Fixed size confidence regions for parameters of threshold AR(1) models

For parameters of single and multiple threshold autoregressive models of order one, sequential procedures are proposed for constructing fixed size confidence ellipsoids. Sequential procedures are also proposed for constructing fixed proportional accuracy confidence ellipsoids and fixed width confidence intervals for linear combination of parameters. The confidence ellipsoids and intervals are shown to be asymptotically consistent and the associated stopping rules are shown to be asymptotically efficient as the size/width of the region becomes small.     

Statistics in seismology

A range of problems in the applications of statistics to seismology is surveyed. In each case, brief notes are provided on the seismological background to the problem, the essential character of the statistical questions which arise, some key references, and the direction of current work. Two broad sections are included, the first covering the analysis of raw data from the seismogram traces, the second covering the analysis of derived data such as lists of earthquake epicentres and magnitudes.     

Confidence regions for parameters in linear models with additional information

Using given significant additional information it is possible to improve different confidence regions for the regression parameters in a linear model. Thereby, the given informations may concern the expectation and (or) the variance of the observations, and an improvement is possible in the sense of the decrease of the confidence regions' size. In particular it is possible to improve the so called confidence ellipsoids which are often used to estimate the considered parameters.     

A general central limit theorem and a subsampling variance estimator for α‐mixing point processes

We establish a central limit theorem for multivariate summary statistics of nonstationary α‐mixing spatial point processes and a subsampling estimator of the covariance matrix of such statistics. The central limit theorem is crucial for establishing asymptotic properties of estimators in statistics for spatial point processes. The covariance matrix subsampling estimator is flexible and model free. It is needed, for example, to construct confidence intervals and ellipsoids based on asymptotic normality of estimators. We also provide a simulation study investigating an application of our results to estimating functions.     

ASYMPTOTIC POSTERIOR NORMALITY FOR STOCHASTIC PROCESSES: A NON-ERGODIC EXAMPLE

Sweeting & Adekola (1987) presented a fairly general set of conditions, covering a wide class of problems, that establish asymptotic posterior normality for stochastic processes. In this paper, this theory is illustrated via a non-ergodic example, namely, the class of non-homogeneous birth processes.     

Size distribution stereology for quasiellipsoids in r

Weakly stationary fields of random quasiellipsoids (rigid or flat ellipsoids) in Rⁿ are intersected with a fixed hyperplane H. The stereological problem consists in determining the size and shape distribution of a “typoical” quasiellipsoid of the sample by selectional data. The size is assumed to be independent of shape and directins. In general the problem cannot be solved uniquely (s.[1]). In the present paper the question is answered for which shape–direction distributions the stereological formulas for all size distributions are the same as in the well–known spherical case     

Influence measures based on confidence ellipsoids in general linear regression model with correlated regressors

In this paper, we investigated the Andrews–Pregibon (AP), COVRATIO and Cook–Weisberg (CW) statistics to determine the influential observations on the confidence ellipsoids in linear regression model with correlated errors and correlated regressors. A real example and a Monte Carlo simulation study are given to detect the effects of autocorrelation coefficient and ridge parameter on the AP, COVRATIO and CW statistics.     

Machine covering with combined partial information

Machine scheduling and covering problems may occur in many applications such as load balancing in network communication channel assignment, parallel processing in large-size computing, task arrangement in flexible manufacturing systems, etc. In this paper we study machine covering problems with combined partial information on m   parallel identical machines. We consider sequences where the processing time of all jobs are at most 1/k$1/k$ times of the optimal value (for an integer k). For the case where the optimal value is not known in advance, we show that LS algorithm is optimal. For the case where the optimal value is known in advance, we give lower bounds and present semi-online algorithms.     

Trimmed least squares estimator as best trimmed linear conditional estimator for linear regression model

A class of trimmed linear conditional estimators based on regression quantiles for the linear regression model is introduced. This class serves as a robust analogue of non-robust linear unbiased estimators. Asymptotic analysis then shows that the trimmed least squares estimator based on regression quantiles ( Koenker and Bassett ( 1978 ) ) is the best in this estimator class in terms of asymptotic covariance matrices. The class of trimmed linear conditional estimators contains the Mallows-type bounded influence trimmed means ( see De Jongh et al ( 1988 ) ) and trimmed instrumental variables estimators. A large sample methodology based on trimmed instrumental variables estimator for confidence ellipsoids and hypothesis testing is also provided.     

General ridge predictors in a mixed linear model

This paper mainly aims to put forward two estimators for the linear combination of fixed effects and random effects, and to investigate their properties in a general mixed linear model. First, we define the notion of a Type-I general ridge predictor (GRP) and obtain two sufficient conditions for a Type-I GRP to be superior over the best linear unbiased predictor (BLUP). Second, we establish the relationship between a Type-I GRP and linear admissibility, which results in the notion of Type-II GRP. We show that a linear predictor is linearly admissible if and only if it is a Type-II GRP. The superiority of a Type-II GRP over the BLUP is also obtained. Third, the problem of confidence ellipsoids based on the BLUP and Type-II GRP is investigated.     

