Asymptotic coverage probabilities of bootstrap percentile confidence intervals for constrained parameters

The asymptotic behaviour of the commonly used bootstrap percentile confidence interval is investigated when the parameters are subject to linear inequality constraints. We concentrate on the important one- and two-sample problems with data generated from general parametric distributions in the natural exponential family. The focus of this paper is on quantifying the coverage probabilities of the parametric bootstrap percentile confidence intervals, in particular their limiting behaviour near boundaries. We propose a local asymptotic framework to study this subtle coverage behaviour. Under this framework, we discover that when the true parameters are on, or close to, the restriction boundary, the asymptotic coverage probabilities can always exceed the nominal level in the one-sample case; however, they can be, remarkably, both under and over the nominal level in the two-sample case. Using illustrative examples, we show that the results provide theoretical justification and guidance on applying the bootstrap percentile method to constrained inference problems.Comment: 22 pages, 6 figure

Genomic multiple sequence alignments: refinement using a genetic algorithm

BACKGROUND: Genomic sequence data cannot be fully appreciated in isolation. Comparative genomics – the practice of comparing genomic sequences from different species – plays an increasingly important role in understanding the genotypic differences between species that result in phenotypic differences as well as in revealing patterns of evolutionary relationships. One of the major challenges in comparative genomics is producing a high-quality alignment between two or more related genomic sequences. In recent years, a number of tools have been developed for aligning large genomic sequences. Most utilize heuristic strategies to identify a series of strong sequence similarities, which are then used as anchors to align the regions between the anchor points. The resulting alignment is globally correct, but in many cases is suboptimal locally. We describe a new program, GenAlignRefine, which improves the overall quality of global multiple alignments by using a genetic algorithm to improve local regions of alignment. Regions of low quality are identified, realigned using the program T-Coffee, and then refined using a genetic algorithm. Because a better COFFEE (Consistency based Objective Function For alignmEnt Evaluation) score generally reflects greater alignment quality, the algorithm searches for an alignment that yields a better COFFEE score. To improve the intrinsic slowness of the genetic algorithm, GenAlignRefine was implemented as a parallel, cluster-based program. RESULTS: We tested the GenAlignRefine algorithm by running it on a Linux cluster to refine sequences from a simulation, as well as refine a multiple alignment of 15 Orthopoxvirus genomic sequences approximately 260,000 nucleotides in length that initially had been aligned by Multi-LAGAN. It took approximately 150 minutes for a 40-processor Linux cluster to optimize some 200 fuzzy (poorly aligned) regions of the orthopoxvirus alignment. Overall sequence identity increased only slightly; but significantly, this occurred at the same time that the overall alignment length decreased – through the removal of gaps – by approximately 200 gapped regions representing roughly 1,300 gaps. CONCLUSION: We have implemented a genetic algorithm in parallel mode to optimize multiple genomic sequence alignments initially generated by various alignment tools. Benchmarking experiments showed that the refinement algorithm improved genomic sequence alignments within a reasonable period of time

Doctor of Philosophy

dissertationGiven the trend of globalization, more and more firms are outsourcing their Research and Development (R&D) projects to a second party overseas or domestically. Through outsourcing, firms not only save costs but also build strategic capabilities such as tapping global talents, building partnerships, boosting innovation, and maintaining a lean and flexible operation. These capabilities help shorten the duration of R&D projects and mitigate the risk of failures. However, the complexity of collaborative relationship in outsourcing and risks inherent in an R&D project pose challenges to both the firm who is doing the outsourcing (referred to as the principal) and the firm that the project is outsourced to (referred to as the agent). It is likely that either or both parties have private information regarding their capabilities as well as the likelihood of the success of the project. In addition, the efforts of the firm that the project is outsourced to may be unobservable to the firm who is doing outsourcing. In the dissertation, I investigate whether stage-gate contracts can help firms manage the outsourcing of R&D projects and determine the optimal form of the stage-gate contract when information asymmetry (adverse selection) and unobservable effort (moral hazard) exist. In Chapter 1, I explore the use of stage-gate contracts in the case where the agent has private information and his effort is unobservable. The principal offers multiple contracts to "screen" the agent. The main tool of the analysis is the screening model in the principalagent problem. In Chapter 2, I examine the opposite case, the one where the principle is the firm with the private information (the agent's effort is again unobservable). In this situation a principal may use the stage-gate contract to signal her private information with regard to the new product development project. The main tool of the analysis is the signaling games. In Chapter 3, I investigate the case of bilateral asymmetric information, namely, both the principal and the agent have their own private information on the project. The main tool of the analysis is the screening model and the signaling games

Uniform lower bound for the least common multiple of a polynomial sequence

Let $n$ be a positive integer and $f(x)$ be a polynomial with nonnegative integer coefficients. We prove that ${\rm lcm}_{\lceil n/2\rceil \le i\le n} \{f(i)\}\ge 2^n$ except that $f(x)=x$ and $n=1, 2, 3, 4, 6$ and that $f(x)=x^s$ with $s\ge 2$ being an integer and $n=1$, where $\lceil n/2\rceil$ denotes the smallest integer which is not less than $n/2$. This improves and extends the lower bounds obtained by Nair in 1982, Farhi in 2007 and Oon in 2013.Comment: 6 pages. To appear in Comptes Rendus Mathematiqu

The elementary symmetric functions of a reciprocal polynomial sequence

Erd\"{o}s and Niven proved in 1946 that for any positive integers $m$ and $d$, there are at most finitely many integers $n$ for which at least one of the elementary symmetric functions of $1/m, 1/(m+d), ..., 1/(m+(n-1)d)$ are integers. Recently, Wang and Hong refined this result by showing that if $n\geq 4$, then none of the elementary symmetric functions of $1/m, 1/(m+d), ..., 1/(m+(n-1)d)$ is an integer for any positive integers $m$ and $d$. Let $f$ be a polynomial of degree at least $2$ and of nonnegative integer coefficients. In this paper, we show that none of the elementary symmetric functions of $1/f(1), 1/f(2), ..., 1/f(n)$ is an integer except for $f(x)=x^{m}$ with $m\geq2$ being an integer and $n=1$.Comment: 4 pages. To appear in Comptes Rendus Mathematiqu