Orthogonal arrays are widely used in manufacturing and high-tech industries for quality and productivity improvement experiments. For reasons of run size economy or flexibility, nearly orthogonal arrays are also used. The construction of orthogonal or nearly orthogonal arrays can be quite challenging. Most existing methods are complex and produce limited types of arrays. This article describes a simple and effective algorithm for constructing mixed-level orthogonal and nearly orthogonal arrays. It can construct a variety of small-run arrays with good statistical properties efficiently.

The Nordstrom and Robinson code is a well-known nonlinear code in coding theory. This paper explores the statistical properties of this nonlinear code. Many nonregular designs with 32, 64, 128, 256 runs and 7-16 factors are derived from it. It is shown that these nonregular designs are better than regular designs of the same size in terms of resolution, aberration and projectivity. Furthermore, many of these nonregular designs are shown to have generalized minimum aberration among all possible designs. Seven orthogonal arrays are shown to have unique wordlength pattern and four of them are shown to be unique up to isomorphism.

Nonregular designs are used widely in experiments due to their run size economy and flexibility. These designs include the Plackett-Burman designs and many other symmetrical and asymmetrical orthogonal arrays. Supersaturated designs have become increasingly popular in recent years because of the potential in saving run size and its technical novelty. In this paper, a novel combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs. The new criterion, which is to sequentially minimize the power moments of the number of coincidence among runs, is a good surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G2-aberrration, generalized minimum aberration and E(s2). In addition, the minimum moment aberration is conceptually simple and convenient for theoretical development. The general theory developed here not only unifies several separate results, but also provides many novel results on nonregular designs and supersaturated designs.

This paper considers the construction of minimum aberra- tion (MA) blocked factorial designs. Based on coding theory, the con- cept of minimum moment aberration due to Xu (2003) for unblocked designs is extended to blocked designs. The coding theory approach studies designs in a row-wise fashion and therefore links blocked designs with nonregular and supersaturated designs. A lower bound on blocked wordlength pattern is established. It is shown that a blocked design has MA if it originates from an unblocked MA design and achieves the lower bound. It is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros. Sufficient conditions are given for constructing MA blocked designs from unblocked MA designs. The theory is then applied to construct MA blocked designs for all 32 runs, 64 runs up to 32 factors, and all 81 runs with respect to four combined wordlength patterns.

A common problem experimenters face is the choice of fractional factorial designs. Minimum aberration designs are commonly used in practice. There are situations in which other designs meet practical needs better. A catalogue of designs would help experimenters choose the best design. Based on coding theory, new methods are proposed to efficiently classify and rank fractional factorial designs. A collection of three-level fractional factorial designs with 27, 81, 243 and 729 runs is given. This extends the work of Chen, Sun and Wu (1993), who gave a collection of fractional factorial designs with 16, 27, 32 and 64 runs.

In 2020, the coronavirus crisis disrupted and dominated the news about the stock market. It was difficult to predict what would happen in the stock market over the short term or long term. However, the market for day trading (buying and selling stocks within the same day) was not significantly affected by each daily news because the risks of day trading were lower than those of other trading methods at that time. Therefore, overall, there were relatively lower risks associated with day trading. This thesis evaluates day-trading algorithms in an attempt to enhance trading methods. I developed five day-trading algorithms, which were evaluated. The algorithms bought 505 stocks from the S&P 500 index, and all stocks were sold before the market closed for the trading day. Value at risk (VaR) and conditional value at risk (CVaR) were used as risk measures. To evaluate performance, the cumulative gross log returns of each algorithm were compared with those of the S&P 500 index fund, SPDR S&P 500 ETF. The experimental results show that model D, based on the last nine days’ data, performed better and had a lower risk than the other methods.

Deep learning techniques have become commonplace tools for complex prediction, classification, and recognition tasks. Yet, the performance of such learning techniques is highly influenced by user-set hyperparameters. As a result, efficient hyperparameter tuning and optimization is an increasingly important area of study. Traditional model-free tuning methods are often computationally inefficient and may miss optimal settings, while model-based approaches rely on parametric models and cannot easily be parallelized. In this thesis, we propose the use of experimental design techniques, a Design of Experiments (DOE) Approach, to more efficiently and intuitively optimize hyperparameters. We use fractional factorial designs, nearly orthogonal arrays, sliced Latin hypercube designs, and composite variations of these three small-run designs to identify relationships between continuous, discrete and categorical hyperparameters and test accuracy in convolutional neural networks using beta regression. We find that our proposed methodology successfully identifies optimal hyperparameter settings for convolutional neural networks trained on the MNIST dataset.

The objective of this research is to apply techniques of randomized controlled experimentation including experimental design and analysis in user experience optimization and mobile app development. Online controlled experiments started to be used in the late 1990s with the growth of the Internet. Nowadays, many Internet companies leverage controlled experiments, especially A/B testing, to understand and make decisions at every step of product development. Large sites, including Facebook, Google, and Airbnb, run hundreds of A/B testing every month on features from UX design to algorithms for growth.

The power of running controlled experiments is the ability to establish causal inference and quickly validate new product ideas with statistical evidence of success. This process can ultimately help organizations, especially Agile software, optimize products with iterations by better understanding the corresponding impact on the user experience and recognizing the best performer from a list of variations.

Space-filling designs are commonly used in computer experiments and other scenarios for investigating complex systems, but the construction of such designs is challenging. In this thesis, we construct a series of maximin-distance Latin hypercube designs via Williams transformations of good lattice point designs. Some constructed designs are optimal under the maximin L1-distance criterion, while others are asymptotically optimal. Moreover, these designs are also shown to have small pairwise correlations between columns. The procedure is further extended to the construction of multi-level nonregular fractional factorial designs which have better properties than regular designs. Existing research on the construction of nonregular designs focuses on two-level designs. We construct a novel class of multilevel nonregular designs by permuting levels of regular designs via the Williams transformation. The constructed designs can reduce aliasing among effects without increasing the run size. They are more efficient than regular designs for studying quantitative factors. In addition, we explore the application of experimental design strategies to data-driven problems and develop a subsampling framework for big data linear regression. The subsampling procedure inherits optimality from the design matrices and therefore minimizes the mean squared error of coefficient estimations for sufficiently large data. It works especially well for the problem of label-constrained regression where a large covariate dataset is available but only a small set of labels are observable. The subsampling procedure can also be used for big data reduction where computation and storage issues are the primary concern.