Different estimators of the spectral matrix: an empirical comparison testing a new shrinkage estimator

ABSTRACT

In this paper we propose a new non parametric estimator of the spectral matrix of a multivariate stationary stochastic process, with the main goal to locally improve the deficiencies of the smoothed periodogram in terms of mean square error of the estimates. Our estimator is based on a convex linear combination of the frequency averaged periodogram and an estimate of the true mean spectral matrix across frequencies. In a wide simulation study we show that our estimator turns out to be able to markedly improve the frequency averaged periodogram especially at central frequencies.     

Estimation of k-Factor GIGARCH Process: A Monte Carlo Study

In this article, we discuss the parameter estimation for a k-factor generalized long-memory process with conditionally heteroskedastic noise. Two estimation methods are proposed. The first method is based on the conditional distribution of the process and the second is obtained as an extension of Whittle's estimation approach. For comparison purposes, Monte Carlo simulations are used to evaluate the finite sample performance of these estimation techniques, using four different conditional distribution functions.     

The Contribution of Irish Immigrants to the Quebec (Canada) Gene Pool: An Estimation Using Data from Deep-Rooted Genealogies

European settlement in Quebec (Canada) began in the early 17th century, with the arrival of French pioneers. After the British Conquest in 1760, immigrants from the British Isles began to settle in some parts of Quebec. Many of these immigrants were Irish Catholics. Historians and genealogists have identified several names of Irish origin in the French Canadian population, and many scholars have wondered about the importance of the integration of Irish migrants and their descendants within this population. The purposes of this study are to identify and characterize the founders of Irish origin to estimate the importance of their genetic contribution to the contemporary Quebec population, and to measure the variability of this contribution according to the founders’ period of arrival and county of origin in Ireland. Data was obtained from a set of 2,223 ascending genealogies going back as far as the early 17th century. The average genealogical depth is a little more than 9 generations, with many branches reaching 16 or 17 generations. Although Irish founders explain less than 1% of the total Quebec gene pool, results show that nearly 21% of the genealogies contain at least one Irish founder. These founders contributed to the peopling of all regions of Quebec, but there are some important variations from one region to another. A majority of the Irish founders immigrated during the 19th century, and most of them came from the counties of Southern Ireland.     

How are Time-Dependent Childbearing Intentions Realized? Realization,Postponement, Abandonment,Bringing Forward

Our study aims to identify factors that facilitate or inhibit the realization of fertility intentions. The analysis uses data collected in the first two waves of a Hungarian longitudinal survey. Fertility intentions recorded at the first wave pertain to the subsequent 3-year period, just similar to the behavior variable measuring the realization of intentions, i.e., a birth within the 3-year period in question. For this analysis, we used the respondents’ demographic, socio-structural, and orientational traits recorded at the first interview. Our findings show that age, parity, and partnership play a determining role in the realization of fertility intentions, but employment status, religious affiliation, and overall life satisfaction all exhibit significant effects. A marked gender difference was detected not only with regard to employment status but in the area of values and orientations as well.     

A Model of Minimal Probabilistic Belief Revision

In the literature there are at least two models for probabilistic belief revision: Bayesian updating and imaging [Lewis, D. K. (1973), Counterfactuals, Blackwell, Oxford; Gärdenfors, P. (1988), Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, Cambridge, MA]. In this paper we focus on imaging rules that can be described by the following procedure: (1) Identify every state with some real valued vector of characteristics, and accordingly identify every probabilistic belief with an expected vector of characteristics; (2) For every initial belief and every piece of information, choose the revised belief which is compatible with this information and for which the expected vector of characteristics has minimal Euclidean distance to the expected vector of characteristics of the initial belief. This class of rules thus satisfies an intuitive notion of minimal belief revision. The main result in this paper is to provide an axiomatic characterization of this class of imaging rules.     

Bayesian adaptive bandwidth selector for multivariate discrete kernel estimator

We treat a non parametric estimator for joint probability mass function, based on multivariate discrete associated kernels which are appropriated for multivariate count data of small and moderate sample sizes. Bayesian adaptive estimation of the vector of bandwidths using the quadratic and entropy loss functions is considered. Exact formulas for the posterior distribution and the vector of bandwidths are obtained. Numerical studies indicate that the performance of our approach is better, comparing with other bandwidth selection techniques using integrated squared error as criterion. Some applications are made on real data sets.     

Effect of autocorrelation when estimating the trend of a time series via penalized least squares with controlled smoothness

This paper studies the effect of autocorrelation on the smoothness of the trend of a univariate time series estimated by means of penalized least squares. An index of smoothness is deduced for the case of a time series represented by a signal-plus-noise model, where the noise follows an autoregressive process of order one. This index is useful for measuring the distortion of the amount of smoothness by incorporating the effect of autocorrelation. Different autocorrelation values are used to appreciate the numerical effect on smoothness for estimated trends of time series with different sample sizes. For comparative purposes, several graphs of two simulated time series are presented, where the estimated trend is compared with and without autocorrelation in the noise. Some findings are as follows, on the one hand, when the autocorrelation is negative (no matter how large) or positive but small, the estimated trend gets very close to the true trend. Even in this case, the estimation is improved by fixing the index of smoothness according to the sample size. On the other hand, when the autocorrelation is positive and large the simulated and estimated trends lie far away from the true trend. This situation is mitigated by fixing an appropriate index of smoothness for the estimated trend in accordance to the sample size at hand. Finally, an empirical example serves to illustrate the use of the smoothness index when estimating the trend of Mexico’s quarterly GDP.     

A practical comparison of blinded methods for sample size reviews in survival data clinical trials

This paper presents practical approaches to the problem of sample size re-estimation in the case of clinical trials with survival data when proportional hazards can be assumed. When data are readily available at the time of the review, on a full range of survival experiences across the recruited patients, it is shown that, as expected, performing a blinded re-estimation procedure is straightforward and can help to maintain the trial's pre-specified error rates. Two alternative methods for dealing with the situation where limited survival experiences are available at the time of the sample size review are then presented and compared. In this instance, extrapolation is required in order to undertake the sample size re-estimation. Worked examples, together with results from a simulation study are described. It is concluded that, as in the standard case, use of either extrapolation approach successfully protects the trial error rates.     

Discounting health and money: New evidence using a more robust method

This study compares discounting for money and health in a field study. We applied the direct method, which measures discounting independent of utility, in a representative French sample, interviewed at home by professional interviewers. We found more discounting for money than for health. The median discount rates (6.5% for money and 2.2% for health) were close to market interest rates, suggesting that at the aggregate level the direct method solves the puzzle of unrealistically high discount rates typically observed in applied economics. Constant discounting fitted the data better than the hyperbolic discounting models that we considered. The substantial individual heterogeneity in discounting was correlated with age and occupation.     

Guilt and shame: an axiomatic analysis

Using the machinery of Game Theory, this article analyzes how shame and guilt affect preferences. Based on abundant psychological literature, we posit that the preference ordering of someone who can feel shame (or guilt) must satisfy a number of axioms and prove that it can be represented by a particular utility function. Understanding how shame and guilt work is important to explain why people respect social norms and exhibit prosocial behavior, many times contrary to their material interest.