Alternative Tests for Parameter Stability

ABSTRACT

We propose new tests for parameter stability based on estimates computed from a sequence of subsamples moving forward and backward across the sample. We obtain a sequence of moving estimates tests and we derive their asymptotic null distribution based on the functional central limit theorem. The critical values are approximated using Durbin's method. Our simulation results show that these tests have comparable size and slightly higher power in detecting structural change than other competing tests.     

Central limit theorems of range-based estimators for diffusion models

Abstract

In this article, we consider non parametric range-based estimation procedure for diffusion processes and propose a instantaneous volatility estimator. Under some weak conditions, we certify that the proposed estimator has convergence in probability. Adding some necessary conditions, we prove a central limit theorem. By inference, we reach a conclusion that, with high frequency data in hand, the proposed estimator is more precise than those pure realized instantaneous volatility ones. Numerical simulation illustrates the finite sample properties of the proposed estimator.     

Generation of pseudo random numbers and estimation under Cox models with time-dependent covariates

ABSTRACT

We study the method for generating pseudo random numbers under various special cases of the Cox model with time-dependent covariates when the baseline hazard function may not be constant and the random variable may equal infinity with a positive probability. During our simulation studies in computing the partial likelihood estimates, in between 3% and 20% of the time with a moderate sample size, it happens that the partial likelihood estimate of the regression coefficient is ∞ for the data from the Cox model. We propose a semi-parametric estimator as a modification for such a case. We present simulation results on the asymptotic properties of the semi-parametric estimator.     

TESTING FOR LINEAR DEPENDENCE IN HEAVY-TAILED DATA

ABSTRACT

We use the sample covariation to develop tests for lagged linear dependence in symmetric time series data. We propose tests for both finite and infinite variance processes. The finite sample performance of the tests is investigated using simulated data and compared to tests based on the von Neumann ratio.     

Berry–Esseen type bound of conditional mode estimation under truncation and strong mixing assumptions

ABSTRACT

In order to investigate the convergence rate of the asymptotic normality for the estimator of the conditional mode function for the left-truncation model, we derive a Berry–Esseen type bound of the estimator when the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The finite sample performance of the estimator of the conditional mode function is explored through simulations.     

A unified approach to multilevel sample selection models

Abstract

We propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman’s two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation.     

Survival Estimation with Missing Censoring Times for the Generalized Koziol–Green Model

ABSTRACT

When analyzing time-to-event data, there are various situations in which right censoring times for unfailed units are missing. In that context, by taking a supplementary sample of a convenient percentage of unfailed units, we propose a semi-parametric method for estimating a survival function under the natural extension of the Koziol–Green model to double random censoring. Some large sample properties of this estimator are derived. We prove uniform strong consistency and asymptotic weak convergence to a Gaussian process. A simulation study is also presented in order to analyze the behavior of the proposed estimator.     

Convergence Rates of Empirical Bayes Estimation for the Parameter of the Uniform Distribution U(0, θ) Under Random Censorship

ABSTRACT

This article considers the empirical Bayes estimation problem in the uniform distribution U(0, θ) with censored data. For the parameter θ, using the empirical Bayes (EB) approach, we propose an EB estimation of θ which possesses a rate of convergence can be arbitrarily close to O(n ^?1/2) when the historical samples are randomly censored from the right, where n is the number of historical sample. A sample and some simulation results are also presented.     

Adjusted empirical likelihood inference for additive hazards regression

ABSTRACT

This article develops an adjusted empirical likelihood (EL) method for the additive hazards model. The adjusted EL ratio is shown to have a central chi-squared limiting distribution under the null hypothesis. We also evaluate its asymptotic distribution as a non central chi-squared distribution under the local alternatives of order n^{? 1/2}, deriving the expression for the asymptotic power function. Simulation studies and a real example are conducted to evaluate the finite sample performance of the proposed method. Compared with the normal approximation-based method, the proposed method tends to have more larger empirical power and smaller confidence regions with comparable coverage probabilities.     

A self-reliant projected information criterion for the number of factors

Abstract

In this article, we propose a new projected PCA to determine the number of factors. We project variables of interest into the space spanned by cross sectional averages of variables. And then we construct the eigenvalue tests and the information criteria to estimate the number of factors. We derive the large sample consistency and conduct finite sample simulations to demonstrate the better performances of our estimators. In order to show the edge of our estimators in real data analysis, we revisit a large house price data set for which the number of factors is hard to select.     

Forecast Error Variance Decompositions with Local Projections

Abstract

We propose and study properties of an estimator of the forecast error variance decomposition in the local projections framework. We find for empirically relevant sample sizes that, after being bias-corrected with bootstrap, our estimator performs well in simulations. We also illustrate the workings of our estimator empirically for monetary policy and productivity shocks. KEYWORDS: Forecast error variance decomposition; Local projections.     

