{'fraction_non_alphanumeric': 0.07794943820224719, 'fraction_numerical': 0.032303370786516857, 'mean_word_length': 5.142241379310345, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On estimation of regression coefficients of long memory random fields observed on the arrays

It is well known that many of empirical data may exhibit long range dependence structure (see [1], [2], [3], [5], [6], [7], [10]). Thus, there is now a considerable theoretical interest in analysing different long memory models. In particular, results of [9], [12], [17], [20], [21] indicate that regression with long memory may still be very good. The interesting problems regarding estimation of parameter of long memory (fractional or Hurst parameter) are considered in papers [9], [17], [18] among the others. Recently some new models of continuous parameter long memory processes are proposed in papers [5], [6], [7]. Here are the questions about properties of the least squares estimator (LSE) of regression coefficients very important. For discrete parameter long memory time series the conditions for asymptotic normality of LSE are given in [20], [21]. Also there are some results regarding asymptotic properties of the LSE in [11], [14], [15]. In this paper we consider the continuous multidimensional version of some problems attacked in [20] and [21]. Thus, we study the asymptotic properties of the LSE in regression models with multidimensional inputs and long memory errors, not necessarily Gaussian. We don't consider the problem of estimation of fractional (Hurst's) parameter (see [2], [3], [9], [17], [6], [7]).