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A number of viruses and viroids infect solanaceous plants causing severe yield losses. Several seed-borne viroids are listed as quarantine pathogens in many countries. Among them, columnea latent viroid, pepper chat fruit viroid, potato spindle tuber viroid, tomato apical stunt viroid, tomato chlorotic dwarf viroid, and tomato planta macho viroid are of major concerns. The objective of this study was to design and test universal primers that could be used to detect six viroids in solanaceous plants using one-step reverse transcription PCR (RT-PCR) and reverse transcription loop-mediated isothermal amplification (RT-LAMP). Results revealed that a pair of degenerate primers could be used in a one-step RT-PCR to amplify six pospiviroids from Solanaceae seeds and plants. Moreover, five primers were designed and used in RT-LAMP to amplify six pospiviroids. The minimal concentration of viroid RNA required for a successful detection varied, ranging from 1 fg to 10 ng, depending on the species of viroid and detection method. In general, RT-LAMP was more sensitive than RT-PCR, but both assays were rapid and highly sensitive tools to detect six pospiviroids. Detection methods in use for these viroids require at least two different sets of primers. The assays developed in this research could facilitate the ability to screen a large number of solanaceous plants and seeds intended for import and export.

Calibration refers to the estimation of unknown parameters which are present in computer experiments but not available in physical experiments. An accurate estimation of these parameters is important because it provides a scientific understanding of the underlying system which is not available in physical experiments. Most of the work in the literature is limited to the analysis of continuous responses. Motivated by a study of cell adhesion experiments, we propose a new calibration framework for binary responses. Its application to the T cell adhesion data provides insight into the unknown values of the kinetic parameters which are difficult to determine by physical experiments due to the limitation of the existing experimental techniques., Comment: 39 pages, 7 figures

The use of characteristic period τ c and peak displacement amplitude Pd of the initial P wave in earthquake early warning (EEW) was proposed by Wu and Kanamori [1–4] . Here we apply this approach to strong-motion records from a building sensor array installed in Taitung County, Taiwan. This building was damaged during the 2006 M w =6.1 Taitung earthquake with a peak ground velocity (PGV) of up to 38.4 cm/s at an epicentral distance of 14.5 km. According to our analysis, the peak displacement amplitude Pd is a better indicator for the destructiveness of an earthquake than τ c because τ c is more sensitive to the signal-to-noise ratio (SNR) than Pd . In accordance with previous studies, only the structurally damaging Taitung earthquake generated a Pd value larger than 0.5 cm (a threshold for identifying damaging events). Using Pd as an indicator for destructive earthquakes does not lead to missing or false alarms for EEW purposes.

This paper presents selected results measured from a monitoring system with 30 accelerometers installed at six floor levels in 508-m high Taipei 101 Tower located in Taipei City, Taiwan where earthquakes and strong typhoons are common occurrences. Emphasis is placed on analyzing the data recorded during three typhoons (Matsa, Talim, and Krosa) and a seismic event (Wenchuan earthquake occurred on May 12, 2008 in Shichuan, China) to investigate the effects of wind and seismic on the supertall building. Dynamic characteristics of the tall building such as natural frequencies, mode shapes, and damping ratios determined from the measured data are presented and compared with those calculated from the finite-element model of the high-rise structure. The seismic performance of this supertall building to a long distance earthquake (Wenchuan earthquake) is assessed based on the field measurements and numerical analysis. The findings of this study are expected to be of considerable interest and practical use to prof...