A Note on Sample Size Determination for Akaike Information Criterion (AIC) Approach to Clinical Data Analysis

ABSTRACT

Because of its flexibility and usefulness, Akaike Information Criterion (AIC) has been widely used for clinical data analysis. In general, however, AIC is used without paying much attention to sample size. If sample sizes are not large enough, it is possible that the AIC approach does not lead us to the conclusions which we seek. This article focuses on the sample size determination for AIC approach to clinical data analysis. We consider a situation in which outcome variables are dichotomous and propose a method for sample size determination under this situation. The basic idea is also applicable to the situations in which outcome variables have more than two categories or outcome variables are continuous. We present simulation studies and an application to an actual clinical trial.     

On the Distribution of Matrix Quadratic Forms

A characterization of the distribution of the multivariate quadratic form given by X A X′, where X is a p × n normally distributed matrix and A is an n × n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of non central Wishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean.     

Clustering and classification problems in genetics through U-statistics

ABSTRACT

Genetic data are frequently categorical and have complex dependence structures that are not always well understood. For this reason, clustering and classification based on genetic data, while highly relevant, are challenging statistical problems. Here we consider a versatile U-statistics-based approach for non-parametric clustering that allows for an unconventional way of solving these problems. In this paper we propose a statistical test to assess group homogeneity taking into account multiple testing issues and a clustering algorithm based on dissimilarities within and between groups that highly speeds up the homogeneity test. We also propose a test to verify classification significance of a sample in one of two groups. We present Monte Carlo simulations that evaluate size and power of the proposed tests under different scenarios. Finally, the methodology is applied to three different genetic data sets: global human genetic diversity, breast tumour gene expression and Dengue virus serotypes. These applications showcase this statistical framework's ability to answer diverse biological questions in the high dimension low sample size scenario while adapting to the specificities of the different datatypes.     

Bandwidth selector for nonparametric recursive density estimation for spatial data defined by stochastic approximation method

Abstract

In this article we propose an automatic selection of the bandwidth of the recursive kernel density estimators for spatial data defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the MWISE (Mean Weighted Integrated Squared Error), the recursive estimator will be quite similar to the nonrecursive one in terms of estimation error and much better in terms of computational costs. In addition, we obtain the central limit theorem for the nonparametric recursive density estimator under some mild conditions.     

Signed compound poisson integer-valued GARCH processes

Abstract

We propose signed compound Poisson integer-valued GARCH processes for the modeling of the difference of count time series data. We investigate the theoretical properties of these processes and we state their ergodicity and stationarity under mild conditions. We discuss the conditional maximum likelihood estimator when the series appearing in the difference are INGARCH with geometric distribution and explore its finite sample properties in a simulation study. Two real data examples illustrate this methodology.     

Local linear double and asymmetric kernel estimation of conditional quantiles

Abstract

In this work, we propose and investigate a family of non parametric quantile regression estimates. The proposed estimates combine local linear fitting and double kernel approaches. More precisely, we use a Beta kernel when covariate’s support is compact and Gamma kernel for left-bounded supports. Finite sample properties together with asymptotic behavior of the proposed estimators are presented. It is also shown that these estimates enjoy the property of having finite variance and resistance to sparse design.     

A Degrees-Of-Freedom approximation in Multiple imputation

When using multiple imputation to form confidence intervals with missing data, Rubin and Schenker (1986) proposed using a t -distribution with approximate degrees-of-freedom which is a function of the number of multiple imputations and the within and between imputation variance. In this t -approximation, Rubin and Schenker assume there are a finite number of multiple imputations, but an infinite number of observations in the sample. We propose a further degrees-of-freedom approximation which is a function of the within and between imputation variance, the number of multiple imputations, and the number of observations in the sample. When the number of observations in the sample is small, our approximate degrees-of-freedom may be more appropriate, as seen in our simulations.     

Bootstrap confidence intervals for the coefficient of quartile variation

ABSTRACT

In non-normal populations, it is more convenient to use the coefficient of quartile variation rather than the coefficient of variation. This study compares the percentile and t-bootstrap confidence intervals with Bonett's confidence interval for the quartile variation. We show that empirical coverage of the bootstrap confidence intervals is closer to the nominal coverage (0.95) for small sample sizes (n = 5, 6, 7, 8, 9, 10 and 15) for most distributions studied. Bootstrap confidence intervals also have smaller average width. Thus, we propose using bootstrap confidence intervals for the coefficient of quartile variation when the sample size is small.     

The LAD estimation of the change-point linear model with randomly censored data

Abstract

In this paper, a change-point linear model with randomly censored data is investigated. We propose the least absolute deviation estimation procedure for regression and change-point parameters simultaneously. The asymptotic properties of the change-point and regression parameter estimators are obtained. We show that the resulting regression parameter estimator is asymptotically normal, and the change-point estimator converges weakly to the minimizer of a given random process. The extensive simulation studies and the analysis of an acute myocardial infarction data set are conducted to illustrate the finite sample performance of the proposed method.