Hypothesis testing for the dispersion parameter of the hyper-Poisson regression model

The Poisson distribution is widely used to deal with count data, however, it is unable to capture the dispersion problems. The hyper-Poisson distribution is a particular case of the extended Conway–Maxwell distribution which takes into account the dispersion phenomena of the count data. The main motivation to consider this model is the possibility to link the mean to the regressor variables in very natural way to solve testing problems. So, this paper will be focalized in the gradient statistics to detect dispersions and to compare with the classical likelihood ratio statistic. Two illustrative applications are considered.     

A note on estimation of the shape of density level sets of star-shaped distributions

Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be restricted in that the proportional density level sets ought to be ellipsoids. In star-shaped distributions, this restriction is relaxed and the density level sets are allowed to be boundaries of arbitrary proportional star-shaped sets. In this note, we propose a non parametric estimator of the shape of density level sets of star-shaped distributions, and prove its strong consistency with respect to the Hausdorff distance. We illustrate our estimator with simulated and real data.     

On the regularized Laplacian eigenmaps

To find an appropriate low-dimensional representation for complex data is one of the central problems in machine learning and data analysis. In this paper, a nonlinear dimensionality reduction algorithm called regularized Laplacian eigenmaps (RLEM) is proposed, motivated by the method for regularized spectral clustering. This algorithm provides a natural out-of-sample extension for dealing with points not in the original data set. The consistency of the RLEM algorithm is investigated. Moreover, a convergence rate is established depending on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers. Experiments are given to illustrate our algorithm.     

Star-shaped distributions and their generalizations

Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to “star-shaped distributions” with concentric star-shaped contours and show that many results in the former case continue to hold in the more general case. We develop a general theory in the framework of abstract group invariance so that the results can be applied to other cases as well, especially those involving random matrices.     

Bayesian analysis of discrete time warranty data

Summary.  The analysis of warranty claim data, and their use for prediction, has been a topic of active research in recent years. Field data comprising numbers of units returned under guarantee are examined, covering both situations in which the ages of the failed units are known and in which they are not. The latter case poses particular computational problems for likelihood-based methods because of the large number of feasible failure patterns that must be included as contributions to the likelihood function. For prediction of future warranty exposure, which is of central concern to the manufacturer, the Bayesian approach is adopted. For this, Markov chain Monte Carlo methodology is developed.     

所有权结构、负债结构对投资行为影响的研究

上市公司过度投资行为表现得较为明显和严重,投资行为的有效性已成为制约公司质量提升和长期持续发展的主要因素。以中国上市公司2007年与2008年的数据为样本,将其投资行为分为过度投资和投资不足,检验国有与非国有控股公司的负债结构差异,考察所有权结构和负债结构对投资行为有效性的影响。研究发现,随着内部现金流的增加,国有控股公司的过度投资现象比非国有控股公司更为严重,同时第一大股东持股比例的提高也会刺激过度投资行为。     

Credit risk modeling based on survival analysis with immunes

Statistical modeling of credit risk for retail clients is considered. Due to the lack of detailed updated information about the counterparty, traditional approaches such as Merton’s firm-value model, are not applicable. Moreover, the credit default data for retail clients typically exhibit a very small percentage of default rates. This motivates a statistical model based on survival analysis under extreme censoring for the time-to-default variable. The model incorporates the stochastic nature of default and is based on incomplete information. Consistency and asymptotic normality of maximum likelihood estimates of the parameters characterizing the time-to-default distribution are derived. A criterion for constructing confidence ellipsoids for the parameters is obtained from the asymptotic results. An extended model with explanatory variables is also discussed. The results are illustrated by a data example with 670 mortgages.     

Universal codes as a basis for time series testing

We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the distribution law of the codeword lengths is not known. We apply this approach to the following four problems: goodness-of-fit testing (or identity testing), testing for independence, testing of serial independence and homogeneity testing and suggest nonparametric statistical tests for these problems. It is important to note that practically used so-called archivers can be used for suggested testing.     

Sequential design for nonparametric inference

The performance of nonparametric function estimates often depends on the choice of design points. Based on the mean integrated squared error criterion, we propose a sequential design procedure that updates the model knowledge and optimal design density sequentially. The methodology is developed under a general framework covering a wide range of nonparametric inference problems, such as conditional mean and variance functions, the conditional distribution function, the conditional quantile function in quantile regression, functional coefficients in varying coefficient models and semiparametric inferences. Based on our empirical studies, nonparametric inference based on the proposed sequential design is more efficient than the uniform design and its performance is close to the true but unknown optimal design. The Canadian Journal of Statistics 40: 362–377; 2012 © 2012 Statistical Society of Canada     

The Use of Resampling Methods to Simplify Regression Models in Medical Statistics

The number of variables in a regression model is often too large and a more parsimonious model may be preferred. Selection strategies (e.g. all-subset selection with various penalties for model complexity, or stepwise procedures) are widely used, but there are few analytical results about their properties. The problems of replication stability, model complexity, selection bias and an over-optimistic estimate of the predictive value of a model are discussed together with several proposals based on resampling methods. The methods are applied to data from a case–control study on atopic dermatitis and a clinical trial to compare two chemotherapy regimes by using a logistic regression and a Cox model. A recent proposal to use shrinkage factors to reduce the bias of parameter estimates caused by model building is extended to parameterwise shrinkage factors and is discussed as a further possibility to illustrate problems of models which are too complex. The results from the resampling approaches favour greater simplicity of the final regression model.