Measurements in the near field of earthquakes in Japan (Takeo, 1998) and in Taiwan (Huang et al. , 2006; Liu et al. , 2009) indicate that rotational ground motions are many times larger than expected from the classical elasticity theory. The Central Weather Bureau (CWB) deployed four instrumentation sets on the campus of the National Chung-Cheng University, Chia-yi, Taiwan, in order to study in detail earthquakes in the near field for both seismology and earthquake engineering. Both rotational and translational ground motions are being monitored along the active Meishan fault, where a major earthquake occurred in 1906, more than a century ago. The deployed instruments are: (1) a 32-element seismic array in the free field, (2) a 32-element seismic array in a building, (3) a six-channel unit with a broadband seismometer and an accelerometer, and (4) a six-channel unit with an accelerometer and an external rotational velocity sensor. This short note is a progress report on this array deployment. Although 24 local earthquakes were recorded by one or more of the four instrumentation sets from 12 December 2007 to 3 July 2008, we are still in the process of upgrading equipment and improving field operations.

Rotational motions generated by large earthquakes in the far field have been successfully measured, and observations agree well with the classical elasticity theory. However, recent rotational measurements in the near field of earthquakes in Japan and in Taiwan indicate that rotational ground motions are 10 to 100 times larger than expected from the classical elasticity theory. The near-field strong-motion records of the 1999 Mw 7:6 Chi-Chi, Taiwan, earthquake suggest that the ground motions along the 100 km rupture are complex. Some rather arbitrary baseline corrections are necessary in order to obtain reasonable displacement values from double integra- tion of the acceleration data. Because rotational motions can contaminate acceleration observations due to the induced perturbation of the Earth's gravitational field, we started a modest program to observe rotational ground motions in Taiwan. Three papers have reported the rotational observations in Taiwan: (1) at the HGSD station (Liu et al., 2009), (2) at the N3 site from two TAiwan Integrated GEodynamics Research (TAIGER) explosions (Lin et al., 2009), and (3) at the Taiwan campus of the National Chung-Cheng University (NCCU )( Wuet al., 2009). In addition, Langston et al. (2009) reported the results of analyzing the TAIGER explosion data. As noted by several authors before, we found a linear relationship between peak rotational rate (PRR in mrad=sec) and peak ground acceleration (PGA in m=sec 2 ) from local earthquakes in Taiwan, PRR 0:002 1:301 PGA, with a correlation coefficient of 0.988.

Since 1990, digital strong-motion accelerographs and global positioning system (GPS) instruments have been widely deployed in the Taiwan region (Shin et al. 2003; Yu et al. 2001). The 1999 Chi-Chi, Mw 7.6 earthquake and the 2003 Chengkung, Mw 6.8 earthquake were well recorded by both digital accelerographs and GPS instruments. These data offer a good opportunity to determine coseismic displacements from strong-motion records and to compare the results with those derived from GPS measurements. As noted by Boore (2001), a double integration of the acceleration data often leads to unreasonable results, and baseline corrections are therefore required in most cases before the integration. Based on the works of Iwan et al. (1985) and Boore (2001), we developed an improved method for baseline correction and validated it using an extensive set of data from shake-table tests of a known “step” displacement on 249 accelerographs. Our baseline correction method recovered about 97% of the actual displacement from the shake-table data. We then applied this baseline correction method to compute coseismic displacements from the strong-motion data of the Chi-Chi and Chengkung earthquakes. Our results agree favorably with the coseismic displacements determined by the GPS measurements at nearby sites. The ratio of seismic to geodetic displacement varies from 0.78 to 1.41, with an average of about 1.05.

The local magnitude scale M L is an empirically derived scale anchored to a zero magnitude reference event. Richter defined the amplitude of ground shaking at an epicentral distance of 100 km for a zero magnitude earthquake in southern California. The crustal attenuation characteristics of Taiwan result in a relatively high ML when compared to moment magnitude, Mw. We therefore define a revised ML scale for crustal earthquakes in the Taiwan region that is more consistent with Mw. Using observed peak ground shaking and Mw, we determine a new log A0 curve of ground shaking versus hypocentral distance, R, for a zero magnitude earthquake, and station correction factors. The log A0 curve determined in this study is, log A (R) 0.332 1.568 • log(R) 0.280. 0 Using this new log A0 curve and station corrections, the new ML is more consistent with Mw, with a 0.2 magnitude unit uncertainty. The new log A0 curve has a value of 2.80 at the distance of 100 km compared to the anchor point of log A0 3 at the same distance as defined by Richter for southern California. This means that the current ML estimates in Taiwan (which use Richter's definition) average 0.2 magnitude units larger than their Mw. The station correction factors also determined are large, from 0.40 to 0.52 magnitude units. The use of station corrections in routine seismic network operation in Taiwan will improve magnitude estimates. This is particularly important for smaller events when recording stations may be pre- dominantly on either hard rock or soft soil sites, which could lead to under- or overestimates of the magnitude by up to half a magnitude unit.

