Statistical inference for oscillation processes

ABSTRACT

A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a generalized state space model. Identifiability of the model is proved and a method for statistical inference based on a particle smoother and a nonparametric EM algorithm is developed. In particular, the oscillation pattern and the unobserved phase process are estimated. The proposed algorithms are computationally efficient and their performance is assessed through simulations and an application to human electrocardiogram recordings.     

Do As I Say and Not As I Think: Parent Socialisation of Lie‐Telling Behaviour

This study explored parent (N = 146) perspectives about situations in which they think it is acceptable to lie, how this corresponds to how they socialise their children about lie‐telling and their children's actual behaviour. Results indicated the methods parents report using to teach their children about the acceptability of lie‐telling are consistent with what they report teaching their children about lie‐telling overall. Also, the frequency of lies that children told (N = 88) to protect themselves from psychological distress or conflict differed between those who were taught that lying is sometimes acceptable versus those taught it is never acceptable.     

Safe sets in graphs: Graph classes and structural parameters

A safe set of a graph \(G=(V,E)\) is a non-empty subset S of V such that for every component A of G[S] and every component B of \(G[V {\setminus } S]\), we have \(|A| \ge |B|\) whenever there exists an edge of G between A and B. In this paper, we show that a minimum safe set can be found in polynomial time for trees. We then further extend the result and present polynomial-time algorithms for graphs of bounded treewidth, and also for interval graphs. We also study the parameterized complexity. We show that the problem is fixed-parameter tractable when parameterized by the solution size. Furthermore, we show that this parameter lies between the tree-depth and the vertex cover number. We then conclude the paper by showing hardness for split graphs and planar graphs.     

Wavelet shrinkage for unequally spaced data

Wavelet shrinkage (WaveShrink) is a relatively new technique for nonparametric function estimation that has been shown to have asymptotic near-optimality properties over a wide class of functions. As originally formulated by Donoho and Johnstone, WaveShrink assumes equally spaced data. Because so many statistical applications (e.g., scatterplot smoothing) naturally involve unequally spaced data, we investigate in this paper how WaveShrink can be adapted to handle such data. Focusing on the Haar wavelet, we propose four approaches that extend the Haar wavelet transform to the unequally spaced case. Each approach is formulated in terms of continuous wavelet basis functions applied to a piecewise constant interpolation of the observed data, and each approach leads to wavelet coefficients that can be computed via a matrix transform of the original data. For each approach, we propose a practical way of adapting WaveShrink. We compare the four approaches in a Monte Carlo study and find them to be quite comparable in performance. The computationally simplest approach (isometric wavelets) has an appealing justification in terms of a weighted mean square error criterion and readily generalizes to wavelets of higher order than the Haar.     

Paired-domination in generalized claw-free graphs

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998) 199–206). A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G, denoted by , is the minimum cardinality of a paired-dominating set of G. If G does not contain a graph F as an induced subgraph, then G is said to be F-free. Haynes and Slater (Networks 32 (1998) 199–206) showed that if G is a connected graph of order , then and this bound is sharp for graphs of arbitrarily large order. Every graph is -free for some integer a ≥ 0. We show that for every integer a ≥ 0, if G is a connected -free graph of order n ≥ 2, then with infinitely many extremal graphs.     

A note on monotonicity in iterated choice functions

This short paper proves the following conjecture of D. Bouyssou: a preference aggregation function built by iteration of a strictly monotonic and symmetric social choice correspondence cannot be strictly monotonic. Received: 1 October 1998/Accepted: 23 December 1999     

Calibrated Incentive Contracts

This paper studies a dynamic agency problem which includes limited liability, moral hazard, and adverse selection. The paper develops a robust approach to dynamic contracting based on calibrating the incentive properties of simple benchmark contracts that are attractive but infeasible, due to limited liability constraints. The resulting dynamic contracts are detail‐free and satisfy robust performance bounds independently of the underlying process for returns, which need not be i.i.d. or even ergodic.