Adaptive Designs for Optimal Observed Fisher Information

Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information is a better approximation to the variance of the maximum likelihood estimator. Observed Fisher information cannot be known a priori; however, if an experiment is conducted sequentially (in a series of runs) the observed Fisher information from previous runs is available. In the current work two adaptive designs are proposed that use the observed Fisher information from previous runs in the design of the current run.Comment: 19 pages, 2 figure

An Effective Lagrangian for Low-Scale Technicolor

We present an effective Lagrangian for low-scale technicolor. It describes the interactions at energies near the mass of the lowest-lying bound states of the lightest technifermion doublet -- the spin-one $\rho_T,\omega_T, a_T, f_T$ and the corresponding technipions $\pi_T$. This Lagrangian is intended to put on firmer ground the technicolor straw-man phenomenology used for collider searches of low-scale technicolor. The technivectors are described using the hidden local symmetry (HLS) formalism of Bando et al. The Lagrangian is based on $SU(2)\otimes U(1)\otimes U(2)_L \otimes U(2)_R$, where $SU(2)\otimes U(1)$ is the electroweak gauge group and $U(2)_L \otimes U(2)_R$ is the HLS gauge group. Special attention is paid to the higher-derivative standard HLS and Wess-Zumino-Witten interactions needed to describe radiative and other decays of the $a_T$ and $\rho_T/\omega_T$, respectively.Comment: Updated introduction, to appear in Phys. Rev.

Accidental Goldstone Bosons

We study vacuum alignment in theories in which the chiral symmetry of a set of massless fermions is both spontaneously and explicitly broken. We find that transitions occur between different phases of the fermions' CP symmetry as parameters in their symmetry breaking Hamiltonian are varied. We identify a new phase that we call pseudoCP-conserving. We observe first and second-order transitions between the various phases. At a second-order (and possibly first-order) transition a pseudoGoldstone boson becomes massless as a consequence of a spontaneous change in the discrete, but not the continuous, symmetry of the ground state. We relate the masslessness of these ``accidental Goldstone bosons'' (AGBs) bosons to singularities of the order parameter for the phase transition. The relative frequency of CP-phase transitions makes it commonplace for the AGBs to be light, much lighter than their underlying strong interaction scale. We investigate the AGBs' potential for serving as light composite Higgs bosons by studying their vacuum expectation values, finding promising results: AGB vevs are also often much less than their strong scale.Comment: 27 pages, latex, with 12 postscript figure

CP violation and mixing in technicolor models

Vacuum alignment in technicolor models provides an attractive origin for the quarks' CP violation and, possibly, a natural solution for the strong-CP problem of QCD. We discuss these topics in this paper. Then we apply them to determine plausible mixing matrices for left and right-handed quarks. These matrices determine the Cabibbo-Kobayashi-Maskawa matrix as well as new mixing angles and phases that are observable in extended technicolor (ETC) and topcolor (TC2) interactions. We determine the contributions of these new interactions to CP-violating and mixing observables in the K0, Bd and Bs systems. Consistency with mixing and CP violation in the K0 system requires assuming that ETC interactions are electroweak generation-conserving even if technicolor has a walking gauge coupling. Large ETC gauge boson masses and small intergenerational mixing then result in negligibly small ETC contributions to B-meson mixing and CP violation and to Re(ϵ′/ϵ). We confirm our earlier strong lower bounds on TC2 gauge boson masses from Bd–¯¯¯Bd mixing. We then pay special attention to the possibility that current experiments indicate a deviation from standard model expectations of the values of sin2β measured in Bd→J/ψKS, ϕKS, η′KS, and πKS, studying the ability of TC2 to account for these. We also determine the TC2 contribution to ΔMBs and to Re(ϵ′/ϵ), and find them to be appreciable.First author draf

