The number of records within a random interval of the current record value

LetX ₁,X ₂, … be a sequence of i.i.d. random variables with some continuous distribution functionF. LetX(n) be then-th record value associated with this sequence and μ _n ⁻ , μ _n ⁺ be the variables that count the number of record values belonging to the random intervals(f−(X(n)), X(n)), (X(n), f+(X(n))), wheref−, f+ are two continuous functions satisfyingf−(x)<x, f+(x)>x. Properties of μ _n ⁻ , μ _n ⁺ are studied in the present paper. Some statistical applications connected with these variables are also provided.     

Emergence of entrepreneurial behaviour: The role of age-based self-image

This study introduces an individual’s perception of their entrepreneurial potential in terms of their age (age-based self-image) to complement chronological age as a predictor of entrepreneurial behaviour. The principal hypothesis is that a positive age-based self-image enhances the likelihood of individuals turning their intention to start a business into actual behaviour. The empirical analysis based on data collected on the general adult population of Finland in 2011 and 2012 (n = 672) supports this hypothesis. The analysis further shows that this positive effect is independent of the individual’s chronological age, and it is thus applicable to both age groups that are under-represented in entrepreneurship: ‘youngsters’ and ‘seniors’. Promoting the development of a positive age-based self-image is a prospective policy option for fostering entrepreneurship among younger and older age groups. More in-depth research, especially concerning the antecedents of positive age-based self-image, is required for the effectiveness of such policy interventions.     

Penalized contrast estimation in functional linear models with circular data

Our aim is to estimate the unknown slope function in the functional linear model when the response Y is real and the random function X is a second-order stationary and periodic process. We obtain our estimator by minimizing a standard (and very simple) mean-square contrast on linear finite dimensional spaces spanned by trigonometric bases. Our approach provides a penalization procedure which allows to automatically select the adequate dimension, in a non-asymptotic point of view. In fact, we can show that our penalized estimator reaches the optimal (minimax) rate of convergence in the sense of the prediction error. We complete the theoretical results by a simulation study and a real example that illustrates how the procedure works in practice.     

Stationary bootstrapping for panel cointegration tests under cross-sectional dependence

Stationary bootstrapping is applied to panel cointegration tests which are based on the ordinary least-squares estimator and the seemingly unrelated regression (SUR) estimator of the residual unit root. Large sample validity of stationary bootstrapping is established. A finite sample experiment reveals that size performances of the bootstrap tests are much less sensitive to cross-sectional correlation than those of existing tests and a test based on the SUR estimator has substantially better power than existing tests.     

Measures of Association and Visualization of Log Odds Ratio Structure for a Two Way Contingency Table

The odds ratio (OR) is a measure of association used for analysing an I × J contingency table. The total number of ORs to check grows with I and J. Several statistical methods have been developed for summarising them. These methods begin from two different starting points, the I × J contingency table and the two‐way table composed by the ORs. In this paper we focus our attention on the relationship between these methods and point out that, for an exhaustive analysis of association through log ORs, it is necessary to consider all the outcomes of these methods. We also introduce some new methodological and graphical features. In order to illustrate previously used methodologies, we consider a data table of the cross‐classification of the colour of eyes and hair of 5387 children from Scotland. We point out how, through the log OR analysis, it is possible to extract useful information about the association between variables.     

Adaptive Warped Kernel Estimators

In this work, we develop a method of adaptive non‐parametric estimation, based on ‘warped’ kernels. The aim is to estimate a real‐valued function s from a sample of random couples (X,Y). We deal with transformed data (Φ(X),Y), with Φ a one‐to‐one function, to build a collection of kernel estimators. The data‐driven bandwidth selection is performed with a method inspired by Goldenshluger and Lepski (Ann. Statist., 39, 2011, 1608). The method permits to handle various problems such as additive and multiplicative regression, conditional density estimation, hazard rate estimation based on randomly right‐censored data, and cumulative distribution function estimation from current‐status data. The interest is threefold. First, the squared‐bias/variance trade‐off is automatically realized. Next, non‐asymptotic risk bounds are derived. Lastly, the estimator is easily computed, thanks to its simple expression: a short simulation study is presented.     

Data Dependent Cells Chi‐Square Test With Recurrent Events

We consider a recurrent event wherein the inter‐event times are independent and identically distributed with a common absolutely continuous distribution function F. In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q‐dimensional parameter is unknown. We propose a general Chi‐squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi‐square estimator. Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures.     

Estimating the Size of Street-Dwelling Populations Using Mark-Resighting Counts

Mark-resighting constitutes an advanced technology for estimating animal abundance. Joint hypergeometric maximum likelihood, Minta-Mangel and Bowden estimators are usually adopted with mark-resighting data. In presence of any tendency of animals to aggregate into groups, the Bowden estimator is the sole reliable method, providing that marks are quite evenly distributed among groups. In some cetacean surveys, marking disturbances are avoided through natural marking. Natural marking with Bowden criterion is used to estimate the abundance of street-dwelling populations. The marked individuals are persons identified and recorded in the initial part of the survey and recognizable in subsequent occasions. A simulation helps determine the performance of the Bowden estimator under a wide set of situations, taking into account key features of street-dwelling populations. When marked individuals are evenly distributed among groups, the strategy is efficient.