The Chi-Chi earthquake occurred at 17:47 on 20 September 1999 and is the largest earthquake ( M W 7.6) to have occurred on land in Taiwan in the twentieth century. This earthquake caused considerable damage and was named the “921 Chi-Chi Great Earthquake” by the Taiwan government, as the local date was 21 September. Because an extensive strong-motion instrumentation program in Taiwan was completed by the Central Weather Bureau (CWB) in 1996, over 30,000 digital strong-motion records have been obtained from the Chi-Chi earthquake and thousands of its aftershocks. These records form the largest set of strong-motion data recorded from a major earthquake since strong-motion seismology studies began in the 1930s. This data set is important to seismology and earthquake engineering because it includes over 60 recording sites within 20 km of the fault ruptures, which provides a five-fold increase of such near-field records available for the entire world. A prepublication CD was made available in mid-December 1999, and the data on it have been used by many authors in dozens of articles published so far. Since then, we examined about 10,000 strong-motion records and conducted a first-order quality assurance procedure for all the records obtained on 20 September 1999, including the mainshock and hundreds of the early aftershocks. We performed extensive data processing for quality assurance and selected a total of 663 strong-motion data files from 441 accelerographs to construct strong-motion records up to 4-min long for the mainshock whenever possible. In this article, we present a brief description of the processed acceleration data from the Chi-Chi earthquake. The data set (about 500 megabytes) and an extensive 562-page report (documenting the data processing and results of the processed data) are archived on the attached CD in this Special Issue so that users can quickly access this valuable data set for their research. Manuscript received 7 April 2001.

Orthogonal arrays (OAs) are widely used in industrial experiments for factor screening. Suppose that only a few of the factors in the experiments turn out to be important. An OA can be used not only for screening factors, but also for detecting interactions among a subset of active factors. In this article a set of optimality criteria is proposed to assess the performance of designs for factor screening, projection, and interaction detection, and a three-step approach is proposed to search for optimal designs. Combinatorial and algorithmic construction methods are proposed for generating new designs. Permutations of levels are used for improving the eligibility and estimation efficiency of the projected designs. The techniques are then applied to search for best three-level designs with 18 and 27 runs. Many new, efficient, and practically useful nonregular designs are found and their properties are discussed.

In some practical situations the choice of defining generators matters even for the same defining contrast subgroup. Two such examples are blocking schemes for full and fractional factorial designs and split-plot fractional factorial designs. We propose an algorithm to find defining generators with extreme lengths for any s n − k designs, s being a prime power. Some illustrations of the method are given.

The operating window method is a novel tool in quality engineering. It has been practiced in some industrial sectors but has received scant attention in academic research. If a critical factor for competing failure modes can be identified, the probability of failures can be reduced by widening the operating window of this factor, thus improving the system's quality and reliability. A rigorous foundation is given for some existing practice, particularly the operating window signal-to-noise (SN) ratio. A new strategy is given for design, analysis, and system optimization, which is an improvement over existing practice. We illustrate our approach with the analysis of a wave soldering experiment.

Blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation. For 2n-k designs in 2p blocks, others have studied the confounding pattern between blocking effects and treatment effects and proposed some criteria to choose optimal blocking schemes. We propose alternative criteria that allow estimation of more lower-order effects. Extensions to three-level fractional factorial design are considered, and tables of useful designs are given.