Technicolor at the Tevatron

We propose that the 3.2 sigma excess at ~150 GeV in the dijet mass spectrum of W + jets reported by CDF is the technipion $\pi_T$ of low-scale technicolor. Its relatively large cross section is due to production of a narrow $Wjj$ resonance, the technirho, which decays to W + $\pi_T$. We discuss ways to enhance and strengthen the technicolor hypothesis and suggest companion searches at the Tevatron and LHC.Comment: 5 pages, 6 figures. Note added regarding Z(l+l-)+jj signals at the Tevatron and LH

Testing the Technicolor Interpretation of CDF's Dijet Excess at the LHC

Under the assumption that the dijet excess seen by the CDF Collaboration near 150 Gev in Wjj production is due to the lightest technipion of the low-scale technicolor process $\rho_T \rightarrow W \pi_T$, we study its observability in LHC detectors with 1--20 inverse femtobarns of data. We describe interesting new kinematic tests that can provide independent confirmation of this LSTC hypothesis. We find that cuts similar to those employed by CDF, and recently by ATLAS, cannot confirm the dijet signal. We propose cuts tailored to the LSTC hypothesis and its backgrounds at the LHC that may reveal $\rho_T \rightarrow \ell\nu jj$. Observation of the isospin-related channel $\rho^{pm}_T \rightarrow Z \pi^{pm}_T \rightarrow \ell^+ \ell^- jj$ and of $\rho^{pm}_T \rightarrow WZ$ in the three lepton plus neutrino and dilepton plus dijet modes will be important confirmations of the LSTC interpretation of the CDF signal. The $Z\pi_T$ channel is experimentally cleaner than $W\pi_T$ and its rate is known from $W\pi_T$ by phase space. It can be discovered or excluded with the collider data expected in 2012. The $WZ \rightarrow 3\ell\nu$ channel is cleanest of all and its rate is determined from $W\pi_T$ and the LSTC parameter $\sin\chi$. This channel and $WZ \rightarrow \ell^+\ell^- jj$ are discussed as a function of $\sin\chi$.Comment: 24 pages, 24 figure

Testing the Technicolor Interpretation of the CDF Dijet Excess at the 8-TeV LHC

Under the assumption that the dijet excess seen by the CDF Collaboration near 150 Gev in Wjj production is due to the lightest technipion of the low-scale technicolor process $\rho_T \rightarrow W \pi_T$, we study its observability in LHC detectors for 8 TeV collisions and 20 inverse femtobarns of integrated luminosity. We describe interesting new kinematic tests that can provide independent confirmation of this LSTC hypothesis. We show that cuts similar to those employed by CDF, and recently by ATLAS, cannot confirm the dijet signal. We propose cuts tailored to the LSTC hypothesis and its backgrounds at the LHC that may reveal $\rho_T \rightarrow \ell\nu jj$. Observation of the isospin-related channel $\rho^{\pm}_T \rightarrow Z \pi^{\pm}_T \rightarrow \ell^+\ell^- jj$ and of $\rho^{\pm}_T \rightarrow WZ$ in the $\ell^+\ell^-\ell^{pm}\nu_\ell$ and $\ell^+\ell^- jj$ modes will be important confirmations of the LSTC interpretation of the CDF signal. The $Z\pi_T$ channel is experimentally cleaner than $W\pi_T$ and its rate is known from $W\pi_T$ by phase space. It can be discovered or excluded with the collider data expected by the end of 2012. The $WZ \rightarrow 3\ell\nu$ channel is cleanest of all and its rate is determined from $W\pi_T$ and the LSTC parameter $\sin\chi$. This channel and $WZ \to \ell^+\ell^- jj$ are discussed as a function of $\sin\chi$.Comment: 28 pages, 27 figures, submitted to PRD. arXiv admin note: substantial text overlap with arXiv:1201.439

