture these phenomena. Keywords: Multivariate GARCH model; Threshold nonlinearity; Varying correlation;

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Checking the adequacy of a partial linear model

A partial linear model is a model where the response variable depends on some covariates linearly... more A partial linear model is a model where the response variable depends on some covariates linearly and on others nonparametrically. In this article, we construct an empirical process-based test for examining the adequacy of partial linearity of model. A re-sampling approach, called random symmetrization (RS), is applied to obtain the approximation to the null distribution of the test. The procedure is easy to implement. A simulation study is carried out and application to an example is made.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Fast Em Algorithm for Quadratic Optimization Subject to Convex Constraints

Convex constraints (CCs) such as box constraints and linear inequal- ity constraints appear frequ... more Convex constraints (CCs) such as box constraints and linear inequal- ity constraints appear frequently in statistical inference and in applications. The problems of quadratic optimization (QO) subject to CCs occur in isotonic regres- sion, shape-restricted non-parametric regression, variable selection (via the lasso algorithm and bridge regression), limited dependent variables models, image recon- struction, and so on. Existing packages for QO are not generally applicable to CCs. Although EM-type algorithms may be applied to such problems (Tian, Ng and Tan (2005)), the convergence rate/speed of these algorithms is painfully slow, especially for high-dimensional data. This paper develops a fast EM algorithm for QO with CCs. We construct a class of data augmentation schemes indexed by a 'work- ing parameter' r (r 2 R), and then optimize r over R under several convergence criteria. In addition, we use Cholesky decomposition to reduce both the number of latent variables and the ...

Bookmarks Related papers MentionsView impact