Industrial experiments frequently use unreplicated factorial designs, and one method of identifying effects from these experiments is the half-normal plot. One testing method that overcomes the subjectivity of using this graphical method is the Lenth me..

Statistical process control (SPC) monitoring of the special causes of a process, along with engineering feedback control such as proportional-integral-derivative (PID) control, is a major tool for on-line quality improvement. In this paper, a strategy t..

In a quantal response study, there may be insufficient knowledge of the response relationship for the stimulus (or dose) levels to be chosen properly. Information from such a study can be scanty or even unreliable. A two-stage design is proposed for such studies, which can determine whether and how a follow-up (i.e., second-stage) study should be conducted to select additional stimulus levels to compensate for the scarcity of information in the initial study. These levels are determined by using optimal design theory and are based on the fitted model from the data in the initial study. Its advantages are demonstrated using a fishery study.

A general approach is proposed for constructing response surface designs of economical size for qualitative and quantitative factors. It starts with an efficient design (e.g. central composite design) for the quantitative factors and then partitions the design points into groups corresponding to different level combinations of the qualitative factors. Good designs are selected to ensure high estimation efficiency for models that reflect some stated objectives. The method is illustrated with the construction of designs for one qualitative factor. Some designs for two qualitative factors are constructed and extensions considered. Algorithmic construction of designs is briefly discussed.

Two factors are related when one factor's desirable range depends on the level of another factor. For example, in a chemical reaction, the desirable reaction-time range shifts downward as temperature increases. This is reflected in the experimental desi..

In this paper we present an algorithm for estimating state-dependent polynomial coefficients in the nonstationary-state hidden Markov model (or the trended HMM) which allows for the flexibility of linear time warping or scaling in individual model states. The need for the state-dependent time warping arises from the consideration that due to speaking rate variation and other temporal factors in speech, multiple state-segmented speech data sequences used for training a single set of polynomial coefficients often vary appreciably in their sequence lengths. The algorithm is developed based on a general framework with use of auxiliary parameters, which, of no interests in themselves, nevertheless provide an intermediate tool for achieving maximal accuracy for estimating the polynomial coefficients in the trended HMM. It is proved that the proposed estimation algorithm converges to a solution equivalent to the state-optimized maximum likelihood estimate. Effectiveness of the algorithm is demonstrated in experiments designed to fit a single trended HMM simultaneously to multiple sequences of speech data which are different renditions of the same word yet vary over a wide range in the sequence length. Speech recognition experiments have been performed based on the standard acoustic-phonetic TIMIT database. The speech recognition results demonstrate the advantages of the time-warping trended HMMs over the regular trended HMMs measured about 10 to 15% improvement in terms of the recognition rate.

Finney proposed the use of a fiducial interval for the median response dose based on Fieller's theorem. An alternative is to use the asymptotic confidence interval. The simulations by Abdelbasit and Plackett suggest that the two intervals have similar coverage probabilities. We compare the two intervals theoretically and in an expanded simulation study. Our results show that Fieller intervals are generally superior. An attempt is made to characterize how and when the two intervals differ.

SUMMARY An N x N Hadamard matrix can be used to construct a saturated 2 N-1 design with N runs. Furthermore, if an interaction column for two of the columns of the matrix is not fully aliased with any column of the matrix, this interaction column can be used as a supplementary column for studying an additional factor. For some small Hadamard matrices studied by Plackett & Burman (1946), the number of such interaction columns is very large, thus allowing the construction of supersaturated designs whose number of factors far exceeds the number of runs. A general method of construction along these lines is proposed. The efficiency of the constructed designs is studied by using three criteria.

Traditionally, Plackett-Burman (PB) designs have been used in screening experiments for identifying important main effects. The PB designs whose run sizes are not a power of two have been criticized for their complex aliasing patterns, which according t..