Conditional Information and Inference in Response-Adaptive Allocation Designs

Response-adaptive allocation designs refer to a class of designs where the probability an observation is assigned to a treatment is changed throughout an experiment based on the accrued responses. Such procedures result in random treatment sample sizes. Most of the current literature considers unconditional inference procedures in the analysis of response-adaptive allocation designs. The focus of this work is inference conditional on the observed treatment sample sizes. The inverse of information is a description of the large sample variance of the parameter estimates. A simple form for the conditional information relative to unconditional information is derived. It is found that conditional information can be greater than unconditional information. It is also shown that the variance of the conditional maximum likelihood estimate can be less than the variance of the unconditional maximum likelihood estimate. Finally, a conditional bootstrap procedure is developed that, in the majority of cases examined, resulted in narrower confidence intervals than relevant unconditional procedures.Comment: 20 pages, 1 figure, 3 tables, 1 supplemental document 4 pages, 3 table

Efficiency of Observed Information Adaptive Designs

In this work the primary objective is to maximize the precision of the maximum likelihood estimate in a linear regression model through the efficient design of the experiment. One common measure of precision is the unconditional mean square error. Unconditional mean square error has been a primary motivator for optimal designs; commonly, defined as the design that maximizes a concave function of the expected Fisher information. The inverse of expected Fisher information is asymptotically equal to the mean square error of the maximum likelihood estimate. There is a substantial amount of existing literature that argues the mean square error conditioned on an appropriate ancillary statistic better represents the precision of the maximum likelihood estimate. Despite evidence in favor of conditioning, limited effort has been made to find designs that are optimal with respect to conditional mean square error. The inverse of observed Fisher information is a higher order approximation of the conditional mean square error than the inverse of expected Fisher information [Efron and Hinkley (1978)]. In light of this, a more relevant objective is to find designs that optimize observed Fisher information. Unlike expected Fisher information, observed Fisher information depends on the observed data and cannot be used to design an experiment completely in advance of data collection. In a sequential experiment the observed Fisher information from past observations is available to inform the design of the next observation. In this work an adaptive design that incorporates observed Fisher information is proposed for linear regression models. It is shown that the proposed design is more efficient, at the limit, than any fixed design, including the optimal design, with respect to conditional mean square error.Comment: 25 pages, 3 figures, 1 Table, 1 supplemen

Is Achievement Motivation in Basketball Games Affected by Team or Individual Competitive Situations in Elementary Physical Education Classes?

This study examined the relationship between skill, setting and gender. There were three main purposes for conducting this study. The first was to determine whether a child\u27s achievement motivation changes when participating in a team setting compared to an individual setting. The second purpose was to determine and compare any differences between boys\u27 and girls\u27 achievement motivation, in both team and individual settings, and thirdly, to determine and compare any differences between the achievement motivation of high-skilled and low-skilled children, in both team and individual settings. Subjects were administered the Sport Orientation Questionnaire, (Gill and Deeter, 1988), which assesses competitiveness, win-orientation and goal-orientation. Subjects in this study included a total of 117, (70 female, 47 male), 5th and 6th grade students at Jefferson Elementary School in Charleston, Illinois. Participants were categorized into high and low skill ability, (66 high skilled and 51 low skilled participants). Each student completed the Sport Orientation Questionnaire twice, once for team setting and once for individual setting. Students completed the SOQ, referring to feelings about team basketball competition, after four classes involving five-on-five basketball games. Students completed the SOQ a second time after four classes, which were structured on one-on-one competition. In regards to the primary hypothesis, it was determined that a child\u27s achievement motivation does change when participating in a team setting compared to an individual setting. Results using a 3 way MANOVA indicated six significant differences: 1. Boys are more competitive than girls. 2. High-skilled children are more competitive than low-skilled children. 3. High-skilled children prefer to compete in an individual setting while low-skilled children prefer to compete in a team setting. 4. Both genders and skill levels have a stronger desire to win in a team setting compared to an individual setting. 5. Low-skilled children possess a higher motive to accomplish personal goals in a team setting compared to an individual setting. 6. High-skill participants possess a higher motive to achieve personal goals than low-skilled participants