Use of asymmetrical orthogonal arrays (OA's) for planning industrial experiments with mixed levels has become increasingly popular. In addition to applications to experimental investigations in many disciplines, they can also be used in the balanced repeated-replications method of inference from general stratified survey samples. In this article, we propose a general approach to the construction of asymmetrical OA's with economic run size and flexibility in the choice of factor levels. As applications of this approach, we construct several general classes of arrays that include numerous existing classes of arrays as special cases. A large number of known asymmetrical OA's can be reproduced by our approach in a unified and simple manner. Many new arrays are obtained. A list of asymmetrical OA's with moderate run size is given. Our approach consists of three steps. We first construct an OA as the generalized Kronecker sum of an OA and some difference matrices. We then add, to the constructed OA, co...

SUMMARY For stratified samples with arbitrary numbers of primary sampling units per stratum, one can divide the units in the stratum into two groups and then apply the balanced half-samples method to the two groups thus formed. The efficiency loss of the grouped balanced half-samples variance estimator can be substantial. Use of a mixed orthogonal array, whose numbers of symbols correspond to the numbers of units per stratum, gives a set of balanced subsamples. Unlike that of Gupta & Nigam (1987), the proposed method of analysis gives a consistent variance estimator and bias reduction for nonlinear statistics. To further reduce the number of replicates, use of nearly orthogonal arrays is considered. The balanced half-samples method (McCarthy, 1966, 1969) is commonly used for estimating the variance of nonlinear statistics from stratified samples with two primary sampling units per stratum. These samples arise naturally if deep stratification is desired as in some large-scale surveys. The method is extended (Gurney & Jewett, 1975) to the case of p primary sampling units per stratum for prime p. This extension for p > 2 is not adopted in common practice since it requires a much larger number of replicates. Also, in many survey designs the numbers of primary sampling units are unequal. A common practice is to divide the units in the stratum into two groups and then to apply the balanced half-samples method to the two groups thus formed. This has gained popularity because the software for obtaining balanced half-samples is readily available and the number of replicates required is more economical. As shown in ? 2, the resulting variance estimators can be quite inefficient and their bias based on a conditional analysis can be considerable. The conditional analysis also suggests a method of grouping to reduce the bias. The degree of grouping depends on the tradeoff between computational economy and statistical efficiency. If the efficiency loss from grouping is not justifiable, one may draw replicates by using mixed orthogonal arrays with variable numbers of symbols to accommodate the different numbers of units or groups of units in the strata. As long as an orthogonal array is used for drawing replicates, we call the method balanced repeated replications. In ? 3 we show that the analysis method of Gupta & Nigam (1987) based on mixed orthogonal arrays leads to an inconsistent variance estimator for nonlinear statistics, and propose a method that is valid for variance estimation and bias reduction

For product and ordering information: World Wide Web: http://www.usgs.gov/pubprod Telephone: 1-888-ASK-USGS For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment: World Wide Web: http://www.usgs.gov Telephone: 1-888-ASK-USGS Suggested citation: Evans, J.R., Cochard, A., Graizer, Vladimir, Huang, Bor-Shouh, Hudnut, Kenneth W., Hutt, Charles R., Igel, H., Lee, William H.K., Liu, Chun-Chi, Majewski, Eugeniusz, Nigbor, Robert, Safak, Erdal, Savage, William U., Schreiber, U., Teisseyre, Roman, Trifunac, Mihailo, Wassermann, J., and, Wu, Chien-Fu, 2007, Rotational seismology workshop of February 2006: U.S. Geological Survey, Open-File Report. 2007-1145, 20 p. [http://pubs.usgs.gov/of/2007/1145/]. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this report is in the public domain, permission must be secured from the individual copyright owners to reproduce any copyrighted material contained within this report.

[1] A Mw 6.1 earthquake occurred on April 1st, 2006 near Taitung, eastern Taiwan. It produced significant coseismic ground displacements and a large number of aftershocks in the ensuing month. This event provides an opportunity to diagnose the seismogenic structure in the southern Longitudinal Valley (LV) of eastern Taiwan, long viewed as one of the collision sutures between the Philippine Sea and the Eurasian plates. With precisely relocated main- and aftershock hypocenters, focal mechanisms for M ≥ 3.8 events, and coseismic ground displacements from strong motion records, we determine a main shock dislocation model. Our results indicate that the main shock occurred on a high angle fault (azimuth 198°, dip 77°). The model comprises a fault with two segments; the main shock and a large number of aftershocks are associated with the northern segment that exhibited predominantly left-lateral strike-slip motion, in agreement with P-wave first motions and waveform (USGS) solutions. The southern segment exhibits a slightly larger thrust component, in agreement with CMT solutions. Tectonically, this event highlights a NNE-trending fault on the west side of the LV, which is predominantly strike-slip. The aftershocks clustered to the east of the main shock, which exhibit mainly thrust mechanisms, indicate that shortening is still acting on the sedimentary materials deposited between the Coastal and Central ranges prior to collision. As a result, the southern LV is undergoing slip partitioning along different faults, which has never been specified before.

A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu [Ann. Statist. 29 (2001) 1066--1077]. A new lower bound is derived and general construction methods are proposed for multi-level supersaturated designs. Inspired by the Addelman--Kempthorne construction of orthogonal arrays, several classes of optimal multi-level supersaturated designs are given in explicit form: Columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties., Published at http://dx.doi.org/10.1214/009053605000000688 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

[1] The 2003 Chengkung earthquake (Mw 6.8) provided diagnostic evidence for a source model showing the deformation process of the seismogenic Chihshang fault in eastern Taiwan. The aftershocks show a fault-bend at a depth of 18 km. Coseismic ground displacements recorded by strong-motion records allow us to deduce instant rupturing of this event. Our resulting model shows a fault length of ∼33 km and dip-slip dominant rupture on fault-plane deeper than 18 km. Estimated coseismic displacements constrain two fault planes: one at 5–18 km depth dipping 60°E and 18–36 km depth dipping 45°E. The uppermost fault-plane of the Chihshang Fault (0–5 km) did not break immediately after the main shock; however, it may have a major role in after-slip and even interseismic ground deformation. The Taiyuan basin developed in the hanging wall is a geomorphic feature consistent with and adequately explained by coseismic ground displacements.

Wu and Hamada recommend selecting resolution IV designs with the maximum number of clear two-factor interactions (2FIs), called MaxC2 designs. In this paper, we develop a method by using graphical representations, combinatorial and group-theoretic arguments to prove if a given design is a MaxC2 design. In particular, we show that all known minimum aberration designs with resolution IV are MaxC2 designs (except in six cases) and that the second $2^{9-4}$, $2^{13-7}$, $2^{16-10}$ and $2^{17-11}$ designs given in Wu and Hamada are MaxC2 designs. The method also enables us to identify new MaxC2 designs that are too large to be verified by computer search.

The Central Weather Bureau (CWB) of Taiwan completed a deployment of 1200 modern digital strong-motion instruments in 1996 at free-field sites and in buildings and bridges. Consequently, a very extensive set of strong-motion records were obtained for the M W = 7.6 Chi-Chi earthquake in 1999, including over 60 near-field records within 20 km of the fault ruptures. For documentation purposes, we included all relevant data files on the attached CD-ROM from our article, “CWB Free-Field Strong-Motion Data from the 21 September Chi-Chi, Taiwan, Earthquake” in this issue. We presented the data in four different ways to make the data more user friendly: (1) the original recorded data by accelerograph type; (2) the processed data in ASCII text format; (3) the processed data in SUDS format; and (4) the processed …

For any positive definite matrices A and B, it is known that A > B iff B - ’ >A - ‘. This paper investigates the extensions of the above result to any two real nonnegative definite matrices A and B. For any real positive definite matrices A and B, it is known that A > B iff B - ’ >A - ‘. The extension of this result to real nonnegative definite (n.n.d.) matrices A and B is not trivial, since the “inverse” of A or B may not be uniquely defined. In this paper we consider the following question: for any n.n.d. matrices A and B with A > B and any given generalized inverse A - of A (or B - of B), does there exist a generalized inverse B - of I? (or A - of A) such that B - > A -? This question is answered for every possible combination of the ranks of A,B,A-,B-, and A-,B- can be interpreted as any of the {I}-, {2}-, {I,2}-, or { 1,2,3,4}-inverses of A, B. All the matrices considered are real. Before stating the main results of the paper, we need to give some basic facts about generalized inverses. For any matrix A of real elements, a generalized inverse X is defined by one or several of the following conditions due to Penrose [5]

A class of nearly balanced incomplete block designs is defined. This extends the concept of regular graph designs of John and Mitchell (1977) to the unequally replicated case. Some necessary conditions on the existence of such designs are derived. Methods of construction are given for some special cases. For five or six varieties, the 'best' nearly balanced incomplete block designs and their efficiencies are tabulated. (Author)

The regression estimator and the ratio estimator are commonly used in survey practice. In the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs. The ratio estimator is appropriate for populations whose regression line passes close to the origin. If the intercept of the regression line is significantly nonzero, however, it is much less efficient than the regression estimator (Deng 1984). In general, apart from n –2 terms, the mean squared error (MSE) of the former is bigger than that of the latter (Cochran 1977, p. 196). Given the present computing capacity, the computational advantage of the ratio estimator should be less of a concern and the regression estimator will gain wider popularity. The main purpose of this article is to provide a theoretical and empirical comparison of several variance estimators for the regression estimator in simple random sampling without replacement. The companion problem for the...

The problem of optimal design algorithms is treated from the general viewpoint of optimization theory and algorithms. For designs of finite support, several iterative schemes are suggested, including vertex direction, gradient projection, normalized gradient projection and conjugate gradient projection. For an arbitrary design region, a general optimal design algorithm is proposed which incorporates the above algorithms for the finite support case ar.d methods of changing design support. The numerical behavior of these algorithms is investigated in detail on six examples and some experiences with the algorithms are summarized in the last section.

SUMMARY If an experiment is designed sequentially, repeated-sampling inference may not necessarily be made using distributional results that are valid for fixed designs. A few simple illustrative examples and alternative approaches are given. Sometimes the sequential nature of design can be ignored asymptotically. Links are forged with inference for stochastic processes and missing data problems.

In comparing two treatments, suppose the suitable subjects arrive sequentially and must be treated at once. Known or unknown to the experimenter there may be nuisance factors systematically affecting the subjects. Accidental bias is a measure of the influence of these factors in the analysis of data. We show in this paper that the random allocation design minimizes the accidental bias among all designs that allocate n, out of 2n, subjects to each treatment and do not prefer either treatment in the assignment. When the final imbalance is allowed to be nonzero, optimal and efficient designs are given. In particular the random allocation design is shown to be very efficient in this broader setup.

Let S be a random nonnegative definite matrix and let G be an orthogonal matrix such that S=GDG′, where D is the diagonal matrix of the latent roots of S. In this note, we prove the a.s. existence of G−111, where G=[ G 11 G 12 G 21 G 22 ] , under some weak conditions on the distribution of S.

Methods for standard errors and confidence intervals for nonlinear statistics —such as ratios, regression, and correlation coefficients—have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement, in particular, the important special case of two sampled clusters per stratum. These methods include the customary linearization (or Taylor) method and resampling methods based on the jackknife and balanced repeated replication (BRR). Unlike the jackknife or the BRR, the linearization method is applicable to general sampling designs, but it involves a separate variance formula for each nonlinear statistic, thereby requiring additional programming efforts. Both the jackknife and the BRR use a single variance formula for all nonlinear statistics, but they are more computing-intensive. The resampling methods developed here retain these features of the jackknife and the BRR, yet permit extension to more complex designs involving sampling without replace...